http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Alex&feedformat=atomSoft-Matter - User contributions [en]2021-01-26T23:53:11ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4739User:Alex2009-01-13T09:08:06Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4] Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3] Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>\epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be moved at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px|thumb|left|[6] Electrowetting effect on Nanotube Bucky Paper]]<br />
[[Image:Nanotube Graph.png|400px|thumb|center|[6] Contact angle change at different voltages]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px|thumb|center|[7] Contact angle change as a function of voltage of Cytop]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. '''Electrowetting-based actuation of droplets for integrated microfluidics.''' Lab on a Chip (2002)<br />
<br />
[6] Kakade et al. '''Field Induced, Superhydrophobic to Superhydrophilic Switching in Multiwalled Carbon Nanotube Papers'''. Nano Lett (2008)<br />
<br />
[7] Raj et al. '''Composite Dielectrics and Surfactants for Low Voltage Electrowetting Devices'''. University/Government/Industry Micro/Nano Symposium (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4738User:Alex2009-01-13T09:06:52Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4] Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3] Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>\epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px|thumb|left|[6] Electrowetting effect on Nanotube Bucky Paper]]<br />
[[Image:Nanotube Graph.png|400px|thumb|center|[6] Contact angle change at different voltages]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px|thumb|center|[7] Contact angle change as a function of voltage of Cytop]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. '''Electrowetting-based actuation of droplets for integrated microfluidics.''' Lab on a Chip (2002)<br />
<br />
[6] Kakade et al. '''Field Induced, Superhydrophobic to Superhydrophilic Switching in Multiwalled Carbon Nanotube Papers'''. Nano Lett (2008)<br />
<br />
[7] Raj et al. '''Composite Dielectrics and Surfactants for Low Voltage Electrowetting Devices'''. University/Government/Industry Micro/Nano Symposium (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4737User:Alex2009-01-13T09:06:33Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>\epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px|thumb|left|[6] Electrowetting effect on Nanotube Bucky Paper]]<br />
[[Image:Nanotube Graph.png|400px|thumb|center|[6] Contact angle change at different voltages]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px|thumb|center|[7] Contact angle change as a function of voltage of Cytop]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. '''Electrowetting-based actuation of droplets for integrated microfluidics.''' Lab on a Chip (2002)<br />
<br />
[6] Kakade et al. '''Field Induced, Superhydrophobic to Superhydrophilic Switching in Multiwalled Carbon Nanotube Papers'''. Nano Lett (2008)<br />
<br />
[7] Raj et al. '''Composite Dielectrics and Surfactants for Low Voltage Electrowetting Devices'''. University/Government/Industry Micro/Nano Symposium (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4736User:Alex2009-01-13T09:02:42Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>\epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px|thumb|left|[6] Electrowetting effect on Nanotube Bucky Paper]]<br />
[[Image:Nanotube Graph.png|400px|thumb|center|[6] Contact angle change at different voltages]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px|thumb|center|[7] Contact angle change as a function of voltage of Cytop]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] [http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf]<br />
<br />
[2] [http://www.cs.rpi.edu/~sakella/research.html]<br />
<br />
[3] [http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf]<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. '''Electrowetting-based actuation of droplets for integrated microfluidics.''' Lab on a Chip (2002)<br />
<br />
[6] Kakade et al. '''Field Induced, Superhydrophobic to Superhydrophilic Switching in Multiwalled Carbon Nanotube Papers'''. Nano Lett (2008)<br />
<br />
[7] Raj et al. '''Composite Dielectrics and Surfactants for Low Voltage Electrowetting Devices'''. University/Government/Industry Micro/Nano Symposium (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4735User:Alex2009-01-13T09:01:13Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px|thumb|left|[6] Electrowetting effect on Nanotube Bucky Paper]]<br />
[[Image:Nanotube Graph.png|400px|thumb|center|[6] Contact angle change at different voltages]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px|thumb|center|[7] Contact angle change as a function of voltage of Cytop]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] [http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf]<br />
<br />
[2] [http://www.cs.rpi.edu/~sakella/research.html]<br />
<br />
[3] [http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf]<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. '''Electrowetting-based actuation of droplets for integrated microfluidics.''' Lab on a Chip (2002)<br />
<br />
[6] Kakade et al. '''Field Induced, Superhydrophobic to Superhydrophilic Switching in Multiwalled Carbon Nanotube Papers'''. Nano Lett (2008)<br />
<br />
[7] Raj et al. '''Composite Dielectrics and Surfactants for Low Voltage Electrowetting Devices'''. University/Government/Industry Micro/Nano Symposium (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4734User:Alex2009-01-13T09:00:26Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px|thumb|left|[6] Electrowetting effect on Nanotube Bucky Paper]]<br />
[[Image:Nanotube Graph.png|400px|thumb|center|[6] Contact angle change at different voltages]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px|thumb|center|[7] Contact angle change as a function of voltage of Cytop]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. Electrowetting-based actuation of droplets for integrated microfluidics. Lab on a Chip (2002)<br />
<br />
[6] Kakade et al. '''Field Induced, Superhydrophobic to Superhydrophilic Switching in Multiwalled Carbon Nanotube Papers'''. Nano Lett (2008)<br />
<br />
[7] Raj et al. '''Composite Dielectrics and Surfactants for Low Voltage Electrowetting Devices'''. University/Government/Industry Micro/Nano Symposium (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4733User:Alex2009-01-13T08:53:13Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
[[Image:Angle of Advancement.png|300px|thumb|right|[4] Angle of Advancement]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
[5] Pollack et al. Electrowetting-based actuation of droplets for integrated microfluidics. Lab on a Chip (2002)<br />
<br />
[6] Gong et al. '''Direct-Referencing Two-Dimensional-Array Digital Microfluidics Using Multilayer Printed Circuit''' Microelectromechanical Systems (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4732User:Alex2009-01-13T08:49:50Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px|thumb|left|[5] Various device geometries.]]<br />
[[Image:Electrodes.png|500px|thumb|center|[5] Most popular device geometry]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
[5] Pollack et al. Electrowetting-based actuation of droplets for integrated microfluidics. Lab on a Chip (2002)<br />
<br />
Gong et al. '''Direct-Referencing Two-Dimensional-Array Digital Microfluidics Using Multilayer Printed Circuit''' Microelectromechanical Systems (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4731User:Alex2009-01-13T08:45:34Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
[[Image:Basic Electrowetting.png|500px|left|thumb|[5]]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Angles.png|500px|thumb|center|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
[5] Pollack et al. Electrowetting-based actuation of droplets for integrated microfluidics. Lab on a Chip (2002)<br />
<br />
Gong et al. '''Direct-Referencing Two-Dimensional-Array Digital Microfluidics Using Multilayer Printed Circuit''' Microelectromechanical Systems (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4730User:Alex2009-01-13T08:39:39Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px|thumb|[5]]]<br />
[[Image:Angles.png|500px|thumb|[4] Surface tensions and contact angles defined]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
[5] Pollack et al. Electrowetting-based actuation of droplets for integrated microfluidics. Lab on a Chip (2002)<br />
<br />
Gong et al. '''Direct-Referencing Two-Dimensional-Array Digital Microfluidics Using Multilayer Printed Circuit''' Microelectromechanical Systems (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4729User:Alex2009-01-13T08:34:15Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|right|Droplet Moving on a 2D Array]]<br />
[[Image:Dispensing.png|350px|thumb|left|[4]Droplet dispensing from a large reservoir]]<br />
[[Image:Splitting.png|350px|thumb|center|[3]Droplet splitting]]<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px]]<br />
[[Image:Angles.png|500px]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu<br />
<br />
Gong et al. '''Direct-Referencing Two-Dimensional-Array Digital Microfluidics Using Multilayer Printed Circuit''' Microelectromechanical Systems (2008)</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4728User:Alex2009-01-13T08:32:22Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|Droplet Moving on a 2D Array]]<br />
[[Image:Splitting.png|350px|thumb|left|[3]Droplet splitting]]<br />
[[Image:Dispensing.png|350px|thumb|center|[4]Droplet dispensing from a large reservoir]]<br />
<br />
<br />
[<br />
<br />
<br />
Gong et al. '''Direct-Referencing Two-Dimensional-Array Digital Microfluidics Using Multilayer Printed Circuit''' Microelectromechanical Systems (2008)<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px]]<br />
[[Image:Angles.png|500px]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.<br />
<br />
==References==<br />
[1] http://nanofab.caltech.edu/Recent%20Work/Recent%20Work%20Pictures/web-fluidics%20[Compatibility%20Mode].pdf<br />
[2] http://www.cs.rpi.edu/~sakella/research.html<br />
[3] http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
[4] Song et al. '''A scaling model for electrowetting-on-dielectric microfluidic actuators''' microfluidics.ee.duke.edu</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4727User:Alex2009-01-13T08:22:04Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|thumb|right|[2] Example of a theoretical electrowetting based device with separate areas for transport and mixing]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px|thumb|Droplet Moving on a 2D Array]]<br />
[[Image:Splitting.png|350px|Droplet splitting]]<br />
[[Image:Dispensing.png|350px|Droplet dispensing from a large reservoir]]<br />
<br />
<br />
http://www.imtek.de/anwendungen/content/upload/vorlesung/2006/electrowetting.pdf<br />
Song et al. A scaling model for electrowetting-on-dielectric microfluidic actuators. microfluidics.ee.duke.edu<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px]]<br />
[[Image:Angles.png|500px]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4726User:Alex2009-01-13T08:11:48Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Scaling.png|350px|thumb|right|[1] Very complex pneumatic connections]]<br />
[[Image:Device1.png|350px|thumb|left|[1] Example Device Setup]]<br />
[[Image:Device2.png|350px|thumb|center|[1] Example Device Close-Up]]<br />
<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|right]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px]]<br />
[[Image:Splitting.png|350px]]<br />
[[Image:Dispensing.png|350px]]<br />
<br />
<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px]]<br />
[[Image:Angles.png|500px]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4725User:Alex2009-01-13T07:46:16Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Device1.png|350px]]<br />
[[Image:Device2.png|350px]]<br />
[[Image:Scaling.png|350px]]<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
[[Image:Digital Device.png|350px|right]]<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Movement.png|350px]]<br />
[[Image:Splitting.png|350px]]<br />
[[Image:Dispensing.png|350px]]<br />
<br />
<br />
<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (MHz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px]]<br />
[[Image:Angles.png|500px]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Electrodes.png|500px]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
==Conclusion==<br />
With improving surface chemistries and dielectric materials that can be made thinner without electric breakdown, the future for electrowetting digital microfluidic devices is bright. As of now there are already start-up companies such as [http://www.liquid-logic.com Advanced Liquid Logic] creating microfluidic biochips that shuttle around picoliter volumes of fluid exactly with the technique described here. These devices can dispense the various fluids, transport, split, combine, and mix the droplets programmably.</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Movement.png&diff=4724File:Movement.png2009-01-13T07:36:28Z<p>Alex: uploaded a new version of "Image:Movement.png"</p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4723User:Alex2009-01-13T07:27:32Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Device1.png|350px]]<br />
[[Image:Device2.png|350px]]<br />
[[Image:Scaling.png|350px]]<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Digital Device.png|350px]]<br />
<br />
== Types of Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
== Electrowetting Basics ==<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet in air wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
[[Image:Basic Electrowetting.png|500px]]<br />
[[Image:Angles.png|500px]]<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, g = gas (medium), l = liquid [drop])<br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}}{\gamma_{gl}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<br />
<math>cos(\theta) = \frac{\gamma_{sg}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{gl}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
This is the basic equation of electrowetting and is called the "Young-Lippman Equation". The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
==Electrowetting Actuation ==<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
[[Image:Geometries.png|500px]]<br />
[[Image:Movement.png|500px]]<br />
[[Image:Electrodes.png|500px|right]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{gl}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math> and a droplet/electrode pitch <math>L</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)ds = 2\int_0^{\phi} f cos(\theta)\frac{L}{2}d\theta=f L sin(\phi) = \frac{\epsilon L V^2}{2d \gamma_{gl}} sin(\phi)</math><br />
<br />
==Other Forces==<br />
In these systems, the droplet will experience not only the electrowetting forces, but also dissipative forces such as drag from the medium (if it is a fluid like oil) and from the surface. These forces will act against<br />
movement of the droplet. The droplet will quickly reach a steady state terminal velocity upon application of the electrowetting force. For most experiments of this sort, the droplets can be move at speeds in the range of 10s of cm/s which is extremely fast for those size scales.<br />
<br />
==Achieving High Speeds at Low voltages==<br />
Since the drag force at the solid/liquid interface is dependent on friction forces between the media, it is preferable to use superhydrophobic surfaces which have as high as possible a contact angle, to guarantee that over the range of contact angles induced by a voltage, the droplet still remains as non-wetting as possible. For example, given a particular aspect ratio for the device, if the contact angle changes by 40 degrees upon application of a certain voltage, then if a superhydrophobic surface is used with a normal water contact angle of 150 degrees, then the actuated contact angle will be 110 degrees and thus still fairly nonwetting, allowing for higher droplet velocities. <br />
<br />
Currently, most research groups use teflon as a hydrophobic surface and can reach high droplet speeds - however this requires the usage of very high voltages (50-200V). The most attractive design is one that minimizes the actuation voltages down to below 10V as these could enable chips to be portable and powered off a battery. Recent research shows that this is possible by using very thin insulating dielectrics with high dielectric constant and covering them with a thin film superhydrophic layer. <br />
<br />
Examples: <br />
<br />
'''Carbon nanotube "bucky paper" '''<br />
<br />
[[Image:Nanotube Electrowetting.png|400px]]<br />
[[Image:Nanotube Graph.png|400px]]<br />
<br />
---<br />
<br />
'''Cytop'''<br />
<br />
[[Image:Cytop.png|400px]]<br />
<br />
In the second example of Cytop with a layer of <math>Si_3N_4</math>, enormous contact angle changes on the order of 100 degrees or more with < 15 volts. This is from work published in 2008 and thus represents one of the most recent results.<br />
<br />
====Conclusion</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Movement2.png&diff=4722File:Movement2.png2009-01-13T07:15:22Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Cytop.png&diff=4721File:Cytop.png2009-01-13T07:14:47Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Dispensing.png&diff=4720File:Dispensing.png2009-01-13T07:14:13Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Splitting.png&diff=4719File:Splitting.png2009-01-13T07:13:58Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Nanotube_Graph.png&diff=4718File:Nanotube Graph.png2009-01-13T07:13:28Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Nanotube_Electrowetting.png&diff=4717File:Nanotube Electrowetting.png2009-01-13T07:13:06Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4716User:Alex2009-01-13T06:07:26Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Device1.png|350px]]<br />
[[Image:Device2.png|350px]]<br />
[[Image:Scaling.png|350px]]<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Digital Device.png|350px]]<br />
<br />
<br />
<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
[[Image:Basic Electrowetting.png|500px|right]]<br />
[[Image:Angles.png|500px|right]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}}{\gamma_{ml}}</math><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
<br />
[[Image:Geometries.png|500px|right]]<br />
[[Image:Movement.png|500px|right]]<br />
<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
[[Image:Electrodes.png]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
[[Image:Angle of Advancement.png]]<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4715User:Alex2009-01-13T05:58:58Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Device1.png|350px]]<br />
[[Image:Device2.png|350px]]<br />
[[Image:Scaling.png|350px]]<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Digital Device.png|350px]]<br />
<br />
<br />
<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
[[Image:Basic Electrowetting.png|500px|right]]<br />
[[Image:Angles.png|500px|right]]<br />
<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<center><math>C=\frac{\epsilon A}{d}</math></center><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
<br />
[[Image:Geometries.png|500px|right]]<br />
[[Image:Movement.png|500px|right]]<br />
<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
[[Image:Electrodes.png]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></center><br />
[[Image:Angle of Advancement.png]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4714User:Alex2009-01-13T05:46:09Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Device1.png|350px]]<br />
[[Image:Device2.png|350px]]<br />
[[Image:Scaling.png|350px]]<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
[[Image:Digital Device.png|350px]]<br />
[[Image:Movement.png|350px]]<br />
[[Image.Angles.png|350px]]<br />
[[Image:Geometry.png|350px]]<br />
<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <br />
<br />
<center><math>C=\frac{\epsilon A}{d}</math></center><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
[[Image:Basic Electrowetting.png]]<br />
[[Image:Electrodes.png]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></center><br />
[[Image:Angle of Advancement.png]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Angles.png&diff=4713File:Angles.png2009-01-13T05:44:03Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Geometries.png&diff=4712File:Geometries.png2009-01-13T05:43:32Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Movement.png&diff=4711File:Movement.png2009-01-13T05:43:01Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Contact_Angle.png&diff=4710File:Contact Angle.png2009-01-13T05:42:38Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Digital_Device.png&diff=4709File:Digital Device.png2009-01-13T05:42:18Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4708User:Alex2009-01-13T05:09:57Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
[[Image:Device1.png|400px|thumb|right|alt text]]<br />
[[Image:Device2.png|400px|thumb|right|alt text]]<br />
[[Image:Scaling.png|400px|thumb|right|alt text]]<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
<br />
<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
[[Image:Basic Electrowetting.png]]<br />
[[Image:Electrodes.png]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></center><br />
[[Image:Angle of Advancement.png]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4707User:Alex2009-01-13T05:09:07Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
[[Image:Device1.png|400px|thumb|right|alt text]]<br />
[[Image:Device2.png|400px|thumb|right|alt text]]<br />
[[Image:Scaling.png|400px|thumb|right|alt text]]<br />
<br />
<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
[[Image:Basic Electrowetting.png]]<br />
[[Image:Electrodes.png]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></center><br />
[[Image:Angle of Advancement.png]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4663User:Alex2009-01-13T02:16:26Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
[[Image:Device1.png]]<br />
[[Image:Device2.png]]<br />
[[Image:Scaling.png]]<br />
<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
[[Image:Basic Electrowetting.png]]<br />
[[Image:Electrodes.png]]<br />
<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></center><br />
[[Image:Angle of Advancement.png]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Device2.png&diff=4662File:Device2.png2009-01-13T02:15:11Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Device1.png&diff=4661File:Device1.png2009-01-13T02:14:34Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Scaling.png&diff=4660File:Scaling.png2009-01-13T02:14:05Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Electrodes.png&diff=4659File:Electrodes.png2009-01-13T02:11:26Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Basic_Electrowetting.png&diff=4658File:Basic Electrowetting.png2009-01-13T02:11:00Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Angle_of_Advancement.png&diff=4657File:Angle of Advancement.png2009-01-13T02:10:40Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4656User:Alex2009-01-13T02:08:59Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)</math></center></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4655User:Alex2009-01-13T02:07:50Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.<br />
<br />
Given an angle of advancement <math>\phi</math>, the total force on the droplet due to electrowetting is<br />
<br />
<center><math>F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin[/phi] = frac{\epsilon V^2}{d \gamma_{ml}} sin[/phi]</math></center></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4654User:Alex2009-01-13T01:47:40Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math></center><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through <math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<center><math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></center>.<br />
<br />
The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])<br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}</math></center><br />
<br />
Thus the contact angle of the liquid depends on the applied voltage as <br />
<center><math>cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
This is the basic equation of electrowetting. The contact angle changes (decreases) with application of higher voltage, increase of dielectric constant of the insulating medium, decreasing insulator thickness, and decreasing medium/liquid surface tension. These are the 4 parameters that govern the actuation force and scaling of this phenomenon.<br />
<br />
====Electrowetting Actuation ====<br />
<br />
Many different kinds of potential actuation geometries are possible, but the most common is that of a set of electrodes roughly the size of the water droplet, and a transparent top conductive layer of ITO. The droplets are actuated by creating an asymmetry in surface forces acting on the droplet thus creating a net-force that drives a droplet to minimize its overall surface tension. When a droplet straddles two electrodes of differing voltages, the surface tension over one electrode is difference than over the other (due to a different amount of capacitive energy being stored) in each side of the droplet, and the droplet is driven to reside completely over the electrode of higher voltage.<br />
<br />
The net force per unit length is thus<br />
<br />
<center><math>f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}</math></center><br />
<br />
Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4653User:Alex2009-01-13T01:12:51Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Introduction and Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.<br />
<br />
To solve this problem, some research groups have begun to use electrokinetic methods to actuate fluidic flow rather than relying on pneumatic methods which do not scale easily. By using conductive or polarizable fluids, it<br />
is possible to actuate fluidic motion though electromagnetic forces. This strength of this method relies on the amazing re-configurability of the fluidic circuits - the ability to manipulate small volumes of fluids in a geometry<br />
that can be redefined at a moments notice - and thus potentially capable of making a more general type of 'lab-on-a-chip' that can address a wide variety of needs and tests, and require nothing more than a microchip for computing<br />
and power source to do its job. These type of chips could be easily integrated into other devices, and even be disposable.<br />
<br />
Furthermore, electrokinetic actuation frees the chip from having to rely on flows of liquids, and can instead actuate individual droplets, cells, etc. This allows for a "digital microfluidic device" in which the individual operations of dispensing, splitting, combining, mixing, transporting, incubating, and sensing objects is reducible to a programmable set of instructions. It has even been proposed to devote an entire high level programming language that will allow researchers to do all their experiments on one chip, simple by writing the appropriate segment of code.<br />
<br />
== Electrokinetic Actuation ==<br />
<br />
Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena,<br />
the realignment of dipoles or polarizability of the object, and the kinetics of free charges or ions which can be specified by a conductance an capacitance of the object. The strength of the object's conductance, capacitance, and polarizability relative to the medium it is immersed in determines the forces that the object will experience. Generally it is safe to categorize objects into opposite extremes of the values and so highly conductive materials lie on one end of the spectrum, and can be actuated by relying on the free charges/ions, and highly polarizable media can be actuated by relying on dipole forces that arise in field gradients. This is the basis for the two most popular types of electrokinetic actuation methos: electrowetting and dielectrophoresis.<br />
<br />
=== [[Electokinetics#Dielectrophoresis|Dielectrophoresis]]===<br />
Here, high frequency (Mhz) electric fields are used to exploit the fact that an electric field gradient produces a force on a dipole. This method of actuation is well known but less common in digital microfluidics due to problems with heating. In this wiki entry, I will not focus on this force.<br />
<br />
=== Electrowetting ===<br />
In electrowetting, a highly conductive body which is partially wetting a solid surface is exposed to an electric field emanating from the surface, which in turn moves charges to the body's surface. The now polarized object acts in a way to counteract all electric fields within the object and thus experiences no body forces. The charges within the body will accumulate near the object/solid interface and the object will be pulled down towards the surface thus changing the contact angle formed at the tri-phase contact. Thus electric fields are used to change the wetting properties of most commonly a liquid droplet of salt-water. While this method has recently been a popular approach for changing liquid curvature for application in [[Drops%2C_menisci%2C_and_lenses#Another_Example:_Liquid_Optics|liquid lenses]]<br />
<br />
In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.<br />
<br />
==== Electrowetting Basics ====<br />
<br />
The basic setup for an electrowetting experiment is as follows: and conductive droplet wets the surface of an insulated electrode. The surface is made to be hydrophobic with high contact angle. The top of the drop is in contact with an electrode, and upon application of voltage charges rush into the conductive droplet and change the capacitance of the droplet/bottom electrode interface. This pulls the droplet closer down to the solid surface appearing as a change in surface energy which can be observed with a reduction in contact angle. With appropriate choice of medium, droplet liquid and superhydrophobic surface, very high contact angle contrast can be achieved.<br />
<br />
The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density <math>\gamma_{sl}^0</math> of the solid/liquid interface.<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2</math><br />
<br />
The capacitance <math>C</math> of a system of this geometry is described by the the dielectric constant of the insulating layer <math>/epsilon</math>, the height of this layer <math>d</math>, and the area <math>A</math> of contact through<br />
<br />
<math>C=\frac{\epsilon A}{d}</math><br />
<br />
Since we are dealing with surface tensions (surface energy density) we need the capacance per unit area, and thus the solid/liquid surface tension is now<br />
<br />
<math>\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}</math></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=User:Alex&diff=4648User:Alex2009-01-12T23:59:03Z<p>Alex: </p>
<hr />
<div>Alex Nemiroski<br />
<br />
I'm 4th year applied physics student in the Westervelt Lab. I used to study Quantum Computing, but recently switched to biosensing. I'm using this course<br />
to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.<br />
<br />
<br />
'''Final Project: Digital Microfluidics with Electrowetting'''<br />
<br />
==Motivation==<br />
<br />
Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily<br />
for medical applications. This "lab-on-a-chip" concept aims to reduce an entire laboratory worth of highly expensive equipment down the size of one small cheap<br />
device which can not only perform the same tests as its larger counterparts, but also more accurately, faster, with less consumption, and with a potential to someday be<br />
implanted in the human body to do realtime medical testing. The realization of this technology is heavily dependent on liquid transport in small volumes and thus microfluidics.<br />
<br />
Most current microfluidic 'lab-on-a-chip' devices utilize fixed channels for fluid flow and rely on continuous pressure driven flow to actuate the device. Most advanced techniques in<br />
microfluidic channel fabrication allow for extremely dense and complicated patterns to created, with many tens or even hundreds of centers for various biochemical analysis to be performed<br />
in parallel. While this approach has been very successful, it is very limited and rigid in that once a chip is created for a specific purpose, it cannot be used for anything else, and thus for each different<br />
type of test, a different chip is required. This approach also requires high pressures, highly complex fabrication, and most importantly difficult to control, since each different fluid is driven by a separate pressure<br />
source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=Polymer_molecules&diff=3240Polymer molecules2008-12-08T00:42:19Z<p>Alex: </p>
<hr />
<div>[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Common polymers ==<br />
<br />
=== '''Polyethylene''' – Cheap plastic bags ===<br />
[[Image:Polyethylene.png]]<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
=== '''Polypropylene''' – Labware, dishwasher safe! ===<br />
[[Image:Polypropene.png]]<br />
[[Image:Polypropylene2.png]]<br />
<br />
So what is it about polypropylene that makes products dishwasher safe?<br />
<br />
The issue with a dishwasher is that it is a very extreme environment. There is high heat, strong chemicals, and high pressure water. Materials need to be able to cope with all three in order to be deemed 'dishwasher' safe. Often time with hard plastics, you'll see that they get brittle after a few washings and micro-cracks begin to form.<br />
<br />
Polypropylene is particularly well suited to deal well with these issues because its melting point is high compated to other plastic materials. (It is 320°F) This allows the container to not crack or warp due to the high temperature of the water. This is the main advantage it has over another popular plastic, polyethylene. It is also water resistant and highly resistant to cracking. The desired properties are achieved through synthesizing the polymer using a catalyst such as Ziegler-Natta or Kaminsky. These offer a level of control over the tacticity of the polymer by controlling the orientation of the monomers. Commercial polypropylene tends to be isotactic with the methyl group on one side allowing the molecules to coil into a helical shape. It's this shape that allows the formation of the crystals that provide the desired properties.<br />
<br />
<br />
http://askville.amazon.com/SimilarQuestions.do?req=BabyBjorn-Plate-shatterproof-dishwasher-safe<br />
http://www.wisegeek.com/what-is-polypropylene.htm<br />
http://en.wikipedia.org/wiki/Polypropylene<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
=== '''Polystyrene''' – Plastic cups and Styrofoam ===<br />
[[Image:Polystyrene.PNG]]<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
=== '''Polyisoprene''' – Natural rubber ===<br />
[[Image:polyisoprene.png]]<br />
<br />
When samples of rubber first arrived in England, it was observed by Joseph Priestley, in 1770, that a piece of the material was extremely good for rubbing out pencil marks on paper, hence the name "rubber".[http://en.wikipedia.org/wiki/Polyisoprene]<br />
<br />
This can also be made surprisingly well with an organic reaction using the Ziegler-Natta catalyst. <br />
<br />
[[Image:Ziegler.png]]<br />
=== '''Polybutadiene''' – Synthetic rubber ===<br />
[[Image:Polybutadiene.PNG]]<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
<br />
=== '''Polyethylene oxide''' ===<br />
<br />
Water soluble, used in paper making process. A commonly used reagent in biological studies is PEG, a low molecular weight polyethylene oxide, used in osmotic pressure experiments and as a means of concentrating virus particles.<br />
<br />
[[Image:PEG.png]]<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
=== '''Polydimethylsiloxanes''' ===<br />
<br />
Silicones, PDMS~ used in soft lithography in making microfluidic devices, also part of Silly Putty<br />
[[Image:Polydimethylsiloxanes.png]]<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
=== '''Polyesters'''=== <br />
<br />
Polyester is a category of polymers that involves the ester functional group in their main chain (see below). Polyesters include naturally-occurring chemicals, such as in the cutin of plant cuticles, as well as synthetics such as polycarbonate and polybutyrate.<br />
<br />
[[Image:ester_group.gif]]<br />
<br />
Polyesters can be manufactured in many forms such as sheets and three-dimensional shapes. Polyesters as thermoplastics are able to change shape as you apply heat to it. Even though they are combustible at high temperatures, polyesters tend to shrink away from flames and self-extinguish upon ignition. <br />
<br />
Polyesters are also used to produce bottles, synthetic fibers, canoes, holograms, filters, films, dielectric film for capacitors, film insulation for wire, insulating tapes and toners. Polyester fibers have high Bulk modulus as well as low water absorption and minimal shrinkage in comparison with other industrial fibers.<br />
<br />
Synthesis of polyesters is generally achieved by a polycondensation reaction. Most general equation for the reaction of a diol with a diacid is in production of polyesters is: <br />
<br />
(n+1) R(OH)2 + n R´(COOH)2 ---> HO[ROOCR´COO]nROH + 2n H2O<br />
<br />
Some examples of polyesters are shown below:<br />
<br />
[[Image:polyester_resin.jpeg]]<br />
<br />
Polyester Resin<br />
<br />
[[Image:polyester_fabric.jpeg]]<br />
<br />
Polyester Fabric<br />
<br />
[[Image:polyester_fibers.jpeg]]<br />
<br />
Polyester Fibers<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
<br />
=== '''Polypeptides''' ===<br />
<br />
Polypeptides are defined to be chains of amino acids. Proteins are made out of one or more polypeptide chains. In order to form a polypeptide chain, amino acids are connected together using '''peptide bonds'''. For example, we can see a tripeptide molecule in the image below.<br />
<br />
[[Image:tripeptide.jpg]]<br />
[Reference: http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/P/Polypeptides.html]<br />
<br />
Proteins exhibit four levels of structure. '''Primary structure''' is considered to be the chain of amino acids that create a polypeptide chain. '''Secondary structure''' is the ordered arrangement of amino acids in localized regions of a polypeptide molecule. Hydrogen bonding plays important role in stabilizing these patterns. '''Tertiary structure''' of a polypeptide is a three-dimensional arrangement of the atoms within one single polypeptide chain. Finally, '''quaternary structure''' is used to describe proteins made of multiple polypeptides. Hydrophobic interaction is the primary force responsible for stabilizing subunits (polypeptides) in quaternary structure. <br />
<br />
Polypeptide have to be terminated in a specific manner. One end has to be '''amino-terminal''' (ends in nitrogen group), whereas the other has to be '''carboxyl-terminal''' (ends in carbon group). An example is shown below.<br />
<br />
[[Image:peptide.jpg]]<br />
[Reference: http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/P/Polypeptides.html]<br />
<br />
<br />
----<br />
<br />
=== '''Polyamide'''===<br />
<br />
A polyamide is a polymer containing monomers of amides joined by peptide bonds. They can occur both naturally, examples being proteins, such as wool and silk, and can be made artificially, examples being nylons, aramids, and sodium poly(aspartate).<br />
The amide link is produced from the condensation reaction of an amino group and a carboxylic acid or acid chloride group. A small molecule, usually water, or hydrogen chloride, is eliminated.<br />
The amino group and the carboxylic acid group can be on the same monomer, or the polymer can be constituted of two different bifunctional monomers, one with two amino groups, the other with two carboxylic acid or acid chloride groups.<br />
Amino acids can be taken as examples of single monomer (if the difference between R groups is ignored) reacting with identical molecules to form a polyamide:<br />
[[Image:Picture_21.png|400px|thumb|center]]<br />
<br />
Aramid is made from two different monomers which continuously alternate to form the polymer and is an aromatic polyamide:<br />
[[Image:Picture_22.png|400px|thumb|center]]<br />
<br />
<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Isomerism ==<br />
<br />
Isomers are chemical compounds with the same chemical formula, but different structural formulas. Specifically, isomers have the same number of each element, but they are topologically or geometrically distinct.<br />
<br />
For a topological example, consider the following three molecules I,II,III:<br />
<br />
[[Image:Structural_isomers.png | center ]]<br />
<br />
Each of these are isomers, however we can see that they are topologically distinct, in the sense that neither can be deformed into the other (without breaking bonds). For example, I has an O atom connected to a C atom which is connected to 2 H atoms, II has an O atom connected to a C atom that is connected to 2 other C atoms, and III has an O atom connected to 2 C atoms. Each of these properties is distinct to that isomer.<br />
<br />
When two compounds are topologically identical but geometrically distinct, they are called stereoisomers. As an example of what this means, consider the following molecules:<br />
<br />
[[Image:375px-Cis-2-butene.svg.png | center | 200px ]]<br />
[[Image:375px-Trans-2-butene.svg.png | center | 200px ]]<br />
<br />
The top and bottom molecules can clearly be deformed into each other by simply rotating the C=C double bond. Thus we would call these stereoisomers, because they are spatially different, even though they have the same connectivity. Because double-bonds can be considered rigid, these are chemically distinct molecules. Stereoisomers can have radically different chemical properties, largely due to the fact that spatial arrangement can change the dipole moment of the molecule significantly. For example, he two stereoisomers of 2-butenedioic acid are so different that they are given different names: maleic acid fumaric acid. <br />
<br />
Isomerism is important in polymers. For example, if the monomers in a polymer are not symmetric, then head-to-tail is different than tail to head.<br />
<br />
* '''Atatic polymers'''<br />
[[Image:AtaticPolymer.gif |thumb| 500px | center | Witten]]<br />
* '''Syndiotatic polymers'''<br />
[[Image:Syndiotacticpolymer.gif |thumb| 400px | center | Witten]]<br />
* '''Isotatic polymers'''<br />
[[Image:Isotactic_polymer.png |thumb| 400px | center | Witten]]<br />
* '''Copolymers'''<br />
** '''Random'''<br />
** '''Diblock and triblock coploymers'''<br />
***Coplymers of ethylene and propylene are disordered enough to remain liquid at lower temperatures than either homopolymer.<br />
***Diblock and triblock copolymers can (partially) self-associate<br />
<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Types of Polymerization ==<br />
<br />
(Witten p.45-46)<br />
<br />
-'''Addition polymerization''': a catalyst initiates polymerization in a solution of monomers; each chain has a single active end that reacts only with monomers --> molecular uniformity (example: polypeptides and polysaccharides)<br />
<br />
[[Image:addpol.jpg | center ]]<br />
<br />
Free radical polymerization is the most common type of addition polymerization. A free radical is a molecule with an unpaired electron. Free radicals are often created by the division of a molecule (initiator) into two fragments along a single bond. The unpaired electron makes the free radical highly reactive. The free radical will look for an additional electron to form a pair. This is achieved by breaking the bond on another molecule. <br />
<br />
<br />
There are three more types of initiating species for addition polymerization besides free radicals. <br />
They are cations, anions, and coordination (stereospecific) catalysts. Some monomers can use two or more of the initiation processes but others can use only one process.<br />
<br />
<br />
Addition polymerization process takes place in three distinct steps:<br />
1. chain initiation, usually by means of an initiator which starts the chemical process.<br />
2. chain propagation, in which the reactive end-groups of a polymer chain react in each propagation step with a new monomer molecule transferring the reactive group to that last unit.<br />
3. chain termination, which occurs either by combination or disproportionation. Termination, in radical polymerisation, is when the free radicals combine and is the end of the polymerisation process.<br />
<br />
<br />
<br />
-'''Condensation polymerization''': many chains may react with one another (example: polyamide nylon)<br />
<br />
During condensation polymerization, a small molecule such as water will be condensed out by the chemical reaction. One major drawback of utilizing condensation polymerization is the tendency for the reaction to cease before the chain grows to a sufficient length. This is due to the decreased mobility of the chains and reactant chemical species as polymerization progresses. This result in short chains.<br />
<br />
[[Image:condpol.jpg | center ]]<br />
<br />
<br />
<br />
-'''Living polymerization''': various chains are free to exchange monomers amongst themselves--> broad distribution of chain lengths (worm-like micelles)<br />
<br />
Living polymerization is similar to addition polymerization without the chain termination. The process continues until the monomer supply has been exhausted. When this happens, the free radicals become less active due to interactions with solvent molecules. If more monomers are added to the solution, the polymerization will resume. <br />
<br />
<br />
The result is that the polymer chains grow at a more constant rate than seen in traditional chain polymerization and their lengths remain very similar<br />
<br />
<br />
Uniform molecular weights are characteristic of living polymerization. Because the supply of monomers is controlled, the chain length can be manipulated to serve the needs of a specific application. <br />
<br />
<br />
-----------------------<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Polymer dimensionality and structure ==<br />
*Distinctiveness – Length & flexibility?<br />
**Polymers are ordered and inflexible in 1D<br />
**Polymers are random and flexible in 2 and 3 D<br />
**Polymers are tenuous in 2 and 3 D<br />
**Polymers “self-avoid” in 2 and 3 D<br />
*Some are constrained – DNA and RNA<br />
*Scaling with molecular weight<br />
*Scaling with structure – more difficult<br />
*Scaling of diffusion and flow<br />
<br />
<br />
----<br />
[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
=== Kinks and rings in confined polymer structures ===<br />
Some polymers naturally tend to form filamentous structures rather than blobs. Many of the biological polymers (or biopolymers) follow that behavior: actin, fibrin, collagen, tubulin, DNA, RNA and others. Carbon nanotubes can also form very strong linear structures, one of their most promising and applicable properties.<br />
<br />
Like many filaments, those just mentioned have a finite bending stiffness, which means that they have a characteristic length-scale over which they will appear rigid or straight: the persistence length. Segments shorter than the persistence length will behave like rigid beams, while longer segments will appear more floppy. In the limit of very long segments, the filament can fold on itself and behave more like a blob. <br />
<br />
An interesting question arises when these (bio)polymers are forced to grow in a confined space, smaller than their persistence length. This question comes naturally for biological systems like mammalian cells, where the cytoskeleton is comprised of polymeric filaments whose persistence length is on the order of the cell size (e.g. actin) or much larger than the cell (e.g. tubulin). Another example of this is given in an interesting applied math paper by Cohen and Mahadevan (PNAS 2002)[http://www.pnas.org/content/100/21/12141.full.pdf+html], where they talk about growing carbon nanotubes confined in air bubbles. A common phenomenon observed with cytoskeletal proteins and nanotubes, is that they tend to form rings or kinks when growing in a confined space; even more interesting is the fact that the angles of the kinks they form typically take discrete values rather than a broad continuous spectrum.<br />
<br />
A very simple explanation for a discrete kink-angle lies in the fact that these filamentous structures are composed of multiple thin single chains of monomers and that the interaction between these monomers causes them to want to be spaced out (laterally and longitudinally) at very specific length-scales. The longitudinal spacing is obviously the same or close to the size of the monomer and the lateral spacing between single chains is determined by the monomer size and the strength of the attraction between chains. It is clear that when we introduce bending into these multi-chain filaments, some of the chains will have a greater curvature than others and this will tend to create an offset in the monomer positions and how they fit together. Because there is an energy associated with creating local curvature in a filament, it is better to create one point of high curvature than to create many points of low curvature. This will follow a similar behavior to that described by the Frenkel-Kontorova model, which provides a microscopic explanation for the formation of certain dislocations in solids.<br />
<br />
[[Image:Polymers_kinks.jpg | center | 260px]]<br />
<br />
So because these polymers have strong inter-chain interactions and are formed of discrete monomer units, they tend to prefer a rigid rod state locally and will sharply kink to maintain some level of straightness. The paper by Cohen and Mahadevan provides some additional examples of kinks and rings in filamentous structures.<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Renormalization and scaling - The random walk polymer ==<br />
<br />
<br />
<br />
{|-<br />
| Probability that the end-to-end vector has some, ''r'' , for ''n'' segments: <br />
| <math>p\left( n,r \right)</math> is a probability per volume<br />
|-<br />
| The chain must have some length<br />
| <math>\int{p\left( n,r \right)}d^{3}r=1</math><br />
|-<br />
|}<br />
<br />
'''If''' <math>p\left( n,r \right)</math> '''be known, what be known about''' <math>p\left( n+1,r \right)</math>'''?'''<br />
<br />
{|-<br />
| Assume segment is flexible, but no self-avoidance. Probability depends on magnitude only.<br />
| <math>p_{0}\left( r_{1} \right)</math><br />
|-<br />
| Probability is the product<br />
| <math>p\left( n,\vec{r}-\vec{r}_{1} \right)p_{0}\left( \vec{r}_{1} \right)=p\left( n,\vec{r}-\vec{r}_{1} \right)p_{0}\left( r_{1} \right)</math><br />
|-<br />
|For all possible <math>\vec{r}_{1}</math> that have <math>\vec{r}_{{}}-\vec{r}_{1}</math> is<br />
| <math>p\left( n+1,r \right)=\int{p_{0}\left( r_{1} \right)}p\left( n,\vec{r}-\vec{r}_{1} \right)d^{3}r_{1}</math><br />
|-<br />
|}<br />
<br />
'''Consider the case of large''' ''''n''''.<br />
<br />
{|-<br />
| This difference should be small:<br />
| <math>p\left( n+1,r \right)-p\left( n,r \right)=\int{p_{0}\left( r_{1} \right)}\left[ p\left( n,\vec{r}-\vec{r}_{1} \right)-p\left( n,r \right) \right]d^{3}r_{1}</math><br />
|-<br />
| A Taylor expansion around <math>\vec{r}_{1}</math> is:<br />
| <math>p\left( n,\vec{r}-\vec{r}_{1} \right)=p\left( n,r \right)-\vec{r}_{1}\cdot \nabla _{r}p\left( n,r \right)+\frac{1}{6}r_{1}^{2}\nabla _{r}^{2}p\left( n,r \right)+\cdots </math><br />
|-<br />
| If <math>\Delta n=1</math> the RHS remains the same but the LHS is:<br />
| <math>\underset{n\to \infty }{\mathop{\lim }}\,\frac{p\left( n+\Delta n,r \right)-p\left( n,r \right)}{\Delta n}\to \frac{dp}{dn}</math><br />
|-<br />
| And we have:<br />
|<math>\frac{dp}{dn}=-\nabla _{r}p\left( n,r \right)\cdot \int{\vec{r}_{1}p_{0}\left( r_{1} \right)d^{3}r_{1}}+\frac{1}{6}\nabla _{r}^{2}p\left( n,r \right)\int{r_{1}^{2}p_{0}\left( r_{1} \right)d^{3}r_{1}}+\cdots </math><br />
|-<br />
| All odd integrals are zero, therefore:<br />
|<math>\frac{dp}{dn}\cong \frac{1}{6}\nabla _{r}^{2}p\left( n,r \right)\int{r_{1}^{2}p_{0}\left( r_{1} \right)d^{3}r_{1}}+constant\cdot \nabla _{r}^{4}p+\cdots </math><br />
|-<br />
| The integral is <math>\left\langle r^{2} \right\rangle _{1}</math>, therefore:<br />
| <math>\frac{dp}{dn}\cong \frac{1}{6}\left\langle r^{2} \right\rangle _{1}\nabla _{r}^{2}p\left( n,r \right)+constant\cdot \nabla _{r}^{4}p+\cdots </math><br />
|-<br />
|}<br />
<br />
<br />
'''Now the first scaling idea is introduced.'''<br />
{|-<br />
| The “shape” of the distribution should be independent of n.<br />
| <br />
<math>\begin{align}<br />
& p\left( n,r \right)=\eta p\left( \lambda n,\mu r \right) \\ <br />
& p\left( n,r \right)=\tilde{p}\left( \tilde{n},\tilde{r} \right) \\ <br />
\end{align}</math><br />
<br />
|-<br />
| Where:<br />
| <math>\tilde{p}=\eta p,\text{ }\tilde{n}=\lambda n\text{ and }\tilde{r}=\mu r</math><br />
|-<br />
| Hence:<br />
| <math>\begin{align}<br />
& \frac{d}{dn}=\lambda \frac{d}{d\tilde{n}} \\ <br />
& \nabla _{r}^{2}=\mu ^{2}\nabla _{{\tilde{r}}}^{2}\text{ and }\nabla _{r}^{4}=\mu ^{4}\nabla _{{\tilde{r}}}^{4} \\ <br />
\end{align}</math><br />
|-<br />
| Or:<br />
|<math>\frac{d\tilde{p}}{d\tilde{n}}\cong \frac{1}{6}\frac{\mu ^{2}}{\lambda }\left\langle r^{2} \right\rangle _{1}\nabla _{{\tilde{r}}}^{2}\tilde{p}\left( \tilde{n},\tilde{r} \right)+\text{C}\frac{\mu ^{4}}{\lambda }\nabla _{{\tilde{r}}}^{4}\tilde{p}+\cdots </math><br />
|-<br />
|}<br />
<br />
'''Now the second scaling idea is introduced.'''<br />
<br />
{|-<br />
| If ''n'' can be arbitrarily large:<br />
| <math>\mu =\lambda ^{{1}/{2}\;}</math><br />
|-<br />
| Consider the normalization:<br />
| <br />
<math>\begin{align}<br />
& \int{p\left( n,r \right)}d^{3}r=1 \\ <br />
& \int{\eta p\left( \lambda n,\mu r \right)}d^{3}r=1 \\ <br />
& \frac{\eta }{\mu ^{3}}\int{p\left( \lambda n,\mu r \right)}d^{3}\left( \mu r \right)=1 \\ <br />
& \therefore \text{ }\frac{\eta }{\mu ^{3}}=1 \\ <br />
\end{align}</math><br />
<br />
|-<br />
| Or:<br />
| <br />
<math>\eta =\lambda ^{{3}/{2}\;}</math><br />
<br />
|-<br />
| Since <math>\lambda </math> is arbitrary, it can be set to <math>{1}/{n}\;</math> and:<br />
| <math>\tilde{p}=n^{{-3}/{2}\;}p,\text{ }\tilde{n}=1\text{ and }\tilde{r}=n^{{-1}/{2}\;}r</math><br />
|-<br />
| The distribution <br />
|<math>p\left( n,r \right)=n^{-{3}/{2}\;}p\left( \tilde{n},\tilde{r} \right)_{\tilde{n}=1,\tilde{r}=rn^{-{1}/{2}\;}}</math><br />
|-<br />
|is now:<br />
| <math>p\left( n,r \right)=n^{-{3}/{2}\;}f\left( rn^{-{1}/{2}\;} \right)</math><br />
|-<br />
| The moments of the distribution are:<br />
|<math>\begin{align}<br />
& \left\langle r^{p} \right\rangle _{n}=\int{r^{p}\cdot n^{-{3}/{2}\;}}f\left( rn^{-{1}/{2}\;} \right)d^{3}r \\ <br />
& \text{ }=n^{{p}/{2}\;}n^{-{3}/{2}\;}n^{{3}/{2}\;}\int{\left( rn^{-{1}/{2}\;} \right)^{p}\cdot }f\left( rn^{-{1}/{2}\;} \right)d^{3}\left( rn^{-{1}/{2}\;} \right) \\ <br />
& \text{ }=n^{{p}/{2}\;}\int{\left( {\hat{r}} \right)^{p}\cdot }f\left( {\hat{r}} \right)d^{3}\hat{r} \\ <br />
\end{align}</math><br />
|-<br />
| Since the integral is a constant:<br />
| <br />
<math>\left[ \left\langle r^{p} \right\rangle _{n} \right]^{{1}/{p}\;}=K_{p}n^{{1}/{2}\;}</math><br />
<br />
|-<br />
| Now the solution to<br />
| <math>\frac{dp}{dn}=\frac{1}{6}\left\langle r^{2} \right\rangle _{1}\nabla _{{}}^{2}p\left( n,r \right)</math> <br />
|-<br />
|is:<br />
|<math>p\left( n,r \right)=\left[ {2\pi n\left\langle r^{2} \right\rangle _{1}}/{3}\; \right]^{-{3}/{2}\;}\exp \left[ -\frac{3r^{2}}{2n\left\langle r^{2} \right\rangle _{1}} \right]</math><br />
|-<br />
|}<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== What is the energy to stretch a polymer from random packing to fully extended? ==<br />
{|-<br />
| The only component is entropy, hence<br />
| <math>U\left( r \right)=-\left. kT\ln \left( p\left( n,r \right) \right) \right|_{initial}^{final}=\frac{3}{2}kT\frac{r^{2}}{\left\langle r^{2} \right\rangle }</math><br />
|-<br />
|}<br />
<br />
<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== How dense is the polymer? ==<br />
<br />
Remember - No liquid has been mentioned!!<br />
<br />
What is the "size" of a polymer?<br />
<br />
Take any moment of the end-to-end distance: <math>\left[ \left\langle r^{p} \right\rangle _{n} \right]^{{1}/{p}\;}=K_{p}n^{{1}/{2}\;}\sim n^{{1}/{2}\;}</math><br />
<br />
What's the number density? <math>\bar{\rho }\sim \frac{n}{\left\langle r \right\rangle _{n}^{3}}\sim \frac{n}{n^{{3}/{2}\;}}\sim n^{-{1}/{2}\;}</math><br />
<br />
The greater the molecular weight, the more tenuous the polymer.<br />
<br />
<br />
<br />
<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== How does density vary within the polymer chain? ==<br />
<br />
[[Image:Random polymer chain.png |thumb| 200px | center | ]]<br />
<br />
{|-<br />
| Probability of each segment at ''r'':<br />
| <math>\left\langle \rho \left( r \right) \right\rangle _{0}=2\int\limits_{0}^{\infty }{i^{-{3}/{2}\;}}f\left( ri^{-{1}/{2}\;} \right)di</math><br />
|-<br />
| Define a scaled variable: <math>\tilde{i}=i^{{1}/{2}\;}r^{-1}</math><br />
| <math>\left\langle \rho \left( r \right) \right\rangle _{0}=2r^{2}r^{-3}\int\limits_{0}^{\infty }{\tilde{i}^{-{3}/{2}\;}}f\left( \tilde{i}^{-1} \right)d\tilde{i}</math><br />
<br />
|-<br />
| The integral is the local density:<br />
| <math>\left\langle \rho \left( r \right) \right\rangle _{0}={\text{constant}}/{r}\;</math><br />
|-<br />
| The average density is:<br />
| <math>\left\langle M\left( r \right) \right\rangle =\int\limits_{{r}'<r}{\left\langle \rho \left( {{r}'} \right) \right\rangle _{0}}d^{3}{r}'=\int\limits_{{r}'<r}{{r}'^{2}\left\langle \rho \left( {{r}'} \right) \right\rangle _{0}}d{r}'=\left( \text{constant} \right)r^{2}</math><br />
|-<br />
|}<br />
<br />
<br />
<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
<br />
<br />
Therefore the random walk polymer has a fractal dimension of ''D'' = 2.<br />
<br />
== Self-avoidance - Flory theory ==<br />
<br />
<br />
Purely locally or global models do not change the scaling of density.<br />
<br />
Assume that self-avoidance occurs on all length scales.<br />
<br />
On each and every length scale the polymer is expanded by a factor b.<br />
<br />
Replace:<br />
<math>p\left( n,r \right)=n^{-{3}/{2}\;}f\left( rn^{-{1}/{2}\;} \right)</math> with: <br />
<math>p\left( n,r \right)=n^{-\nu d}f\left( rn^{-\nu } \right)</math><br />
<br />
This preserves the normalization and the end-to-end distance as <math>n^{-\nu }</math><br />
<br />
And the previous results are similar: <math>\left\langle \rho \left( r \right) \right\rangle _{0}=\left( \text{constant} \right)r^{{1}/{\nu -3}\;}</math><br />
<br />
and<br />
<math>\left\langle M\left( r \right) \right\rangle =\left( \text{constant} \right)r^{{1}/{v}\;}</math><br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
<br />
<br />
== Universal Ratios ==<br />
<br />
In the previous discussion, we have seen that a polymer has a single asymptotic probability distribution function p(n,r) for any random walk. This is true for all polymers, irregardless of the specific details of how the random walk was created. Furthermore, we have explored the fact that all self-repelling polymers exhibit common behavior, independent of the specifics of the repulsion. Since the aforementioned characteristics are seen for any polymer, we call them '''universal'''. Still, even in these universal functions, there is still room for choosing an arbitrary scaling coefficients e.g. <math>\mu</math> or <math>\lambda</math>. Therefore, some quantities are not going to be dependent '''only''' on p(n,r). But quantity like <math><r^4>/<r^2>^2</math> has both <math><r^4></math> and <math><r^2></math> scaling as <math>\mu^4</math> which cancels out so we can conclude <math><r^4>/<r^2>^2</math> is only dependent on prabability distribution function, and '''not''' on any scaling properties. These kinds of ratios independent of scaling are referred to as '''universal ratios'''.<br />
<br />
[For more information, see Witten p. 72-73]<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
<br />
== Estimating the fractal dimension ''D'' ==<br />
<br />
{|-<br />
| Consider the work to expand a polymer from the “ideal” state.<br />
| <br />
<math>U\sim kT\frac{r^{2}}{\left\langle r^{2} \right\rangle }\sim kT\frac{r^{2}}{n}</math><br />
<br />
|-<br />
| Think of self-avoiding polymers as ones with slightly repulsive interactions.<br />
| <br />
|-<br />
| The number of (non-local) contacts n times the probability that a monomer has a contact:<br />
| <math>V\simeq n\left( {\nu \cdot n}/{r^{3}}\; \right)U^{contact}\sim U^{contact}\frac{n^{2}}{r^{3}}</math><br />
|-<br />
| Equating the energies and re-arranging:<br />
| <br />
<math>\begin{align}<br />
& kT\frac{r^{2}}{n}\sim U^{contact}\frac{n^{2}}{r^{3}} \\ <br />
& n\sim r^{{5}/{3}\;} \\ <br />
\end{align}</math><br />
<br />
|-<br />
|}<br />
'''Therefore the self-avoiding polymer has a fractal dimension of''' '''''D''''' '''= 5/3'''<br />
<br />
<br />
What is a '''fractal dimension''', anyway?<br />
This is the wikipedia page for it (since we all know that that is a fantastically reliable resource): [http://en.wikipedia.org/wiki/Fractal_dimension Fractal Dimension]<br />
<br />
For a biological reference, I found this article on the fractal analysis of lysozyme interesting; I had never heard of fractals in bio polymers, so this was a neat one to read through. Here is the reference, since I'm not sure how GNU this is (you can snag it through the Harvard library system, though):<br />
<br />
''Rigid structure of fractal aggregates of lysozyme<br />
G. C. Fadda et al 2000 Europhys. Lett. 52 712-718'' <br />
<br />
Abstract: The aggregation of hen egg-white lysozyme upon salt addition was studied by quasi-elastic light scattering. Our results agree with the fractal structure of the aggregates already reported in the literature. However, we also demonstrate that these aggregates are rigid, since they do not display any fluctuation of internal concentration. Such a rigid internal structure is a key point to reconcile the fractal structure of the aggregates and their colloid-like ordering. Furthermore, this result has to be considered for understanding crystal nucleation.<br />
<br />
--[[User:BPappas|BPappas]] 22:09, 25 October 2008 (UTC)<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Polymer degradation ==<br />
Polymer degradation is a change in the properties—tensile strength, colour, shape, etc.—of a polymer or polymer-based product under the influence of one or more environmental factors, such as heat, light or chemicals. It is often due to the hydrolysis of the bonds connecting the polymer chain, which in turn leads to a decrease in the molecular mass of the polymer. These changes may be undesirable, such as changes during use, or desirable, as in biodegradation or deliberately lowering the molecular mass of a polymer. Such changes occur primarily because of the effect of these factors on the chemical composition of the polymer. Ozone cracking and UV degradation are specific failure modes for certain polymers.<br />
[[Image:Ozone_cracks_in_tube1.png|200px|thumb|right|Ozone cracks]] <br />
The degradation of polymers to form smaller molecules may proceed by random scission or specific scission. The degradation of polyethylene occurs by random scission—a random breakage of the linkages (bonds) that hold the atoms of the polymer together. When heated above 450°C it degrades to form a mixture of hydrocarbons. Other polymers—like polyalphamethylstyrene—undergo specific chain scission with breakage occurring only at the ends. They literally unzip or depolymerize to become the constituent monomer.<br />
<br />
However, the degradation process can be useful from the viewpoints of understanding the structure of a polymer or recycling/reusing the polymer waste to prevent or reduce environmental pollution. Polylactic acid and polyglycolic acid, for example, are two polymers that are useful for their ability to degrade under aqueous conditions. A copolymer of these polymers is used for biomedical applications, such as hydrolysable stitches that degrade over time after they are applied to a wound. These materials can also be used for plastics that will degrade over time after they are used and will therefore not remain as litter.<br />
<br />
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[[Polymers_and_polymer_solutions#Topics | Back to Topics.]]<br />
<br />
== Polyelectrolytes ==<br />
<br />
Polyelectrolytes are polymers which have electrolyte units. When polyelectrolytes are put into an aqueous solution they become charged. A polyelectrolyte can be simply thought of as a charged chain, which, in solution, conduct electricity, are often viscous, and have complex but interesting physics associated with their structure and conformation. They play major roles in biochemistry; perhaps the most famous electrolyte in the world is DNA. A normal, uncharged linear polymer in solution takes on a random conformation that is close to an approximation given by a self-avoiding three-dimensional random walk theory. This is <b>not</b> true for polyelectrolytes. Because of their charge, the electrolytic units on a polyelectrolyte repel each other, causing the chain to form expand into a rigid-rod conformation. In the presence of multivalent (2+, 3+, etc) salt, however, the charges on the polyelectrolytes get screened, and at a critical point (when the net charge on the polyelectrolyte equals the net charge of the salt), the polyelectrolyte becomes essentially neutral. At this point, the chain is free to conform in a similar way to a neutral chain. After this point, however, the positive ions 'attached' to the polyelectrolyte dominate, and there becomes an effectively positive charge on the system, causing the chain to repel itself again and become rigid and elongated. However, how polyelectrolytes being packaged into a <i>small</i> space in the presence of multi-valent salts is a different question, which I recently explored.<br />
<br><br><br />
Understanding how polymers behave when constrained into tight spaces is a problem whose relevance stretches well beyond the field of polymer physics. Besides the several industrial applications in which this phenomenon plays a crucial role: colloidal stabilization, filtration, drug-delivery and flow injection; the confinement of<br />
bio-polymers is also a ubiquitous phenomenon in nature. Numerous biological processes rely on confinement to perform a diverse set of fundamental tasks, including the release of DNA pre-packaged by molecular-motors inside virus capsids, bacterial gene swapping, and the re-folding of proteins inside double-barreled Chaperonins. The free energy barrier required to insert a flexible neutral chain with radius of gyration RG into a spherical cavity of radius R (< R_G) can be obtained by a simple scaling argument that accounts for the chain loss of entropy. The expression you get is correct in the dilute limit, but becomes inaccurate at large densities, where excluded volume interactions between the monomers dominate over the chain entropy loss, thus causing the free energy penalty to increase at a much steeper rate. Although the physics concerning the confinement of neutral flexible polymers is well understood, such a claim cannot be made for charged chains. While the bulk properties of a charged chain in the presence of monovalent salt can be properly described within the framework of the Poisson-Boltzmann theory--the interaction between the charged monomers can be encoded into an effective chain bending rigidity, kappa, whose value decreases as the electrostatic interactions are screened by addition of salt in solution--the phenomenology is much more complex when the chain is either confined within a small region or when multivalent salt is present in solution. For instance, it is known that the size of a charged chain in the presence of multivalent salt presents a non-monotonic behavior as a function of salt concentration ro, resulting in a conformational collapse when multivalent counterions neutralize the bare charge of the chain, and a subsequent re-expansion, due to the inversion of the chain net charge, at larger values of ro. In a project I recently finished I ran molecular dynamics simulations to account for the role of salt valency and concentration on the packaging of a charged chain into a small, spherical cavity. The results can be summed up as follows: Our goal was not to provide a quantitative estimate for the DNA packaging energy, but to sort out the relevant energy scales dominating the process, and to elucidate the physical mechanisms behind the break-down of the Poisson-Boltzmann treatment of the salt. What we find can be summarized in two points. (1) In the presence of multi-valent counterions, it is easier to confine a charged chainthan a neutral flexible chain, and there exists a threshold salt concentration above which the addition of extra salt does not affect the packaging energy. (2) In the presence of monovalent counterions, the insertion energy is completely independent of salt concentration.<br />
<br />
[[Polyelectrolytes#Topics | Back to Topics.]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Picture_22.png&diff=3239File:Picture 22.png2008-12-08T00:41:12Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=File:Picture_21.png&diff=3238File:Picture 21.png2008-12-08T00:41:04Z<p>Alex: </p>
<hr />
<div></div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=Drops,_menisci,_and_lenses&diff=3231Drops, menisci, and lenses2008-12-08T00:33:17Z<p>Alex: /* Another Example: Liquid Optics */</p>
<hr />
<div>[[Capillarity_and_wetting#Topics | Back to Topics.]]<br />
<br />
== Thickness of a large drop ==<br />
Small drops are spherical segments. Large drops are flattened. The relative size of the radius of drop, in the absence of a surface, to the capillary length determines the extent to which the drop spreads across the surface. <br />
For the case of small droplets (r << <math>\kappa</math>), only capillary forces influence the drop. These drops will be spherical in shape and form a contact angle with the surface that depends on the spreading parameter. <br />
Large droplets (r<< <math>\kappa</math>) are much more interesting. At this size, the droplet is large compared to the capillary length and gravity will play an important role. In this case (as seen in the figure below), the drop will form a pancake on the surface. The thickness of this pancake may be calculated by balancing surface forces with hydrostatic pressure. <br />
[[Image: DeGennes_Fig_2-4.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2.4]]<br />
<br />
To “spread” the drop requires an force per unit length:<math>\sigma _{sv}-\left( \sigma _{lv}+\sigma _{sl} \right)</math><br />
<br />
<br />
The hydrostatic pressure integrated over the depth of the drop is a force per unit length pushing to “spread” the drop: <math>\tilde{P}=\int\limits_{0}^{e}{\rho g\left( e-\tilde{z} \right)d\tilde{z}}=\frac{1}{2}\rho ge^{2}</math><br />
<br />
At equilibrium the sum of the two is zero: <math>\sigma _{sv}-\left( \sigma _{lv}+\sigma _{sl} \right)+\frac{1}{2}\rho ge^{2}=0</math><br />
<br />
Substituting the Young-Dupré equation: <math>\sigma _{lv}\left( 1-\cos \theta _{e} \right)=\frac{1}{2}\rho ge^{2}</math><br />
<br />
<br />
Re-arranging gives: <math>\text{ }e=2\kappa ^{-1}\sin \left( \frac{\theta _{e}}{2} \right)</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
<br />
== Profile of a large drop ==<br />
<br />
The general ideas used to calculate the thickness are used again to calculate the profile. With a couple of modifications.<br />
[[Image: DeGennes_Fig_2-4.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2.4]]<br />
<br />
The limits on the integration are changed: <math>\tilde{P}=\int\limits_{0}^{z}{\rho g\left( e-\tilde{z} \right)d\tilde{z}}=\rho g\left( ez-\frac{z^{2}}{2} \right)</math><br />
<br />
The “spreading” force per unit length is now: Where q<math>\theta </math> is the angle marked in the diagram: <math>\sigma _{sv}-\left( \sigma _{lv}\cos \theta +\sigma _{sl} \right)</math><br />
<br />
“It can be shown” from the diagram that: <math>\cos \theta =\sqrt{1+\dot{z}^{2}}</math><br />
<br />
This results in a differential equation for the shape consistent to the algebraic equation for the drop thickness: <math>\sigma _{lv}\left( \sqrt{1+\dot{z}^{2}}-\cos \theta _{e} \right)=\frac{1}{2}\rho g\left( 2ez-z^{2} \right)</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
<br />
== A brief discription of menisci ==<br />
<br />
[[Image:meniscus.png|300px|thumb|right|An example showing the menisci in a capillary tube.]]'''Meniscus''', plural: ''menisci'', from the Greek for "crescent", is a curve in the surface of a liquid and is produced in response to the surface of the container or another object. It can be either concave or convex. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container. This may be seen between mercury and glass in barometers. Conversely, a concave meniscus occurs when the molecules of the liquid attract those of the container. This can be seen between water and glass. Capillary action acts on concave menisci to pull the liquid up, and on convex menisci to pull the liquid down. This phenomenon is important in transpirational pull in plants. Honey, water, milk all have a lower meniscus. When a tube of a narrow bore, often called a capillary tube, is dipped into a liquid and the liquid “wets” the tube (with zero contact angle), the liquid surface inside the tube forms a concave meniscus, which is a virtually spherical surface having the same radius, ''r'', as the inside of the tube. The tube experiences a downward force.<br />
<br />
When reading a scale on the side of a container filled with liquid, the meniscus must be taken into account in order to obtain a precise measurement. Manufacturers take the meniscus into account and calibrate their measurement marks relative to the resulting meniscus. The measurement is taken with the meniscus at eye level to eliminate error, and at the central point of the curve of the meniscus, i.e. the top of the meniscus, in the unusual case of a liquid like mercury, or more usually, the bottom of the meniscus in water and most other liquids.<br />
----<br />
<br />
== Menisci against a wall ==<br />
<br />
The ascending meniscus against a vertical wall is shown below. (de Gennes, 2004, pp. 45f). The Laplace equation, shown on the diagram, is a differential equation that describes the shape of the meniscus. The curvature increases with height.<br />
<br />
[[Image: Ascending_meniscus_1.png |thumb| 800px | left| ]] <math>\frac{1}{R\left( z \right)}=-\frac{{\ddot{z}}}{\left[ 1+\dot{z}^{2} \right]^{3/2}}</math><br />
<br />
Substituting the curvature into the Laplace equation and integrating twice gives: <br />
<math>x-x_{0}=\kappa ^{-1}\cosh ^{-1}\left( \frac{2\kappa ^{-1}}{z} \right)-2\kappa ^{-1}\left( 1-\frac{z^{2}}{4\kappa ^{-2}} \right)^{1/2}</math><br />
<br />
(Where x0 makes z = h at x = 0) A correct, but not illuminating, result.<br />
<br />
<br />
de Gennes provides a more illuminating derivation by considering the equilibrium of forces.<br />
<br />
[[Image: Pressure_in_a_vertical_meniscus.png|thumb| 400px | left| ]] Along the vertical dotted line, the pressure varies as: <math>p\left( z \right)=p_{0}-\rho gz</math><br />
<br />
This produces a total horizontal force on the line: <math>\tilde{p}=\int\limits_{0}^{z}{\rho gzdz}=\frac{1}{2}\rho gz^{2}</math><br />
<br />
The balance is of hydrostatic force, the horizontal component of surface tension, and the surface tension of the liquid surface (z = 0) gives: <math>\frac{1}{2}\rho gz^{2}+\sigma \sin \theta =\sigma </math><br />
<br />
Evalutating at z = h where the angle is the contact angle and re-arranging gives: <math>h=\sqrt{2}\kappa ^{-1}\left( 1-\sin \theta _{E} \right)^{{1}/{2}\;}</math><br />
'''<br />
Meniscus height << capillary rise''' <math>h\left( \theta _{E}=0 \right)=\sqrt{2}\kappa ^{-1}</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
== Meniscus on a fiber ==<br />
[[Image: De_Gennes_Fig_2-14.gif |thumb| 400px | center | de Gennes, 2004, Fig. 2.14]]<br />
As usual, the meniscus obeys: <br />
<math>p_{0}+\sigma \left( \frac{1}{R_{1}}+\frac{1}{R_{2}} \right)=p_{0}-\rho gz</math><br />
<br />
Since the meniscus height is small, the hydrostatic term is small and the film has no curvature! <math>\left( \frac{1}{R_{1}}+\frac{1}{R_{2}} \right)=0</math><br />
<br />
Assuming <math>\theta =0</math> for simplicity, the profile is a catenary curve: <math>r\left( z \right)=b\cosh \left( \frac{z-h}{b} \right)</math><br />
<br />
Dropping the hydrostatic term left this equation with the wrong limit: <math>r\left( 0 \right)=\kappa ^{-1}</math>,<br />
<br />
<br />
Assuming that the meniscus is lost at the capillary length: <math>\kappa ^{-1}=b\cosh \left( \frac{-h}{b} \right)</math><br />
<br />
<br />
Hence: <math>h\approx b\ln \left( \frac{2\kappa ^{-1}}{b} \right)</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
== Meniscus wetting - AFM tips ==<br />
The end of an atomic force microscope probe has to be of molecular dimensions for best sensitivity:<br />
[[Image: De_Gennes_Fig_2-16.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2-16]]<br />
<br />
They are made by immersion in an etching solution:<br />
[[Image: De_Gennes_Fig_2-15.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2-15]]<br />
<br />
<br />
The mechanism that produces the sharp tip can be explained by the variation in meniscus height as the etched dip becomes smaller and smaller by considering the meniscus height as a function of radius: <math>h\approx b\ln \left( \frac{2\kappa ^{-1}}{b} \right)</math><br />
<br />
Typical capillary lengths are mm’s, so the menisci are also few mm’s.<br />
The meniscus height is a few times the fiber radius or a few 10’s mm.<br />
Therefore the meniscus is much wider than high.<br />
<br />
During the etching of an AFM tip, as the end gets narrower, the meniscus drops, and so on, producing a fine point at the very last.<br />
<br />
<br />
Real-Lab Example:<br />
<br />
I actually did this sort of experiment for a microdrop experiment that I was working on at the University of Illinois, Urbana-Champaign.<br />
<br />
The spirit of the project, done in [http://www.scs.uiuc.edu/mgweb/ Dr. Martin Gruebel's lab], was to find a way to characterize a single protein (a variation on GFP, [http://en.wikipedia.org/wiki/Green_Fluorescent_Protein green-fluorescent protein]) folding and unfolding. One of the interesting parts of this GFP is that the [http://en.wikipedia.org/wiki/Fluorophore fluorophore] remains intact during folding and unfolding, but fluorescence is quenched upon entry of water into the [http://en.wikipedia.org/wiki/Beta_barrel beta barrel] that the fluorophore is residing in. This makes it clear to tell when the protein has unfolded.<br />
<br />
In order to study the folding and unfolding characteristics, Dr. Gruebele and his graduate students designed a cube lens, into which a micron size drop of protein solution would be driven and suspended in a fixed optical trap. This drop would be small enough and the original solution at a low enough concentration that there would statistically be only one GFP present in the trap. The protein would then be excited, and the fluorescence monitored. The cubic lens allows there to be very low loss given the low number of photons coming off of the individual protein. This is a very valuable way of finding and studying the halfway point of the protein in folding kinetics; you can gain a lot from looking at the pH and ionic strength conditions that cause half of the protein solution to be folded and the other half unfolded, dynamically.<br />
<br />
Enter the microdrop generator:<br />
<br />
As always, the goal of a part of my project in the lab was create something cheap, reproducible, and easy to make; the caveat being that it also needed to be able to make drops approximately 10 microns in diameter, which is somewhat unheard of. After a bit of indecision of which way to go, we settled on a modification of the way AFM tips are made and the way inkjet printers work: basically, I tried using HF to etch the capillary tube to a fine point and attaching a peizoelectric driver to force the droplet out of the tube. This driving effect, where the drop is pushed out and then pulled up quickly, would be a really neat force effect to study--ideas on what is acting on the drop throughout? What would change with different fluid properties?<br />
<br />
I really wish that I had seen the de Gennes picture of this before starting my project, as it would had led to a bit more credibility to my theory that the glass really would be etched down to a point if it were just suspended in the acid...<br />
<br />
So: the production. Taking a borosilicate capillary tube, the graduate student that I was working with drew the tube under heat to a very fine point, creating a short tube of about 400 microns in length that narrowed down from about 50 microns to a closed point over the length. I then took this tube and suspended it in an HF solution that was adjusted to give a gradual etch. To make sure that the acid didn't shoot up the fine capillary tube once the micron sized hole opened (which, I assure you, happened to me the first time I did this, and it was quite unpleasant), I applied a very slight opposing pressure using filtered nitrogen; filtered because one of the main frustrations with mircodroplet generation is clogging due to particulate build up in the nozzle. <br />
<br />
Do it work? Sort of, although the evenness that is shown in the de Gennes picture is not exactly what I got under the microscope. I feel like this could be due to a number of things, most likely glass weakening near the pulled tip and micro-cracks from rapid cooling that could have been infiltrated by the HF. The etching was progressing well, though I was quite freaked out by the bone dissolving power of HF, and a little wary of working with it. The graduate student continuing the project was hoping to test out the drop size from the tips created as I was leaving in May this year. <br />
<br />
This book: http://books.google.com/books?id=JKZ8MHbAlEgC&printsec=frontcover has a great bit of information on the physical limitations of making micron sized drops, and a lot on the tricky soft matter aspects of it, including what to do about Newtonian, Shear Thinning, and Shear Thickening fluids, which I found quite interesting. <br />
--[[User:BPappas|BPappas]] 16:35, 14 October 2008 (UTC)<br />
<br />
<br />
== Another Example: Liquid Optics ==<br />
<br />
'''Liquid Lenses'''<br />
<br />
[[Image:Picture_19.png|200px|thumb|left|Electrowetting]]<br />
[[Image:Picture_17.png|200px|thumb|right|Pressure Lens]]<br />
[[Image:Picture_20.png|200px|thumb|right|Droplet under different pressures]]<br />
<br />
In effect, a spherical lens is formed by the meniscus of a liquid. By electrically manipulating the shape of a meniscus it is possible to create an autofocusing lens that can switch from a convex-shaped lens with a tight focus to a concave, divergent lens. The shape-changing process typically requires a few tens of volts and takes just a few milliseconds. The result is a high-quality, compact autofocus lens that can tune its focal length from just a few centimetres to more than one metre.<br />
<br />
By applying an electric field across a hydrophobic coating it is possible to control just how hydrophobic it actually is — an effect known as electrowetting. When sealed in a container, flanked by such a coating, the meniscus or boundary layer between a water-based conducting liquid and an oil-based insulating liquid can be manipulated. With no current the coating remains hydrophobic and the water tries to avoid contact with the edges of the container. This forces the oil to spread itself around the edge to act as a cover. As a result, the water seems to 'bead' within the container and so acts like a concave divergent lens (diagram a - left). When an electric field is then applied the coating loses its hydrophobic properties and the surface tension between the two liquids drops letting the oil relax its state, allowing the water to touch the sides. As a consequence the bulge disappears and the meniscus flattens out to form a slight bulge in the opposite direction — a convex focusing lens (diagram b - left).<br />
<br />
In contrast to the electrowetting approach, a pressure lens can be formed by a single liquid in a channel with two openings that serve as the aperture of the lens. When a piezoelectric pump applies pressure to the liquid, the surface tension of the liquid in the opening can be manipulated. Increase the pressure and the liquid bulges out creating a convex lens. Decrease the pressure and the liquid is sucked back in to form a concave divergent lens. Placing two of these lenses together back-to-back makes it possible to create a zoom lens without having to move any of the lenses.<br />
By controlling the curvature of the meniscus of a liquid droplet it is possible to create a variable focal length lens that mimics the function of the human eye. Here a 2-mm-diameter liquid lens is shown for four different pressures applied by a piezoelectric pump.<br />
FROM: Nature Photonics sample, - pp2 - 4 (2006) [http://www.nature.com/nphoton/journal/vsample/nsample/full/nphoton.2006.2.html]<br />
----<br />
In the October 2008 issue of ''Nature Photonics,'' Carlos Lopez and Amir Hirsa describe a novel application for liquid droplets: as lenses to rapidly focus light. This has been accomplished before using electro-wetting, but these researchers used sound waves to oscillate the shape of the droplet. The water was confined by a millimeter-sized cylinder drilled inside a Teflon plate. The cylinder was overfilled so that a droplet bulged outwards from the opening, but did not spread along the hydrophobic Telfon. Unlike some of the cases considered above, surface tension dominated over gravitational forces, so that the droplets were optically-smooth, spherical segments. By vibrating the Teflon plate, the researchers could cause the bubble to resonate and change its focal plane between 4 and 22 mm away from the Teflon surface.<br />
<br />
Why is this useful? Traditionally, it has been relatively difficult to auto-focus a camera, which leads to a delay before recording an image. However, using a novel algorithm, the researchers are able to find an image that is sharply in focus in less than the time it takes the bubble to make a single oscillation (10 ms) Moreover, by continuously varying the focal plane, it may be possible to enable three-dimensional imaging. <br />
<br />
For a nice summary of the work, see "Liquid optics: Oscillating lenses focus fast" by Claudiu Stan in ''Nature Photonics'' 2, 595 - 596 (2008).<br />
<br />
----<br />
[[Capillarity_and_wetting#Topics | Back to Topics.]]</div>Alexhttp://soft-matter.seas.harvard.edu/index.php?title=Drops,_menisci,_and_lenses&diff=3230Drops, menisci, and lenses2008-12-08T00:32:46Z<p>Alex: /* Another Example: Liquid Optics */</p>
<hr />
<div>[[Capillarity_and_wetting#Topics | Back to Topics.]]<br />
<br />
== Thickness of a large drop ==<br />
Small drops are spherical segments. Large drops are flattened. The relative size of the radius of drop, in the absence of a surface, to the capillary length determines the extent to which the drop spreads across the surface. <br />
For the case of small droplets (r << <math>\kappa</math>), only capillary forces influence the drop. These drops will be spherical in shape and form a contact angle with the surface that depends on the spreading parameter. <br />
Large droplets (r<< <math>\kappa</math>) are much more interesting. At this size, the droplet is large compared to the capillary length and gravity will play an important role. In this case (as seen in the figure below), the drop will form a pancake on the surface. The thickness of this pancake may be calculated by balancing surface forces with hydrostatic pressure. <br />
[[Image: DeGennes_Fig_2-4.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2.4]]<br />
<br />
To “spread” the drop requires an force per unit length:<math>\sigma _{sv}-\left( \sigma _{lv}+\sigma _{sl} \right)</math><br />
<br />
<br />
The hydrostatic pressure integrated over the depth of the drop is a force per unit length pushing to “spread” the drop: <math>\tilde{P}=\int\limits_{0}^{e}{\rho g\left( e-\tilde{z} \right)d\tilde{z}}=\frac{1}{2}\rho ge^{2}</math><br />
<br />
At equilibrium the sum of the two is zero: <math>\sigma _{sv}-\left( \sigma _{lv}+\sigma _{sl} \right)+\frac{1}{2}\rho ge^{2}=0</math><br />
<br />
Substituting the Young-Dupré equation: <math>\sigma _{lv}\left( 1-\cos \theta _{e} \right)=\frac{1}{2}\rho ge^{2}</math><br />
<br />
<br />
Re-arranging gives: <math>\text{ }e=2\kappa ^{-1}\sin \left( \frac{\theta _{e}}{2} \right)</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
<br />
== Profile of a large drop ==<br />
<br />
The general ideas used to calculate the thickness are used again to calculate the profile. With a couple of modifications.<br />
[[Image: DeGennes_Fig_2-4.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2.4]]<br />
<br />
The limits on the integration are changed: <math>\tilde{P}=\int\limits_{0}^{z}{\rho g\left( e-\tilde{z} \right)d\tilde{z}}=\rho g\left( ez-\frac{z^{2}}{2} \right)</math><br />
<br />
The “spreading” force per unit length is now: Where q<math>\theta </math> is the angle marked in the diagram: <math>\sigma _{sv}-\left( \sigma _{lv}\cos \theta +\sigma _{sl} \right)</math><br />
<br />
“It can be shown” from the diagram that: <math>\cos \theta =\sqrt{1+\dot{z}^{2}}</math><br />
<br />
This results in a differential equation for the shape consistent to the algebraic equation for the drop thickness: <math>\sigma _{lv}\left( \sqrt{1+\dot{z}^{2}}-\cos \theta _{e} \right)=\frac{1}{2}\rho g\left( 2ez-z^{2} \right)</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
<br />
== A brief discription of menisci ==<br />
<br />
[[Image:meniscus.png|300px|thumb|right|An example showing the menisci in a capillary tube.]]'''Meniscus''', plural: ''menisci'', from the Greek for "crescent", is a curve in the surface of a liquid and is produced in response to the surface of the container or another object. It can be either concave or convex. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container. This may be seen between mercury and glass in barometers. Conversely, a concave meniscus occurs when the molecules of the liquid attract those of the container. This can be seen between water and glass. Capillary action acts on concave menisci to pull the liquid up, and on convex menisci to pull the liquid down. This phenomenon is important in transpirational pull in plants. Honey, water, milk all have a lower meniscus. When a tube of a narrow bore, often called a capillary tube, is dipped into a liquid and the liquid “wets” the tube (with zero contact angle), the liquid surface inside the tube forms a concave meniscus, which is a virtually spherical surface having the same radius, ''r'', as the inside of the tube. The tube experiences a downward force.<br />
<br />
When reading a scale on the side of a container filled with liquid, the meniscus must be taken into account in order to obtain a precise measurement. Manufacturers take the meniscus into account and calibrate their measurement marks relative to the resulting meniscus. The measurement is taken with the meniscus at eye level to eliminate error, and at the central point of the curve of the meniscus, i.e. the top of the meniscus, in the unusual case of a liquid like mercury, or more usually, the bottom of the meniscus in water and most other liquids.<br />
----<br />
<br />
== Menisci against a wall ==<br />
<br />
The ascending meniscus against a vertical wall is shown below. (de Gennes, 2004, pp. 45f). The Laplace equation, shown on the diagram, is a differential equation that describes the shape of the meniscus. The curvature increases with height.<br />
<br />
[[Image: Ascending_meniscus_1.png |thumb| 800px | left| ]] <math>\frac{1}{R\left( z \right)}=-\frac{{\ddot{z}}}{\left[ 1+\dot{z}^{2} \right]^{3/2}}</math><br />
<br />
Substituting the curvature into the Laplace equation and integrating twice gives: <br />
<math>x-x_{0}=\kappa ^{-1}\cosh ^{-1}\left( \frac{2\kappa ^{-1}}{z} \right)-2\kappa ^{-1}\left( 1-\frac{z^{2}}{4\kappa ^{-2}} \right)^{1/2}</math><br />
<br />
(Where x0 makes z = h at x = 0) A correct, but not illuminating, result.<br />
<br />
<br />
de Gennes provides a more illuminating derivation by considering the equilibrium of forces.<br />
<br />
[[Image: Pressure_in_a_vertical_meniscus.png|thumb| 400px | left| ]] Along the vertical dotted line, the pressure varies as: <math>p\left( z \right)=p_{0}-\rho gz</math><br />
<br />
This produces a total horizontal force on the line: <math>\tilde{p}=\int\limits_{0}^{z}{\rho gzdz}=\frac{1}{2}\rho gz^{2}</math><br />
<br />
The balance is of hydrostatic force, the horizontal component of surface tension, and the surface tension of the liquid surface (z = 0) gives: <math>\frac{1}{2}\rho gz^{2}+\sigma \sin \theta =\sigma </math><br />
<br />
Evalutating at z = h where the angle is the contact angle and re-arranging gives: <math>h=\sqrt{2}\kappa ^{-1}\left( 1-\sin \theta _{E} \right)^{{1}/{2}\;}</math><br />
'''<br />
Meniscus height << capillary rise''' <math>h\left( \theta _{E}=0 \right)=\sqrt{2}\kappa ^{-1}</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
== Meniscus on a fiber ==<br />
[[Image: De_Gennes_Fig_2-14.gif |thumb| 400px | center | de Gennes, 2004, Fig. 2.14]]<br />
As usual, the meniscus obeys: <br />
<math>p_{0}+\sigma \left( \frac{1}{R_{1}}+\frac{1}{R_{2}} \right)=p_{0}-\rho gz</math><br />
<br />
Since the meniscus height is small, the hydrostatic term is small and the film has no curvature! <math>\left( \frac{1}{R_{1}}+\frac{1}{R_{2}} \right)=0</math><br />
<br />
Assuming <math>\theta =0</math> for simplicity, the profile is a catenary curve: <math>r\left( z \right)=b\cosh \left( \frac{z-h}{b} \right)</math><br />
<br />
Dropping the hydrostatic term left this equation with the wrong limit: <math>r\left( 0 \right)=\kappa ^{-1}</math>,<br />
<br />
<br />
Assuming that the meniscus is lost at the capillary length: <math>\kappa ^{-1}=b\cosh \left( \frac{-h}{b} \right)</math><br />
<br />
<br />
Hence: <math>h\approx b\ln \left( \frac{2\kappa ^{-1}}{b} \right)</math><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
----<br />
== Meniscus wetting - AFM tips ==<br />
The end of an atomic force microscope probe has to be of molecular dimensions for best sensitivity:<br />
[[Image: De_Gennes_Fig_2-16.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2-16]]<br />
<br />
They are made by immersion in an etching solution:<br />
[[Image: De_Gennes_Fig_2-15.gif|thumb| 400px | center | de Gennes, 2004, Fig. 2-15]]<br />
<br />
<br />
The mechanism that produces the sharp tip can be explained by the variation in meniscus height as the etched dip becomes smaller and smaller by considering the meniscus height as a function of radius: <math>h\approx b\ln \left( \frac{2\kappa ^{-1}}{b} \right)</math><br />
<br />
Typical capillary lengths are mm’s, so the menisci are also few mm’s.<br />
The meniscus height is a few times the fiber radius or a few 10’s mm.<br />
Therefore the meniscus is much wider than high.<br />
<br />
During the etching of an AFM tip, as the end gets narrower, the meniscus drops, and so on, producing a fine point at the very last.<br />
<br />
<br />
Real-Lab Example:<br />
<br />
I actually did this sort of experiment for a microdrop experiment that I was working on at the University of Illinois, Urbana-Champaign.<br />
<br />
The spirit of the project, done in [http://www.scs.uiuc.edu/mgweb/ Dr. Martin Gruebel's lab], was to find a way to characterize a single protein (a variation on GFP, [http://en.wikipedia.org/wiki/Green_Fluorescent_Protein green-fluorescent protein]) folding and unfolding. One of the interesting parts of this GFP is that the [http://en.wikipedia.org/wiki/Fluorophore fluorophore] remains intact during folding and unfolding, but fluorescence is quenched upon entry of water into the [http://en.wikipedia.org/wiki/Beta_barrel beta barrel] that the fluorophore is residing in. This makes it clear to tell when the protein has unfolded.<br />
<br />
In order to study the folding and unfolding characteristics, Dr. Gruebele and his graduate students designed a cube lens, into which a micron size drop of protein solution would be driven and suspended in a fixed optical trap. This drop would be small enough and the original solution at a low enough concentration that there would statistically be only one GFP present in the trap. The protein would then be excited, and the fluorescence monitored. The cubic lens allows there to be very low loss given the low number of photons coming off of the individual protein. This is a very valuable way of finding and studying the halfway point of the protein in folding kinetics; you can gain a lot from looking at the pH and ionic strength conditions that cause half of the protein solution to be folded and the other half unfolded, dynamically.<br />
<br />
Enter the microdrop generator:<br />
<br />
As always, the goal of a part of my project in the lab was create something cheap, reproducible, and easy to make; the caveat being that it also needed to be able to make drops approximately 10 microns in diameter, which is somewhat unheard of. After a bit of indecision of which way to go, we settled on a modification of the way AFM tips are made and the way inkjet printers work: basically, I tried using HF to etch the capillary tube to a fine point and attaching a peizoelectric driver to force the droplet out of the tube. This driving effect, where the drop is pushed out and then pulled up quickly, would be a really neat force effect to study--ideas on what is acting on the drop throughout? What would change with different fluid properties?<br />
<br />
I really wish that I had seen the de Gennes picture of this before starting my project, as it would had led to a bit more credibility to my theory that the glass really would be etched down to a point if it were just suspended in the acid...<br />
<br />
So: the production. Taking a borosilicate capillary tube, the graduate student that I was working with drew the tube under heat to a very fine point, creating a short tube of about 400 microns in length that narrowed down from about 50 microns to a closed point over the length. I then took this tube and suspended it in an HF solution that was adjusted to give a gradual etch. To make sure that the acid didn't shoot up the fine capillary tube once the micron sized hole opened (which, I assure you, happened to me the first time I did this, and it was quite unpleasant), I applied a very slight opposing pressure using filtered nitrogen; filtered because one of the main frustrations with mircodroplet generation is clogging due to particulate build up in the nozzle. <br />
<br />
Do it work? Sort of, although the evenness that is shown in the de Gennes picture is not exactly what I got under the microscope. I feel like this could be due to a number of things, most likely glass weakening near the pulled tip and micro-cracks from rapid cooling that could have been infiltrated by the HF. The etching was progressing well, though I was quite freaked out by the bone dissolving power of HF, and a little wary of working with it. The graduate student continuing the project was hoping to test out the drop size from the tips created as I was leaving in May this year. <br />
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This book: http://books.google.com/books?id=JKZ8MHbAlEgC&printsec=frontcover has a great bit of information on the physical limitations of making micron sized drops, and a lot on the tricky soft matter aspects of it, including what to do about Newtonian, Shear Thinning, and Shear Thickening fluids, which I found quite interesting. <br />
--[[User:BPappas|BPappas]] 16:35, 14 October 2008 (UTC)<br />
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== Another Example: Liquid Optics ==<br />
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'''Liquid Lenses'''<br />
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[[Image:Picture_19.png|200px|thumb|left|Electrowetting]]<br />
[[Image:Picture_17.png|200px|thumb|right|Pressure Lens]]<br />
[[Image:Picture_20.png|200px|thumb|right|Droplet under different pressures]]<br />
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In effect, a spherical lens is formed by the meniscus of a liquid. By electrically manipulating the shape of a meniscus it is possible to create an autofocusing lens that can switch from a convex-shaped lens with a tight focus to a concave, divergent lens. The shape-changing process typically requires a few tens of volts and takes just a few milliseconds. The result is a high-quality, compact autofocus lens that can tune its focal length from just a few centimetres to more than one metre.<br />
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By applying an electric field across a hydrophobic coating it is possible to control just how hydrophobic it actually is — an effect known as electrowetting. When sealed in a container, flanked by such a coating, the meniscus or boundary layer between a water-based conducting liquid and an oil-based insulating liquid can be manipulated. With no current the coating remains hydrophobic and the water tries to avoid contact with the edges of the container. This forces the oil to spread itself around the edge to act as a cover. As a result, the water seems to 'bead' within the container and so acts like a concave divergent lens (diagram a - left). When an electric field is then applied the coating loses its hydrophobic properties and the surface tension between the two liquids drops letting the oil relax its state, allowing the water to touch the sides. As a consequence the bulge disappears and the meniscus flattens out to form a slight bulge in the opposite direction — a convex focusing lens (diagram b - left).<br />
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In contrast to the electrowetting approach, a pressure lens can be formed by a single liquid in a channel with two openings that serve as the aperture of the lens. When a piezoelectric pump applies pressure to the liquid, the surface tension of the liquid in the opening can be manipulated. Increase the pressure and the liquid bulges out creating a convex lens. Decrease the pressure and the liquid is sucked back in to form a concave divergent lens. Placing two of these lenses together back-to-back makes it possible to create a zoom lens without having to move any of the lenses.<br />
By controlling the curvature of the meniscus of a liquid droplet it is possible to create a variable focal length lens that mimics the function of the human eye. Here a 2-mm-diameter liquid lens is shown for four different pressures applied by a piezoelectric pump.<br />
FROM: Nature Photonics sample, - pp2 - 4 (2006)<br />
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In the October 2008 issue of ''Nature Photonics,'' Carlos Lopez and Amir Hirsa describe a novel application for liquid droplets: as lenses to rapidly focus light. This has been accomplished before using electro-wetting, but these researchers used sound waves to oscillate the shape of the droplet. The water was confined by a millimeter-sized cylinder drilled inside a Teflon plate. The cylinder was overfilled so that a droplet bulged outwards from the opening, but did not spread along the hydrophobic Telfon. Unlike some of the cases considered above, surface tension dominated over gravitational forces, so that the droplets were optically-smooth, spherical segments. By vibrating the Teflon plate, the researchers could cause the bubble to resonate and change its focal plane between 4 and 22 mm away from the Teflon surface.<br />
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Why is this useful? Traditionally, it has been relatively difficult to auto-focus a camera, which leads to a delay before recording an image. However, using a novel algorithm, the researchers are able to find an image that is sharply in focus in less than the time it takes the bubble to make a single oscillation (10 ms) Moreover, by continuously varying the focal plane, it may be possible to enable three-dimensional imaging. <br />
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For a nice summary of the work, see "Liquid optics: Oscillating lenses focus fast" by Claudiu Stan in ''Nature Photonics'' 2, 595 - 596 (2008).<br />
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[[Capillarity_and_wetting#Topics | Back to Topics.]]</div>Alex