# User:Alex

Alex Nemiroski

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 to gain new perspective on physics and also get back into the habit of thinking about new concepts on a weekly basis.

Final Project: Digital Microfluidics with Electrowetting

## Introduction and Motivation

Over the past decade there has been a large amount of attention given to developing miniaturized systems capable of doing biochemical analysis primarily 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 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 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.

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 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 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 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 source, which requires in many cases an unmanageably large volume of tubes to interface with the chip.

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 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 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.

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.

## Electrokinetic Actuation

Each body can be characterized by electrical presence/response to applied electric fields. The interaction of the body can be reduced to two phenomena, 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.

### Dielectrophoresis

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.

### Electrowetting

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 liquid lenses

In contrast with dielectrophoresis, low frequencies must be used such that the free charges can respond in time to the change in field polarity.

#### Electrowetting Basics

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.

The electrostatic energy stored between the droplet and bottom electrode is capacitive in nature and acts to reduce the surface energy density $\gamma_{sl}^0$ of the solid/liquid interface.

$\gamma_{sl} = \gamma_{sl}^0 - \frac{1}{2}cV^2$

The capacitance $C$ of a system of this geometry is described by the the dielectric constant of the insulating layer $/epsilon$, the height of this layer $d$, and the area $A$ of contact through $C=\frac{\epsilon A}{d}$

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

$\gamma_{sl} = \gamma_{sl}^0 - \frac{\epsilon V^2}{2 d}$
.

The Young equation for the contact angle of a liquid is where (s = solid, m = medium, l = liquid [drop])

$cos(\theta) = \frac{\gamma_{sm}-\gamma{sl}}{\gamma_{ml}}$

Thus the contact angle of the liquid depends on the applied voltage as

$cos(\theta) = \frac{\gamma_{sm}-\gamma_{sl}^0 + \frac{\epsilon V^2}{2 d}}{\gamma_{ml}}=cos(\theta_0)+\frac{\epsilon V^2}{2 d \gamma_{ml}}$

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.

#### Electrowetting Actuation

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.

The net force per unit length is thus

$f = \gamma_{sl}^0 - \gamma_{sl}(V) = \frac{\epsilon V^2}{2 d \gamma_{ml}}$

Note that this assumes negligible contact angle hysteresis, which as long as confined to only a few degrees is still accurate.

Given an angle of advancement $\phi$, the total force on the droplet due to electrowetting is

$F=2\int_0^{\phi} f cos(\theta)d\theta=2 f sin(\phi) = \frac{\epsilon V^2}{d \gamma_{ml}} sin(\phi)$