http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Borkin&feedformat=atomSoft-Matter - User contributions [en]2021-04-23T14:54:04ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Undulatory_locomotion&diff=13576Undulatory locomotion2009-12-02T18:28:51Z<p>Borkin: </p>
<hr />
<div>== Definition ==<br />
[[Image:snake_motion.jpg|500px|right|thumb|alt=Snake motion.|Schematic of lateral undulation locomotion for a snake (the black dots indicate the location of inflection points and the thick line illustrate the pattern and amplitude of muscle activity. (From "[[Limbless undulatory propulsion on land]]" (Guo & Mahadevan 2008).)]]<br />
<br />
Undulatory locomotion is movement via propagating waves with the most tangible example being that of limbless creatures (e.g. snakes) on land or water. The lateral (side-ways) forces brace the animal's body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward. Viscoelasticity plays an important role both in the mechanics of the muscular tissue and how the animal's body responds to its environment.<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Undulatory_locomotion<br />
* [[Limbless undulatory propulsion on land]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=File:Snake_motion.jpg&diff=13575File:Snake motion.jpg2009-12-02T18:27:36Z<p>Borkin: </p>
<hr />
<div></div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Undulatory_locomotion&diff=13574Undulatory locomotion2009-12-02T18:27:27Z<p>Borkin: </p>
<hr />
<div>== Definition ==<br />
[[Image:snake_motion.jpg|700px|right|thumb|alt=Snake motion.|Schematic of lateral undulation locomotion for a snake (the black dots indicate the location of inflection points and the thick line illustrate the pattern and amplitude of muscle activity. ([[Limbless undulatory propulsion on land]] (Guo & Mahadevan 2008).]]<br />
<br />
Undulatory locomotion is movement via propagating waves with the most tangible example being that of limbless creatures (e.g. snakes) on land or water. The lateral (side-ways) forces brace the animal's body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward. Viscoelasticity plays an important role both in the mechanics of the muscular tissue and how the animal's body responds to its environment.<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Undulatory_locomotion<br />
* [[Limbless undulatory propulsion on land]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Undulatory_locomotion&diff=13573Undulatory locomotion2009-12-02T17:38:21Z<p>Borkin: New page: == Definition == Currently writing... == References == * http://en.wikipedia.org/wiki/Undulatory_locomotion * Limbless undulatory propulsion on land</p>
<hr />
<div>== Definition ==<br />
<br />
Currently writing...<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Undulatory_locomotion<br />
* [[Limbless undulatory propulsion on land]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13572Limbless undulatory propulsion on land2009-12-02T17:36:44Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
[[Undulatory locomotion]], [[Viscoelastic]], Voigt model<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.<br />
<br />
The key to understanding this movement is in the tissue's response and resistance to deformation. They model this by the linear [http://en.wikipedia.org/wiki/Kelvin%E2%80%93Voigt_material Voigt model] for viscoelasticity:<br />
<br />
<math>\sigma = E \epsilon + \eta \dot{\epsilon}</math><br />
<br />
where <math>\sigma</math> is the uniaxial stress in the bulk tissue, <math>E</math> is Young's modulus, <math>\eta</math> is viscosity of the tissue, <math>\epsilon</math> is the strain and <math>\dot{\epsilon}</math> dot is the strain rate. (This is schematically drawn in part '''(c)''' of the figure.) Thus the passive moment of the tissue is the sum of the elastic and viscous moments of the tissue (<math>M_{p} = M_{e} + M_{\nu}</math>). (This is reflected in the alternating muscle contractions shown in part '''(a)'''.) Finally, the force per unit length <math>p</math> can be described by the situation where the snake is pushing against an array of pegs (see schematic), is proportional to the active moment, or determined by the local shape of the snake.<br />
<br />
Based on the above discussion, the non-dimensionalized set of equations describing the system are:<br />
<br />
[[Image:Guo-Maha_equations.jpg|400px|center|alt=Equations.|]]<br />
<br />
where <math>T</math> is the tension, <math>N</math> is the transverse shear force, <math>s</math> is the coordinate in the traveling wave frame, <math>\kappa</math> is the curvature of the centerline, <math>\nu_{w}</math> and <math>\nu_{p}</math> are the longitudinal and lateral coefficients of friction, Mo is the dimensionless amplitude of active moment, Pr is the dimensionless lateral resistive force, Be is the dimensionless passive elastic bending stiffness of the organism, and Vi is the dimensionless passive viscous bending stiffness of the organism. These factors characterize the exogenous (<math>\nu_{w}</math>, <math>\nu_{p}</math>, Pr) and the endogenous (Mo, Be, Vi) dynamics in the system. Based on further mathematical analysis of these equations, they find that: the normalized shape for steady motion depends only on exogenous factors (frictional and resistive forces from substrate) and the wave amplitude is small for non-deformable surface and large for deformable surfaces, increasing the viscous bending stiffness of the animal reduces the mechanical efficiency, and that there is an optimal substrate to achieve maximal velocities using this lateral undulatory motion.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=13571Michelle A Borkin2009-12-02T17:36:32Z<p>Borkin: </p>
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[[Limbless undulatory propulsion on land]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Vocabulary&diff=13570Vocabulary2009-12-02T17:36:04Z<p>Borkin: </p>
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<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]], Voigt model<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.<br />
<br />
The key to understanding this movement is in the tissue's response and resistance to deformation. They model this by the linear [http://en.wikipedia.org/wiki/Kelvin%E2%80%93Voigt_material Voigt model] for viscoelasticity:<br />
<br />
<math>\sigma = E \epsilon + \eta \dot{\epsilon}</math><br />
<br />
where <math>\sigma</math> is the uniaxial stress in the bulk tissue, <math>E</math> is Young's modulus, <math>\eta</math> is viscosity of the tissue, <math>\epsilon</math> is the strain and <math>\dot{\epsilon}</math> dot is the strain rate. (This is schematically drawn in part '''(c)''' of the figure.) Thus the passive moment of the tissue is the sum of the elastic and viscous moments of the tissue (<math>M_{p} = M_{e} + M_{\nu}</math>). (This is reflected in the alternating muscle contractions shown in part '''(a)'''.) Finally, the force per unit length <math>p</math> can be described by the situation where the snake is pushing against an array of pegs (see schematic), is proportional to the active moment, or determined by the local shape of the snake.<br />
<br />
Based on the above discussion, the non-dimensionalized set of equations describing the system are:<br />
<br />
[[Image:Guo-Maha_equations.jpg|400px|center|alt=Equations.|]]<br />
<br />
where <math>T</math> is the tension, <math>N</math> is the transverse shear force, <math>s</math> is the coordinate in the traveling wave frame, <math>\kappa</math> is the curvature of the centerline, <math>\nu_{w}</math> and <math>\nu_{p}</math> are the longitudinal and lateral coefficients of friction, Mo is the dimensionless amplitude of active moment, Pr is the dimensionless lateral resistive force, Be is the dimensionless passive elastic bending stiffness of the organism, and Vi is the dimensionless passive viscous bending stiffness of the organism. These factors characterize the exogenous (<math>\nu_{w}</math>, <math>\nu_{p}</math>, Pr) and the endogenous (Mo, Be, Vi) dynamics in the system. Based on further mathematical analysis of these equations, they find that: the normalized shape for steady motion depends only on exogenous factors (frictional and resistive forces from substrate) and the wave amplitude is small for non-deformable surface and large for deformable surfaces, increasing the viscous bending stiffness of the animal reduces the mechanical efficiency, and that there is an optimal substrate to achieve maximal velocities using this lateral undulatory motion.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13568Limbless undulatory propulsion on land2009-12-02T17:30:27Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]], Voigt model<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.<br />
<br />
The key to understanding this movement is in the tissue's response and resistance to deformation. They model this by the linear [http://en.wikipedia.org/wiki/Kelvin%E2%80%93Voigt_material Voigt model] for viscoelasticity:<br />
<br />
<math>\sigma = E \epsilon + \eta \dot{\epsilon}</math><br />
<br />
where <math>\sigma</math> is the uniaxial stress in the bulk tissue, <math>E</math> is Young's modulus, <math>\eta</math> is viscosity of the tissue, <math>\epsilon</math> is the strain and <math>\dot{\epsilon}</math> dot is the strain rate. (This is schematically drawn in part '''(c)''' of the figure.) Thus the passive moment of the tissue is the sum of the elastic and viscous moments of the tissue (<math>M_{p} = M_{e} + M_{\nu}</math>). (This is reflected in the alternating muscle contractions shown in part '''(a)'''.) Finally, the force per unit length <math>p</math> can be described by the situation where the snake is pushing against an array of pegs (see schematic), is proportional to the active moment, or determined by the local shape of the snake.<br />
<br />
Based on the above discussion, the non-dimensionalized set of equations describing the system are:<br />
<br />
[[Image:Guo-Maha_equations.jpg|400px|center|alt=Equations.|]]<br />
<br />
where <math>\nu_{w}</math> and <math>\nu_{p}</math> are the longitudinal and lateral coefficients of friction, Mo is the dimensionless amplitude of active moment, Pr is the dimensionless lateral resistive force, Be is the dimensionless passive elastic bending stiffness of the organism, and Vi is the dimensionless passive viscous bending stiffness of the organism. These factors characterize the exogenous (<math>\nu_{w}</math>, <math>\nu_{p}</math>, Pr) and the endogenous (Mo, Be, Vi) dynamics in the system. Based on further mathematical analysis of these equations, they find that: the normalized shape for steady motion depends only on exogenous factors (frictional and resistive forces from substrate) and the wave amplitude is small for non-deformable surface and large for deformable surfaces, increasing the viscous bending stiffness of the animal reduces the mechanical efficiency, and that there is an optimal substrate to achieve maximal velocities using this lateral undulatory motion.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=File:Guo-Maha_equations.jpg&diff=13567File:Guo-Maha equations.jpg2009-12-02T17:28:06Z<p>Borkin: </p>
<hr />
<div></div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13566Limbless undulatory propulsion on land2009-12-02T17:26:05Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]], Voigt model<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.<br />
<br />
The key to understanding this movement is in the tissue's response and resistance to deformation. They model this by the linear [http://en.wikipedia.org/wiki/Kelvin%E2%80%93Voigt_material Voigt model] for viscoelasticity:<br />
<br />
<math>\sigma = E \epsilon + \eta \dot{\epsilon}</math><br />
<br />
where <math>\sigma</math> is the uniaxial stress in the bulk tissue, <math>E</math> is Young's modulus, <math>\eta</math> is viscosity of the tissue, <math>\epsilon</math> is the strain and <math>\dot{\epsilon}</math> dot is the strain rate. (This is schematically drawn in part '''(c)''' of the figure.) Thus the passive moment of the tissue is the sum of the elastic and viscous moments of the tissue (<math>M_{p} = M_{e} + M_{\nu}</math>). (This is reflected in the alternating muscle contractions shown in part '''(a)'''.) Finally, the force per unit length <math>p</math> can be described by the situation where the snake is pushing against an array of pegs (see schematic), is proportional to the active moment, or determined by the local shape of the snake.<br />
<br />
Based on the above discussion, the non-dimensionalized set of equations describing the system are:<br />
<br />
[[Image:Guo-Maha_equations.jpg|400px|center|alt=Equations.|]]<br />
<br />
where <math>\nu_{w}</math> and <math>\nu_{p}</math> are the longitudinal and lateral coefficients of friction, Mo is the dimensionless amplitude of active moment, Pr is the dimensionless lateral resistive force, Be is the dimensionless passive elastic bending stiffness of the organism, and Vi is the dimensionless passive viscous bending stiffness of the organism. These factors characterize the exogenous (<math>\nu_{w}</math>, <math>\nu_{p}</math>, Pr) and the endogenous (Mo, Be, Vi) dynamics in the system. Based on further mathematical analysis of these equations, they find that: the normalized shape for steady motion depends only on exogenous factors (frictional and resistive forces from substrate) and the wave amplitude is small for non-deformable surface and large for deformable surfaces, increasing the viscous bending stiffness of the animal reduces the mechanical efficiency, and that there is an optimal substrate to achieve maximal velocities using this lateral undulatory motion.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13565Limbless undulatory propulsion on land2009-12-02T17:18:57Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]]<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.<br />
<br />
The key to understanding this movement is in the tissue's response and resistance to deformation. They model this by the linear Voigt model for viscoelasticity:<br />
<br />
<math>\sigma = E \epsilon + \eta \dot{\epsilon}</math><br />
<br />
where <math>\sigma</math> is the uniaxial stress in the bulk tissue, <math>E</math> is Young's modulus, <math>\eta</math> is viscosity of the tissue, <math>\epsilon</math> is the strain and <math>\dot{\epsilon}</math> dot is the strain rate. (This is schematically drawn in part '''(c)''' of the figure.) Thus the passive moment of the tissue is the sum of the elastic and viscous moments of the tissue (<math>M_{p} = M_{e} + M_{\nu}</math>). (This is reflected in the alternating muscle contractions shown in part '''(a)'''.) Finally, the force per unit length <math>p</math> can be described by the situation where the snake is pushing against an array of pegs (see schematic), is proportional to the active moment, or determined by the local shape of the snake.<br />
<br />
Based on the above discussion, the non-dimensionalized set of equations describing the system are:<br />
<br />
....<br />
<br />
where .... Based on further mathematical analysis of these equations, they find that: the normalized shape for steady motion depends only on exogenous factors (frictional and resistive forces from substrate) and the wave amplitude is small for non-deformable surface and large for deformable surfaces, increasing the viscous bending stiffness of the animal reduces the mechanical efficiency, and that there is an optimal substrate to achieve maximal velocities using this lateral undulatory motion.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13564Limbless undulatory propulsion on land2009-12-02T17:07:10Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]]<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.<br />
<br />
The key to understanding this movement is in the tissue's response and resistance to deformation. They model this by the linear Voigt model for viscoelasticity:<br />
<br />
<math></math><br />
<br />
where sigma is the uniaxial stress in the bulk tissue, E is Young's modulus, eta is viscosity of the tissue, epsilon is the strain and epsilon dot is the strain rate. (This is schematically drawn in part '''(c)''' of the figure.) Thus the passive moment of the tissue is the sum of the elastic and viscous moments of the tissue (math). (This is reflected in the alternating muscle contractions shown in part '''(a)'''.) Finally, the force per unit length <math>p</math> can be described as the situation where the snake is pushing against an array of pegs (see schematic), is proportional to the active moment, or determined by the local shape of the snake.<br />
<br />
Based on the above discussion, the non-dimensionalized set of equations describing the system are:<br />
<br />
....<br />
<br />
where .... Based on further mathematical analysis of these equations, they find that: the normalized shape for steady motion depends only on exogenous factors (frictional and resistive forces from substrate) and the wave amplitude is small for non-deformable surface and large for deformable surfaces, increasing the viscous bending stiffness of the animal reduces the mechanical efficiency, and that there is an optimal substrate to achieve maximal velocities using this lateral undulatory motion.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13563Limbless undulatory propulsion on land2009-12-02T16:50:44Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]]<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
<br />
The lateral undulatory motion works by propagating a wave down the creature's body. As show in '''Figure 1''', the lateral (side-ways) forces brace the body (the motion in each lateral direction cancels itself out) against the substrate thus allowing the in-plane forces to propel it in a forward (or backward) direction. In part '''(a)''', the thickness of the black line illustrates the muscle contractions and black dots the points of inflection. This paper approximates this kind of movement on a solid substrate and takes into account frictional forces.</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13562Limbless undulatory propulsion on land2009-12-02T16:36:34Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]]<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes or worms to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
[[Image:Guo-Maha_figure1.jpg|700px|right|thumb|alt=Motion schematic.|]]<br />
<br />
currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=File:Guo-Maha_figure1.jpg&diff=13561File:Guo-Maha figure1.jpg2009-12-02T16:34:04Z<p>Borkin: </p>
<hr />
<div></div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13560Limbless undulatory propulsion on land2009-12-02T16:33:49Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]]<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes or worms to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
<br />
currently writing...<br />
<br />
[[Image:Guo-Maha_figure1.jpg|500px|thumb|right|alt=Motion schematic.|]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13559Limbless undulatory propulsion on land2009-12-02T16:24:04Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, [[Viscoelastic]]<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes or worms to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
<br />
currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13558Limbless undulatory propulsion on land2009-12-02T16:23:23Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, viscoelasticity<br />
<br />
== Summary ==<br />
<br />
This paper presents analytical and numerical models of lateral undulatory motion commonly employed by limbless creatures such as snakes or worms to "swim" on land. The critter propagates undulatory waves along its body via muscle contractions. To model this system and determine the important factors effecting this motion, a mathematical model is presented: a nonlinear boundary value problem which takes into account the viscous and elastic features in the muscle tissue and the frictional forces exerted by the environment. In summary, they find that the normalized shape of the animal is determined by its interaction with its environment, and the speed at which it moves is determined by the muscle contraction generated wave's frequency and amplitude. In addition to be of interest to biologists, this active area of research is of key interest to robotics where designing robots to deal with extreme terrains is important. (Dealing with movement across sand or other fluid-like surfaces is important for things ranging from terrestrial robots on beaches or desserts to robots on Mars.)<br />
<br />
== Soft Matter ==<br />
<br />
currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=13165Michelle A Borkin2009-11-28T01:47:42Z<p>Borkin: </p>
<hr />
<div>Definitions:<br />
<br />
[[Soft Machines]]<br />
<br />
[[Meniscus]]<br />
<br />
[[Hydrodynamics]]<br />
<br />
[[Depletion interactions]]<br />
<br />
[[Self-assembled monolayers]]<br />
<br />
[[Thin film]]<br />
<br />
[[Electrohydrodynamics]]<br />
<br />
[[Debye Length]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Statistical dynamics of flowing red blood cells by morphological image processing]]<br />
<br />
[[Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range]]<br />
<br />
[[Hydrodynamical models for the chaotic dripping faucet]]<br />
<br />
[[Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity]]<br />
<br />
[[Crystallization in Patterns: A Bio-Inspired Approach]]<br />
<br />
[[Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition.]]<br />
<br />
[[Electrohydrodynamic size stratification and flow separation of giant vesicles]]<br />
<br />
[[Charge Stabilization in Nonpolar Solvents]]<br />
<br />
[[Limbless undulatory propulsion on land]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13164Limbless undulatory propulsion on land2009-11-28T01:46:46Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
undulatory locomotion, viscoelasticity<br />
<br />
== Summary ==<br />
<br />
currently writing...<br />
<br />
== Soft Matter ==<br />
<br />
currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Limbless_undulatory_propulsion_on_land&diff=13163Limbless undulatory propulsion on land2009-11-28T01:45:45Z<p>Borkin: New page: Original Entry by Michelle Borkin, AP225 Fall 2009 == Overview == [http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.] Z. Guo and L. Mahad...</p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.seas.harvard.edu/softmat/downloads/2008-05.pdf Limbless undulatory propulsion on land.]<br />
<br />
Z. Guo and L. Mahadevan, Proceedings of the National Academy of Sciences (USA), 105, 3179, 2008. <br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
currently writing...<br />
<br />
== Soft Matter ==<br />
<br />
currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=13133Michelle A Borkin2009-11-27T22:47:57Z<p>Borkin: </p>
<hr />
<div>Definitions:<br />
<br />
[[Soft Machines]]<br />
<br />
[[Meniscus]]<br />
<br />
[[Hydrodynamics]]<br />
<br />
[[Depletion interactions]]<br />
<br />
[[Self-assembled monolayers]]<br />
<br />
[[Thin film]]<br />
<br />
[[Electrohydrodynamics]]<br />
<br />
[[Debye Length]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Statistical dynamics of flowing red blood cells by morphological image processing]]<br />
<br />
[[Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range]]<br />
<br />
[[Hydrodynamical models for the chaotic dripping faucet]]<br />
<br />
[[Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity]]<br />
<br />
[[Crystallization in Patterns: A Bio-Inspired Approach]]<br />
<br />
[[Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition.]]<br />
<br />
[[Electrohydrodynamic size stratification and flow separation of giant vesicles]]<br />
<br />
[[Charge Stabilization in Nonpolar Solvents]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Debye_Length&diff=13132Debye Length2009-11-27T22:47:09Z<p>Borkin: </p>
<hr />
<div>== Definition ==<br />
<br />
The Debye length (<math>\kappa ^{-1}</math>), or Debye screening length, is the length scale over which charge carriers screen-out electric fields. One version of this equation when describing this length in a colloidal dispersion (or electrolyte solution) is:<br />
<br />
<math> \kappa^{-1} = \sqrt{\frac{\varepsilon_0 \varepsilon_r k T}{2 N_A e^2 I}}</math><br />
<br />
where ''I'' is the ionic strength of the electrolyte, ε<sub>0</sub> is the permittivity of free space, ε<sub>r</sub> is the dielectric constant, ''k'' is the Boltzmann constant, ''T'' is the absolute temperature in kelvins, ''N<sub>A</sub>'' is Avogadro's number, and ''e'' is the elementary charge.<br />
<br />
For more information on Peter Debye's original acoustic experiments, go to [http://soft-matter.seas.harvard.edu/index.php/Electokinetics#Electroacoutic_measurements Electokinetics: Electroacoutic measurements].<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Debye_length#Debye_length_in_an_electrolyte<br />
* R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Debye_Length&diff=13130Debye Length2009-11-27T22:39:38Z<p>Borkin: </p>
<hr />
<div>== Definition ==<br />
<br />
The Debye length (<math>\kappa ^{-1}</math>), or Debye screening length, is the length scale over which charge carriers screen-out electric fields. One version of this equation when describing this length in a colloidal dispersion (or electrolyte solution) is:<br />
<br />
<math> \kappa^{-1} = \sqrt{\frac{\varepsilon_0 \varepsilon_r k T}{2 N_A e^2 I}}</math><br />
<br />
where ''I'' is the ionic strength of the electrolyte, ε<sub>0</sub> is the permittivity of free space, ε<sub>r</sub> is the dielectric constant, ''k'' is the Boltzmann constant, ''T'' is the absolute temperature in kelvins, ''N<sub>A</sub>'' is Avogadro's number, and ''e'' is the elementary charge.<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Debye_length#Debye_length_in_an_electrolyte<br />
* R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Debye_Length&diff=13129Debye Length2009-11-27T22:34:16Z<p>Borkin: New page: == Definition == The Debye length (<math>\kappa^{-1}</math>, or Debye screening length, is the length scale over which charge carriers screen-out electric fields. == References == * htt...</p>
<hr />
<div>== Definition ==<br />
<br />
The Debye length (<math>\kappa^{-1}</math>, or Debye screening length, is the length scale over which charge carriers screen-out electric fields.<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Debye_length#Debye_length_in_an_electrolyte<br />
* R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Vocabulary&diff=13128Vocabulary2009-11-27T22:31:37Z<p>Borkin: </p>
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<br />
[[Vesicle]]<br />
<br />
[[Viscoelastic]]<br />
<br />
[[Weber number]]<br />
<br />
[[Young's modulus]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13124Charge Stabilization in Nonpolar Solvents2009-11-27T22:18:55Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles effect charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before ''(a)'' and after ''(b)'' adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
They observe a strong dependence on AOT concentration in controlling the interactions, specifically by controlling the range of interaction among the particles. As shown in '''Figure 2 (b)''', is "soft" and long ranged - the interparticle repulsion is greater than the thermal energy for 5x the particle radius and the interactions become "stiffer" and short ranged as the micelle concentration is increased. However, the surface potential barley changes with micelle concentration. Other striking observations include that the measured zeta potential is comporable to those measured in water with highly charged particles (the Debye screening lengths are also much larger than those measured in such a solution).<br />
<br />
Finally, to further investigate screening lengths the ionic strength of conductivity was measured. The measured conductivity (''<math>\sigma</math>'') as a function of AOT concentration is shown in '''Figure 3 (a)'''. The conductivity values span more than two orders of magnitude and the fraction of ionized micelles is independent of concentration. The derived inverse screening lengths are also plotted in '''Figure 3 (b)'''. Also, instead of following a standard charge exchange description as found in weak electrolytes, a neutral micelle reversibly exchanges charge through collision <math>A + A \rightleftharpoons A^{+} + A^{-}</math> leading to an ionization fraction independent of concentration (schematic in '''Figure 3''').<br />
<br />
[[Image:Hsu-etal-figure3.jpg|500px|thumb|right|alt=Conductivity and screen lengths.|'''Figure 3:''' ''(a)'' Conductivity (<math>\sigma</math>) of solution without particles. Symbols represent measurements. The schematic inset shows the two-body process that creates charge in the system. ''(b)'' Inverse screen lengths versus AOT concentration showing how the reverse micelle concentration strongly effects the screening length.]]<br />
[[Image:Hsu-etal-figure2.jpg|500px|thumb|center|alt=Interaction potentials.|'''Figure 2:''' ''(a)'' Measured pair potentials (''u(r)/kT'') versus varying cell thicknesses (''h'') with screen Coulomb potentials fitted (see inset table for parameters). This shows how interparticle potentials strongly depend on the cell thickness. ''(b)'' Interaction potentials at different AOT concentrations (squares, circles, diamonds, and triangles represent 3.1, 13, 50, and 200mM of AOT). Screen Coulomb potentials are fitted with parameters inset. This graph shows how the reverse micelle concentration controls the range of interaction.]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13123Charge Stabilization in Nonpolar Solvents2009-11-27T22:13:21Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles effect charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before ''(a)'' and after ''(b)'' adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
They observe a strong dependence on AOT concentration in controlling the interactions, specifically by controlling the range of interaction among the particles. As shown in '''Figure 2 (b)''', is "soft" and long ranged - the interparticle repulsion is greater than the thermal energy for 5x the particle radius and the interactions become "stiffer" and short ranged as the micelle concentration is increased. However, the surface potential barley changes with micelle concentration. Other striking observations include that the measured zeta potential is comporable to those measured in water with highly charged particles (the Debye screening lengths are also much larger than those measured in such a solution).<br />
<br />
Finally, to further investigate screening lengths the ionic strength of conductivity was measured. The measured conductivity (''<math>\sigma</math>'') as a function of AOT concentration is shown in '''Figure 3 (a)'''. The conductivity values span more than two orders of magnitude and the fraction of ionized micelles is independent of concentration. The derived inverse screening lengths are also plotted in '''Figure 3 (b)'''. Also, instead of following a standard charge exchange description as found in weak electrolytes, a neutral micelle reversibly exchanges charge through collision <math>A + A \rightleftharpoons A^{+} + A^{-}</math> leading to an ionization fraction independent of concentration (schematic in '''Figure 3''').<br />
<br />
[[Image:Hsu-etal-figure3.jpg|500px|thumb|right|alt=Conductivity and screen lengths.|'''Figure 3:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
[[Image:Hsu-etal-figure2.jpg|500px|thumb|center|alt=Interaction potentials.|'''Figure 2:''' ''(a)'' Measured pair potentials (''u(r)/kT'') versus varying cell thicknesses (''h'') with screen Coulomb potentials fitted (see inset table for parameters). This shows how interparticle potentials strongly depend on the cell thickness. ''(b)'' Interaction potentials at different AOT concentrations (squares, circles, diamonds, and triangles represent 3.1, 13, 50, and 200mM of AOT). Screen Coulomb potentials are fitted with parameters inset.]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=File:Hsu-etal-figure3.jpg&diff=13122File:Hsu-etal-figure3.jpg2009-11-27T22:04:10Z<p>Borkin: </p>
<hr />
<div></div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=File:Hsu-etal-figure2.jpg&diff=13121File:Hsu-etal-figure2.jpg2009-11-27T22:03:29Z<p>Borkin: </p>
<hr />
<div></div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13120Charge Stabilization in Nonpolar Solvents2009-11-27T21:59:27Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles effect charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
[[Image:Hsu-etal-figure2.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
[[Image:Hsu-etal-figure3.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
They observe a strong dependence on AOT concentration in controlling the interactions, specifically by controlling the range of interaction among the particles. As shown in '''Figure 2 (b)''', is "soft" and long ranged - the interparticle repulsion is greater than the thermal energy for 5x the particle radius and the interactions become "stiffer" and short ranged as the micelle concentration is increased. However, the surface potential barley changes with micelle concentration. Other striking observations include that the measured zeta potential is comporable to those measured in water with highly charged particles (the Debye screening lengths are also much larger than those measured in such a solution).<br />
<br />
Finally, to further investigate screening lengths the ionic strength of conductivity was measured. The measured conductivity (''<math>\sigma</math>'') as a function of AOT concentration is shown in '''Figure 3 (a)'''. The conductivity values span more than two orders of magnitude and the fraction of ionized micelles is independent of concentration. The derived inverse screening lengths are also plotted in '''Figure 3 (b)'''. Also, instead of following a standard charge exchange description as found in weak electrolytes, a neutral micelle reversibly exchanges charge through collision <math>A + A \rightleftharpoons A^{+} + A^{-}</math> leading to an ionization fraction independent of concentration (schematic in '''Figure 3''').</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13119Charge Stabilization in Nonpolar Solvents2009-11-27T21:48:09Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles effect charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
[[Image:Hsu-etal-figure2.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
[[Image:Hsu-etal-figure3.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
They observe a strong dependence on AOT concentration in controlling the interactions, specifically by controlling the range of interaction among the particles. As shown in '''Figure 2 (b)''', is "soft" and long ranged - the interparticle repulsion is greater than the thermal energy for 5x the particle radius and the interactions become "stiffer" and short ranged as the micelle concentration is increased. However, the surface potential barley changes with micelle concentration. Other striking observations include that the measured zeta potential is comporable to those measured in water with highly charged particles (the Debye screening lengths are also much larger than those measured in such a solution).<br />
<br />
Finally, to further investigate screening lengths the ionic strength of conductivity was measured.<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13118Charge Stabilization in Nonpolar Solvents2009-11-27T20:49:05Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles effect charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
Currently writing...<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Charge stabilization.|'''Figure 1:''' Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13117Charge Stabilization in Nonpolar Solvents2009-11-27T20:45:50Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles control charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
Currently writing...<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Charge stabilization.|Charge stabilization of a nonpolar suspension before (a) and after (b) adding reverse micelles (AOT solution above cmc). The field of view is 135 x 108 <math>\mu m ^2</math>.]]<br />
<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=File:Hsu-etal-figure1.jpg&diff=13116File:Hsu-etal-figure1.jpg2009-11-27T20:42:55Z<p>Borkin: </p>
<hr />
<div></div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13115Charge Stabilization in Nonpolar Solvents2009-11-27T20:40:20Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles control charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
Currently writing...<br />
<br />
== Soft Matter ==<br />
[[Image:Hsu-etal-figure1.jpg|500px|thumb|right|alt=Schematic of the experiment.|]]<br />
For the experiments, the reverse micelles were created using aerosol-OT (AOT) which forms nanometer sized reversed micelles (contains ~30 surfactant molecules) above its 1mM in dodecane critical micelle concentration (cmc). The colloid particles in the system are PMMA particles with PHSA grafted to their surface for steric stabilization (radius = 780 nm). The solution is contained in cells between glass plates thus the model and results presented are based on 2D descriptions and analysis. As shown in '''Figure 1''', when AOT (i.e. the reverse micelles) is added to the solution '''(b)''' the colloidal particles evenly disperse due to the electrostatic forces.<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13114Charge Stabilization in Nonpolar Solvents2009-11-27T20:28:48Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on nanometer sized reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain how the micelles control charge. As opposed to simple salt ions, these large reverse micelles have low ionization energies and charge surfaces by stabilizing counterions. They find very strong surface potentials (2.0-4.4 ''kT'') and Debye screening lengths (0.2-1.4 <math>\mu m</math>) that strongly depend on the concentration of reverse micelles in the system.<br />
<br />
Currently writing...<br />
<br />
== Soft Matter ==<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=13113Charge Stabilization in Nonpolar Solvents2009-11-27T20:21:49Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005).<br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, Reverse [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
This paper investigates the use of surfactants to control charges is nonpolar solvents (<math>\epsilon \approx 2</math> versus for an aqueous solution <math>\epsilon \approx 80</math>) where the electrostatic charge barrier is much greater than ''kT''. Understanding nonpolar solvents and colloid interactions are important for industrial and commercial applications such as [http://en.wikipedia.org/wiki/Electronic_paper#Electrophoretic electrophoretic ink] or the stabilization of soot particles in oil. Surfactants play the key role in creating in such solutions the charge-stabilizing aggregates. The research presented in this paper focuses on reverse micelles in nonpolar solvents and investigates the electrokinetics and thermodynamic properties to explain on the micelles control charge.<br />
<br />
<br />
Currently writing...<br />
<br />
== Soft Matter ==<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=12614Michelle A Borkin2009-11-16T23:30:59Z<p>Borkin: </p>
<hr />
<div>Definitions:<br />
<br />
[[Soft Machines]]<br />
<br />
[[Meniscus]]<br />
<br />
[[Hydrodynamics]]<br />
<br />
[[Depletion interactions]]<br />
<br />
[[Self-assembled monolayers]]<br />
<br />
[[Thin film]]<br />
<br />
[[Electrohydrodynamics]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Statistical dynamics of flowing red blood cells by morphological image processing]]<br />
<br />
[[Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range]]<br />
<br />
[[Hydrodynamical models for the chaotic dripping faucet]]<br />
<br />
[[Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity]]<br />
<br />
[[Crystallization in Patterns: A Bio-Inspired Approach]]<br />
<br />
[[Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition.]]<br />
<br />
[[Electrohydrodynamic size stratification and flow separation of giant vesicles]]<br />
<br />
[[Charge Stabilization in Nonpolar Solvents]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=12613Michelle A Borkin2009-11-16T23:30:48Z<p>Borkin: </p>
<hr />
<div>Definitions:<br />
<br />
[[Soft Machines]]<br />
<br />
[[Meniscus]]<br />
<br />
[[Hydrodynamics]]<br />
<br />
[[Depletion interactions]]<br />
<br />
[[Self-assembled monolayers]]<br />
<br />
[[Thin film]]<br />
<br />
[[Electrohydrodynamics]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Statistical dynamics of flowing red blood cells by morphological image processing]]<br />
<br />
[[Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range]]<br />
<br />
[[Hydrodynamical models for the chaotic dripping faucet]]<br />
<br />
[[Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity]]<br />
<br />
[[Crystallization in Patterns: A Bio-Inspired Approach]]<br />
<br />
[[Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition]]<br />
<br />
[[Electrohydrodynamic size stratification and flow separation of giant vesicles]]<br />
<br />
[[Charge Stabilization in Nonpolar Solvents]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=12612Michelle A Borkin2009-11-16T23:30:12Z<p>Borkin: </p>
<hr />
<div>Definitions:<br />
<br />
[[Soft Machines]]<br />
<br />
[[Meniscus]]<br />
<br />
[[Hydrodynamics]]<br />
<br />
[[Depletion interactions]]<br />
<br />
[[Self-assembled monolayers]]<br />
<br />
[[Thin film]]<br />
<br />
[[Electrohydrodynamics]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Statistical dynamics of flowing red blood cells by morphological image processing]]<br />
<br />
[[Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range]]<br />
<br />
[[Hydrodynamical models for the chaotic dripping faucet]]<br />
<br />
[[Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity]]<br />
<br />
[[Crystallization in Patterns: A Bio-Inspired Approach]]<br />
<br />
[[Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition.]]<br />
<br />
[[Electrohydrodynamic size stratification and flow separation of giant vesicles]]<br />
<br />
[[Charge Stabilization in Nonpolar Solvents]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=12611Charge Stabilization in Nonpolar Solvents2009-11-16T23:29:38Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005) <br />
<br />
== Keywords ==<br />
<br />
[[Colloidal Dispersion]], interaction potential, [[Micelle]], surface potential, Debye length<br />
<br />
== Summary ==<br />
<br />
Currently writing...<br />
<br />
<br />
== Soft Matter ==<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Charge_Stabilization_in_Nonpolar_Solvents&diff=12610Charge Stabilization in Nonpolar Solvents2009-11-16T23:26:11Z<p>Borkin: New page: Original Entry by Michelle Borkin, AP225 Fall 2009 == Overview == [http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.] ...</p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
<br />
== Overview ==<br />
[http://www.deas.harvard.edu/projects/weitzlab/papers/hsu.langmuir.2005.pdf Charge Stabilization in Nonpolar Solvents.]<br />
<br />
M. F. Hsu, E. R. Dufresne, and D. A. Weitz, Langmuir 21, 4881-4887 (2005) <br />
<br />
== Keywords ==<br />
<br />
Currently writing...<br />
<br />
== Summary ==<br />
<br />
Currently writing...<br />
<br />
<br />
== Soft Matter ==<br />
<br />
Currently writing...</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Electrohydrodynamic_size_stratification_and_flow_separation_of_giant_vesicles&diff=12150Electrohydrodynamic size stratification and flow separation of giant vesicles2009-11-09T00:44:16Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
== Overview ==<br />
[http://link.aip.org/link/?APPLAB/92/104105/1 Electrohydrodynamic size stratification and flow separation of giant vesicles.]<br />
<br />
S. Lecuyer, W. D. Ristenpart, O. Vincent, and H. A. Stone, Appl. Phys. Lett., 92, 104105, 2008 <br />
<br />
== Keywords ==<br />
<br />
[[Electrohydrodynamics]], [[Vesicle]], suspensions<br />
<br />
== Summary ==<br />
[[Image:Lecuyer-etal-figure1.jpg|500px|thumb|right|alt=Schematic of the experiment.|]]<br />
<br />
An electrohydrodynamic (EHD) method for separating small from giant unilamellar vesicles (GUVs) is presented in this paper. GUVs are fragile and common suspension separation techniques (e.g. centrifugation) can damage them so are ineffective. Thus having an effective way to separate them is desirable. GUVs are of particular interest due to their ability to model biophysical systems since GUVs have similar sizes and structures (e.g. lipid bilayers, membranes) as living cells. There is also interest in using GUVs for new technology including nanoreactors and designable drug carriers. In summary, the process for separating the vesicles involves applying an oscillatory electric field which generates an EHD flow around each vesicle close to an electrode. The result is that the smaller vesicles are pulled underneath the larger ones thus lifting the larger ones off the electrode and shielding them. A brief spike in the electric field is applied to keep the smaller vesicles on the bottom while a flow is applied to push the larger vesicles into a separate container. The result is the removal of >90% of the small vesicles from the GUVs.<br />
<br />
== Soft Matter ==<br />
[[Image:Lecuyer-etal-figure2.jpg|500px|right|thumb|alt=Schematic of the experiment.|]]<br />
<br />
The unilamellar vesicles studied in this paper are self-assembled phospholipid vesicles in which spherical molecular bilayers separate a specific internal volume from the external environment. The giant unilamellar vesicles (GUVs) that the researchers are attempting to isolate are on the order of tens of micrometers in diameter. When an external electric field is applied, a dipole field is induced around each vesicle and this field distorts the charge polarization layer near the electrode thus giving rise to an electrohydrodynamic (EHD) flow. A schematic of this experimental set-up and a sketch of the EHD streamlines can be seen in '''Figure 1'''.<br />
<br />
When a field of 1V or greater is applied with a frequency in the range of 10-100 Hz, the following phenomena were observed: similarly sized vesicles formed planar clusters, and small vesicles (<10 micrometers) near larger vesicles (>20 micrometers) would either “orbit” the larger vesicle or more commonly “lift” the larger vesicle as they went underneath. For a schematic of these behaviors, see '''Figure 2 (b-c)'''. After the lifting occurred (~10 minutes of an applied field applied), a dc field (1 V) was applied for ~10 seconds in order to make the smaller vesicles adhere to the electrode (the larger ones don't stick since they are shielded by the smaller vesicles below them). A flow was then applied to push the larger vesicles into a separate collection chamber resulting in >90% of the smaller vesicles being separated from the larger ones, as shown in '''Figure 2 (d)'''. The effectiveness of this separation technique can also be seen in '''Figure 3''' which shows the distribution of vesicle sizes before and after the EHD process was applied to a sample.<br />
<br />
This paper also includes excellent videos displaying the observed vesicle behavior as part of its supplemental material. They are as follows:<br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/aggregation.avi aggregation.avi]: Example of vesicles aggregating when the electric field is applied (i.e. '''Figure 2 (b)''').<br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/transition.mpg transition.mpg]: Example of a transition from the small vesicles "orbiting" to "lifting".<br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/reversibility.avi reversibility.avi]: Demonstration of the frequency dependence (frequency is increased in one step from 30 Hz to 500 Hz) and reversibility of the aggregation process. <br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/flow.avi flow.avi]: Demonstration of the removal of larger vesicles after a spike in the field has been applied (i.e. '''Figure 2 (d)''').<br />
<br />
[[Image:Lecuyer-etal-figure3.jpg|450px|thumb|center|alt=Schematic of the experiment.|]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Michelle_A_Borkin&diff=12149Michelle A Borkin2009-11-09T00:43:35Z<p>Borkin: </p>
<hr />
<div>Definitions:<br />
<br />
[[Soft Machines]]<br />
<br />
[[Meniscus]]<br />
<br />
[[Hydrodynamics]]<br />
<br />
[[Depletion interactions]]<br />
<br />
[[Self-assembled monolayers]]<br />
<br />
[[Thin film]]<br />
<br />
[[Electrohydrodynamics]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Statistical dynamics of flowing red blood cells by morphological image processing]]<br />
<br />
[[Modeling Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range]]<br />
<br />
[[Hydrodynamical models for the chaotic dripping faucet]]<br />
<br />
[[Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity]]<br />
<br />
[[Crystallization in Patterns: A Bio-Inspired Approach]]<br />
<br />
[[Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition.]]<br />
<br />
[[Electrohydrodynamic size stratification and flow separation of giant vesicles]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Electrohydrodynamics&diff=12148Electrohydrodynamics2009-11-09T00:42:30Z<p>Borkin: </p>
<hr />
<div>== Definition ==<br />
<br />
Electrohydrodynamics (EHD) is the study of the dynamics of electrically charged fluids. (It is also sometimes referred to as electro-fluid-dynamics (EFD), electrokinetics, or [[Electokinetics]].) These dynamics are the motions of ionised particles and/or molecules and their interactions with electric fields and the surrounding fluid. Transport mechanisms relating to EHD include electrophoresis and electro-osmosis.<br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Electrohydrodynamics<br />
* [http://soft-matter.seas.harvard.edu/index.php/Electrohydrodynamic_size_stratification_and_flow_separation_of_giant_vesicles S. Lecuyer, W. D. Ristenpart, O. Vincent, and H. A. Stone, Appl. Phys. Lett., 92, 104105, 2008]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Electrohydrodynamics&diff=12147Electrohydrodynamics2009-11-09T00:34:31Z<p>Borkin: New page: == Definition == Currently writing... == References == * http://en.wikipedia.org/wiki/Electrohydrodynamics * [http://soft-matter.seas.harvard.edu/index.php/Electrohydrodynamic_size_str...</p>
<hr />
<div>== Definition ==<br />
<br />
Currently writing... <br />
<br />
== References ==<br />
<br />
* http://en.wikipedia.org/wiki/Electrohydrodynamics<br />
* [http://soft-matter.seas.harvard.edu/index.php/Electrohydrodynamic_size_stratification_and_flow_separation_of_giant_vesicles S. Lecuyer, W. D. Ristenpart, O. Vincent, and H. A. Stone, Appl. Phys. Lett., 92, 104105, 2008]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Vocabulary&diff=12146Vocabulary2009-11-09T00:32:02Z<p>Borkin: </p>
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<div>[[Main_Page | ''Home'']]<br />
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[[Young's modulus]]</div>Borkinhttp://soft-matter.seas.harvard.edu/index.php?title=Electrohydrodynamic_size_stratification_and_flow_separation_of_giant_vesicles&diff=12145Electrohydrodynamic size stratification and flow separation of giant vesicles2009-11-09T00:30:59Z<p>Borkin: </p>
<hr />
<div>Original Entry by Michelle Borkin, AP225 Fall 2009 <br />
== Overview ==<br />
[http://link.aip.org/link/?APPLAB/92/104105/1 Electrohydrodynamic size stratification and flow separation of giant vesicles.]<br />
<br />
S. Lecuyer, W. D. Ristenpart, O. Vincent, and H. A. Stone, Appl. Phys. Lett., 92, 104105, 2008 <br />
<br />
== Keywords ==<br />
<br />
electrohydrodynamics, [[Vesicle]], suspensions<br />
<br />
== Summary ==<br />
[[Image:Lecuyer-etal-figure1.jpg|500px|thumb|right|alt=Schematic of the experiment.|]]<br />
<br />
An electrohydrodynamic (EHD) method for separating small from giant unilamellar vesicles (GUVs) is presented in this paper. GUVs are fragile and common suspension separation techniques (e.g. centrifugation) can damage them so are ineffective. Thus having an effective way to separate them is desirable. GUVs are of particular interest due to their ability to model biophysical systems since GUVs have similar sizes and structures (e.g. lipid bilayers, membranes) as living cells. There is also interest in using GUVs for new technology including nanoreactors and designable drug carriers. In summary, the process for separating the vesicles involves applying an oscillatory electric field which generates an EHD flow around each vesicle close to an electrode. The result is that the smaller vesicles are pulled underneath the larger ones thus lifting the larger ones off the electrode and shielding them. A brief spike in the electric field is applied to keep the smaller vesicles on the bottom while a flow is applied to push the larger vesicles into a separate container. The result is the removal of >90% of the small vesicles from the GUVs.<br />
<br />
== Soft Matter ==<br />
[[Image:Lecuyer-etal-figure2.jpg|500px|right|thumb|alt=Schematic of the experiment.|]]<br />
<br />
The unilamellar vesicles studied in this paper are self-assembled phospholipid vesicles in which spherical molecular bilayers separate a specific internal volume from the external environment. The giant unilamellar vesicles (GUVs) that the researchers are attempting to isolate are on the order of tens of micrometers in diameter. When an external electric field is applied, a dipole field is induced around each vesicle and this field distorts the charge polarization layer near the electrode thus giving rise to an electrohydrodynamic (EHD) flow. A schematic of this experimental set-up and a sketch of the EHD streamlines can be seen in '''Figure 1'''.<br />
<br />
When a field of 1V or greater is applied with a frequency in the range of 10-100 Hz, the following phenomena were observed: similarly sized vesicles formed planar clusters, and small vesicles (<10 micrometers) near larger vesicles (>20 micrometers) would either “orbit” the larger vesicle or more commonly “lift” the larger vesicle as they went underneath. For a schematic of these behaviors, see '''Figure 2 (b-c)'''. After the lifting occurred (~10 minutes of an applied field applied), a dc field (1 V) was applied for ~10 seconds in order to make the smaller vesicles adhere to the electrode (the larger ones don't stick since they are shielded by the smaller vesicles below them). A flow was then applied to push the larger vesicles into a separate collection chamber resulting in >90% of the smaller vesicles being separated from the larger ones, as shown in '''Figure 2 (d)'''. The effectiveness of this separation technique can also be seen in '''Figure 3''' which shows the distribution of vesicle sizes before and after the EHD process was applied to a sample.<br />
<br />
This paper also includes excellent videos displaying the observed vesicle behavior as part of its supplemental material. They are as follows:<br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/aggregation.avi aggregation.avi]: Example of vesicles aggregating when the electric field is applied (i.e. '''Figure 2 (b)''').<br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/transition.mpg transition.mpg]: Example of a transition from the small vesicles "orbiting" to "lifting".<br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/reversibility.avi reversibility.avi]: Demonstration of the frequency dependence (frequency is increased in one step from 30 Hz to 500 Hz) and reversibility of the aggregation process. <br />
<br />
[http://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-92-075810/flow.avi flow.avi]: Demonstration of the removal of larger vesicles after a spike in the field has been applied (i.e. '''Figure 2 (d)''').<br />
<br />
[[Image:Lecuyer-etal-figure3.jpg|450px|thumb|center|alt=Schematic of the experiment.|]]</div>Borkin