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Copyright Brian J. Kirby. With questions, contact Prof. Kirby here. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.

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Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

16.5 Summary [AC electrokinetics top]

In this chapter, we have addressed the dynamics of diffuse charge in electrical double layers near non-Faradaic electrodes and identified the characteristic times for these double layers as a function of the double layer capacitance and the bulk solution resistance. A key result is that, for symmetric electrolytes, the characteristic time of the equilibration of Debye-Hückel electrical double layers on electrodes spaced by L is given by

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

indicating that the characteristic time is a function both of double layer thickness and electrode separation. In general, the differential capacitance of the electrical double layer can be modeled with varying degrees of accuracy by the Debye-Hückel model:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

the Poisson-Boltzmann model:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

the Gouy-Chapman-Stern model:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

and the modified Poisson-Boltzmann model:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

With a specified electrical double layer capacitance, RC circuit models can predict the double layer potential drop φ0 as a function of the frequency of the applied signal, and φ0 can be combined with the Navier-Stokes equations to predict the fluid flow. Two examples of this type of fluid flow areAC electroosmosis andinduced-charge electroosmosis.

In the presence of spatially-varying fluid properties (usually owing to thermal variations), applied electric fields lead to diffuse charge throughout the flowfield, leading to an electrostatic body force term and electrothermal flows. This electrostatic body force term can be written in time-averaged form for sinusoidal fields:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

[Return to Table of Contents]



Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.


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