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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]

9.2 Fluid flow in the Gouy-Chapman electrical double layer [electrical double layer top]

Recall from Chapter 6 that the inner solution for purely electroosmotic flow is given by

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

This inner solutionassumes that microfluidics textbook nanofluidics textbook Brian Kirby Cornellext is uniform on the length scales corresponding to the double layer thickness, and thus is valid only near the wall.

Now that we have determined the spatial dependence of φ in a variety of situations, we can write the spatial variation of the fluid velocity as well. For example, in the Debye-Hückel limit, the inner velocity solution is given by

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

and analogous relations can be written for other flow conditions. For example, for flow between two plates located at y = ±d, in the Debye-Hückel limit:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

This solution, while only valid for the linearized system, gives a good qualitative picture ofelectroosmotic flow between two parallel plates. Some example solutions are shown in Figure 9.6.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 9.6: Normalized electroosmotic flow distribution (u(y)∕μEOE) between two parallel plates located at y = ±d*, as predicted by the linearized Poisson-Boltzmann equation (and thus representative of the flow if the wall potential is small as compared to RT ∕zF ). Velocity distributions are shown for several d* values. The distribution for d* = 50 is a representative point at which the thin double layer approximation becomes accurate for the flow distribution.


With the inner solutions calculated from the Gouy-Chapman model of the electrical double layer, the description of electroosmotic flow in a microchannel can now be obtained through a composite asymptotic solution (see Exercise 9.16).


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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