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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]
[InducedCharge Effects]
[DEP]
[Solution Chemistry]
9.2 Fluid flow in the GouyChapman electrical double layer [electrical double layer top]
Recall from Chapter 6 that the inner solution for purely electroosmotic flow is given by
This inner solutionassumes that _{ext} 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 DebyeHückel limit, the inner velocity solution is given
by
and analogous relations can be written for other flow conditions. For example, for flow between two plates located at
y = ±d, in the DebyeHückel limit:
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.
With the inner solutions calculated from the GouyChapman 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).
[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]
[InducedCharge 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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