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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]

6.1 Matched asymptotics in electroosmotic flow [electroosmosis top]

VIDEO: electroosmosis -- concept map.

VIDEO: matched asymptotics for electroosmosis.

Because the thin electrical double layer assumption implies scale separation between the electrical double layer and the bulk flowfield, we often find it useful to analyze electroosmotic flow in terms ofmatched asymptotics. In this case, we find two asymptotic solutions: (1) theinner solution, corresponding to the electrical double layer, in which we keep track of the details of the Coulomb forces and the resulting velocity gradients and vorticity, but we assume that the extrinsic electric field is uniform, and (2) theouter solution, where we assume that the fluid is electroneutral and irrotational, but allow the extrinsic electric field to vary spatially (Figure 6.2). The inner solution is valid in the electrical double layer, but gives incorrect results far from the wall if the extrinsic field varies with distance from the wall. The outer solution is valid outside the electrical double layer, but gives incorrect results near the wall and violates the no-slip condition.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 6.2: Left: Inner and outer solutions for electroosmotic flow. The inner solution is valid in the electrical double layer, but is generally invalid in the bulk. The outer solution is valid in the bulk, but invalid in the electrical double layer and at the wall. Right: The composite solution smoothly transitions from the inner solution to the outer solution.


[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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