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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]

11.4 Logarithmic transform of the Nernst-Planck equations [species/charge transport top]

The Nernst-Planck equations:
microfluidics textbook nanofluidics textbook Brian Kirby Cornell
(11.24)

can be difficult to solve numerically for microfluidic systems, since the variation in charged species in microfluidic systems (for example, near charged walls) is typically exponential and the derivatives are difficult to handle. Numerical simulations performed without extreme care often lead to non-physical solutions, for example negative concentrations, or numerical instability. One technique that greatly helps to address this is to make the substitution ci = exp(γi), leading to the equation

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

This transformed equationhas two key advantages. First, it governs the transport of γi, not ci, and small errors no longer lead to nonphysical solutions such as negative concentrations. Second, the logarithm (γi) of the concentration is expected to vary linearly when the concentration ci varies exponentially, and thus γi is well suited for solving numerically on regular meshes.

[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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