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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]

11.8 Exercises [species/charge transport top]

  1. Consider the distribution of an ion of valence z in a 1D potential field φ(y). Derive the Einstein relation by:

    • writing c(φ),
    • writing the 1D Nernst-Planck equations for ion transport in the y-direction, and
    • showing that equilibrium requires that the Einstein relation holds.
  2. Consider the 1D ion flux equation for a chemical species i:
    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (11.29)

    and show that the normalized flux ji∕ci is proportional to the spatial gradient of the electrochemical potential gi = gi+RT lnmicrofluidics textbook nanofluidics textbook Brian Kirby Cornell +zi.

  3. Most exercises are excluded from this web posting. Follow the links to buy the text at Cambridge or Amazon or Powell's or Barnes and Noble.

[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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