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Nonlinear dynamics of ion concentration polarization in porous media: The leaky membrane model

Authors

  • E. Victoria Dydek,

    1. Dept. of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA
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  • Martin Z. Bazant

    Corresponding author
    1. Dept. of Mathematics, Massachusetts Institute of Technology, Cambridge, MA
    • Dept. of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA
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    • This article is dedicated to the memory of Neal R. Amundson by Martin Z. Bazant.


Correspondence concerning this article should be addressed to M. Z. Bazant at bazant@mit.edu.

Abstract

The conductivity of highly charged membranes is nearly constant, due to counterions screening pore surfaces. Weakly charged porous media, or “leaky membranes,” also contain a significant concentration of coions, whose depletion at high current leads to ion concentration polarization and conductivity shock waves. To describe these nonlinear phenomena in the absence of electro-osmotic flow, a simple leaky membrane model is formulated, based on macroscopic electroneutrality and Nernst–Planck ionic fluxes. The model is solved in cases of unsupported binary electrolytes: steady conduction from a reservoir to a cation-selective surface, transient response to a current step, steady conduction to a flow-through porous electrode, and steady conduction between cation-selective surfaces in cross flow. The last problem is motivated by separations in leaky membranes, such as shock electrodialysis. The article begins with a tribute to Neal Amundson, whose pioneering work on shock waves in chromatography involved similar mathematics. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3539–3555, 2013

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