Nonlinear dynamics of ion concentration polarization in porous media: The leaky membrane model
Name
Bazant_Nonlinear dynamics.pdf
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3.72 MB
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Author(s)
Dydek, E. Victoria
Bazant, Martin Z.
Date Issued
August 2013
Journal
AIChE Journal
Publisher
Wiley Blackwell
Citation
Dydek, E. Victoria, and Martin Z. Bazant. “Nonlinear Dynamics of Ion Concentration Polarization in Porous Media: The Leaky Membrane Model.” AIChE Journal 59, no. 9 (August 8, 2013): 3539–3555.
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/aic.14200
