Nonlinear Dynamics of Ion Concentration Polarization in Porous Media: The Leaky Membrane Model

TL;DR

This paper introduces a Leaky Membrane Model to describe nonlinear ion concentration polarization phenomena in porous media, capturing effects like conductivity shocks and steady-state behaviors relevant to separation processes.

Contribution

The paper develops a simple, macroscopic model for leaky membranes that explains nonlinear ion transport phenomena without electro-osmotic flow, extending understanding of ion concentration polarization.

Findings

Model successfully describes steady and transient ion transport behaviors.

Predicts conductivity shock waves in leaky membranes.

Applicable to separation technologies like shock electrodialysis.

Abstract

The conductivity of highly charged membranes is nearly constant, due to counter-ions screening pore surfaces. Weakly charged porous media, or "leaky membranes", also contain a significant concentration of co-ions, whose depletion at high current leads to ion concentration polarization and conductivity shock waves. To describe these nonlinear phenomena 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.