Effect of geometry on concentration polarization in realistic heterogeneous permselective systems

TL;DR

This paper develops an analytical model for concentration polarization in a realistic 3D heterogeneous ion-permselective system, revealing how geometry asymmetry causes current rectification and affects conductance behavior.

Contribution

It extends previous models by deriving an analytical solution for a 3D heterogeneous system, accounting for geometry asymmetry and microchamber resistance effects.

Findings

Asymmetry causes current rectification.

Conductance decreases with low concentration when microchamber resistance is significant.

Analytical solutions enable direct comparison with experimental data.

Abstract

This study extends previous analytical solutions of concentration-polarization occurring solely in the depleted region, to the more realistic geometry consisting of a three dimensional (3D) heterogeneous ion-permselective medium connecting two opposite microchambers (i.e. 3 layers system). Under the local electro-neutrality approximation, the separation of variable methods is used to derive an analytical solution of the electro-diffusive problem for the two opposing asymmetric microchambers. Assuming an ideal permselective medium allows for the analytic calculation of the 3D concentration and electric potential distributions as well as a current-voltage relation. It is shown that any asymmetry in the microchamber geometries will result in current rectification. Moreover, it is demonstrated that for non-negligible microchamber resistances the conductance does not exhibit the expected saturation at low concentrations but instead shows a continuous decrease. The results are intended to facilitate a more direct comparison between theory and experiments as now the voltage drop is across a realistic 3D and 3-layer system.