Effect of geometry on concentration polarization in realistic heterogeneous permselective systems

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., a three-layer system). Under the local electroneutrality approximation, the separation of variable methods is used to derive an analytical solution of the electrodiffusive problem for the two opposing asymmetric microchambers. The assumption of 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 three-layer system.