Effects of three-dimensional geometric field focusing on concentration polarization in a heterogeneous permselective system

The current study extends previous two-dimensional (2D) analysis of concentration polarization to account for three-dimensional effects in realistic heterogeneous ion-permselective systems, e. g., microchamber-nanoslot devices. An analytical solution of the electrodiffusive problem, decoupled from electroconvection along with the local electroneutrality approximation, was obtained using the separation of variables technique. It is able to account for the previously neglected effects of microchamber and nanoslot heights on concentration polarization in terms of concentration profiles, limiting current, and current-voltage curves. The resultant heterogeneity in the third dimension adds to that already existing in the 2D in plane problem to further increase geometric field-focusing effects. As a result the currents no longer scale linearly with the nanoslot area, but rather depend on its shape and relative size compared to that of the nonconducting region (i.e., level of heterogeneity). This is turn leads to pronounced current density intensification with increased system heterogeneity found to be in qualitative agreement with previously reported experiments in which both microchamber and nanoslot geometries were varied.