Hydrodynamics, electroosmosis, and electrokinetic instability in imperfect electric membranes

Abstract

For the first time within the framework of the Nernst−Planck−Poisson−Stokes set, the behavior of an electrolytic solution in imperfect electric membranes is investigated numerically. The distributions of the electric potential, fluid velocities, charge density, and other values in the zones of the depleted and enriched solution and a porous membrane for all current modes are obtained: prelimit, limit, and superlimit. The dependence of selectivity of a membrane on the density of its space charge is obtained. The boundaries of superlimit modes, when the one-dimensional solution loses stability, are found and replaced by the twodimensional solution with the formation of microvortices in both the desalination and enriched-solution zones. The basic types of current arising at supercritical currents are investigated.