Nonlinear Electrokinetic Flow near Permselective Membrane

Abstract

We conducted numerical studies on the nonlinear electrokinetic flow developing near permselective membrane. Numerical methods were developed to solve for the Poisson-Nernst-Planck-Navier-Stokes equations. It was demonstrated that, under a significantly high electric field, an electroconvective instability occurs near the membrane surface. In quiescent electrolyte, the instability induces strong paired vortices. These vortices transport more ions to the membrane to promote an overlimiting current. Importantly, we observed hysteretic behaviors of electric current and fluid flow in the transition between the limiting and overlimiting regimes. In sheared electrolyte flow, a new kind of electroconvective instability, namely sheared electroconvective instability, was investigated. This kind of instability exhibits a unidirectional vortices flow and growing depletion zones on the membrane surface. Our findings are in agreement with experimental results. This agreement allows us to gain a fuller understanding of the mechanism for overlimiting conductance in electrodialysis cells.