Unstable Electrochemical Flows in a Pore System

Abstract

Starting from the Navier-Stokes and Nernst-Planck equations, an explanation is proposed for the so-called pressure-volume flow limit cycle which can be observed when a polymer filter of weak ion-exchange capacity is subjected to both an electrochemical and pressure gradient. It is indicated that the streaming current cannot be neglected in cases of unstable flow, whereas it may be left out of consideration for stationary regimes. The source of oscillation is shown to arise from non-linearity in the Maxwell pressure tensor. Although not including inertial forces, the present treatment seems satisfactory as a first approach, if boundary conditions are carefully evaluated.