Space charge effect on competitive ion transport through ion-exchange membranes

A mathematical model of the competitive electro-transport of two counter-ions through an ion exchange membrane based on the Nernst-Planck and Poisson equations is developed. A three-layer system is considered: the membrane and two adjacent diffusion layers. Concentration profiles in the three layers, effective transport numbers as functions of the current and current-voltage characteristics are calculated. Deviation from the local electroneutrality in space charge region near the depleted solution/membrane interface is taken into account. It is shown that the space charge region grows with the voltage applied. However the fluxes of the competitive counter-ions at over-limiting currents are determined by their transfer through the electroneutral part of the depleted diffusion layer.