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.

The problem studied may be considered as a generalization of two previously developed problems: the transport of binary electrolyte through a diffusion layer with disturbed electroneutrality adjacent to an ion-exchange membrane, and the competitive transfer of two counter-ions through a three-layer membrane system where the electroneutrality is hold in all the three layers. The structure of the depleted diffusion layer is similar to that in the case of binary electrolyte: four zones can be distinguished, one of which being electroneutral and three other forming a space charge region. At i < ilim the membrane behavior does not differ from that of three-layer electroneutral membrane system. At i ≥ i lim t he fluxes are governed exclusively by the ion transfer through the electroneutral zone of the depleted diffusion layer. Hence, the ratio of the counter-ions effective transport numbers through the membrane (T1/T2) is proportional to that of the (electro-migration) transport numbers in the bulk of the depleted diffusion layer (t1I/t2I); Ti does not depend on the membrane and space charge region properties.