Theory of concentration polarization effects in electrodialysis on counter-ion selectivity of ion-exchange membranes with differing counter-ion distribution coefficients

This paper is concerned with the theory of the effect of concentration polarization under direct current upon the counter-ion selectivity of an ion-exchange electrodialysis membrane. The equilibrium selectivity is induced by the differing uptake of the counter-ions by the membrane, owing to the difference in their distribution coefficients between the membrane and solution phases. The numerical calculations are supplemented by an asymptotic analysis for a certain range of bulk concentrations and distribution coefficients, which provides an analytical expression for the dependence of selectivity on the electric current in the entire current range.