Effect of concentration polarization upon the valency-induced counterion selectivity of ion-exchange membranes

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Abstract
The paper contains a theoretical study of the variation of steady-state membrane selectivity for counterions of different valencies in the course of concentration polarization. The computations show that the system loses most of its counterion selectivity before the concentration polarization results in a pronounced deviation from the linear ohmic voltage against current dependence. This is explained by the enhanced depletion of the Nernst layer of the preferred counterion, resulting in the relative inpoverishment of the membrane in the latter, under conditions at which the membrane still controls the counterion selectivity. At higher currents, when a strong concentration polarization sets in and the limiting stage of counterion transfer shifts to the Nernst layer, the selectivity is almost totally lost, except for a small residual effect, due to a different contribution of migration into the limiting ionic fluxes for species of different valencies.

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