The diffusion of electrolytes in a cation-exchange resin membrane I. Theoretical

An equation for the flux of electrolyte through a water-swollen cation-exchange resin membrane separating two solutions of the same electrolyte at different concentrations is derived on the basis of several assumptions regarding the physical nature of a swollen resinous exchanger. The complete flux equation contains three terms, one determined by the concentration difference across the membrane, another determined by the variation of the activity coefficient of the electrolyte with concentration in the membrane and a third concerned with the rate of osmotic or hydrostatic flow through the membrane. If ions in the resin are transported entirely in an internal aqueous phase, the mobilities required for the flux equation can be related to mobilities in aqueous solution and to the volume fraction of resin in the swollen membrane. The treatment is readily extended to anion exchangers.