An analytical solution for the diffusion of electrolytes through a charge-mosaic membrane

Abstract

The problem of electrolyte diffusion through charge-mosaic membranes has been analytically solved for the model of alternating infinite slabs of homogeneous cation- and anion-exchangers. The solution has been obtained in terms of Fourier series as a system of linear algebraic equations for the coefficients. The solution revealed that at not too small unstirred layer thickness and sufficiently small fragment size the membrane diffusional resistance is a linear function of fragment size. The proportionality coefficient has been found to be an almost explicit function of fragment perm-selectivity and the ratio of fragment to solution electrical conductivities. The dependences of membrane diffusional resistance on those parameters have been considered in terms of Donnan potential and hindrance factor for the ion electro-diffusion in the fragments to yield some practical recommendations on the optimal properties of a membrane for the separation of electrolyte/non-electrolyte mixtures by dialysis.