Studies of membrane phenomena. Part 5.—Bulk flow through membrane

Abstract

A theory was developed for the bulk flow of liquid through an ionized membrane which separates aqueous solutions of a 1:1 electrolyte of different concentrations, C₁ and C₂(C₁ < C₂). The main assumptions used were : (i) the activity coefficients and mobilities of mobile ions in the membrane phase are given by the expressions proposed previously; (ii) the velocity of the local centre of mass is proportional to the sum of mechanical and electric forces acting on the volume element considered; (iii) the osmotic pressure acting between two phases at the membrane surface is proportional to RT times the difference in molar concentration of thermodynamically effective ions across the phase boundary considered. The derived expression for the volume rate of bulk flow (J_ν)_c was the sum of three effects : interdiffusion of solute and solvent components, flow due to pressure gradient, and electro-osmotic flow due to electric-potential gradient. Methods to evaluate three parameters associated with these three kinds of flow from a set of experimental data for (J_ν)_c were developed, and applied to systems of oxidized collodion membrane and typical 1 : 1 electrolyte (KCl, LiCl, KIO₃). With the values of the parameters so determined, the values of (J_ν)_c at various fixed values of C₂/C₁ were calculated as a function of ln C₁ from the theoretical equation derived. The resulting curves displayed an N-shaped feature similar to the observed results and agreed numerically with the latter in all cases examined.