Transient diffusion through a membrane with a selective skin

Abstract

A model is introduced for a membrane with a skin. The isothermal nonstationary diffusion through the membrane is described for a system with, on one side of the membrane, a binary solution with a constant concentration, and, on the other side, a binary solution with an initially uniform concentration, contained in a closed cell with a finite volume. The orientation of the asymmetric membrane toward the external phases is taken into account. Diffusion of solute through the membrane results in a decay of the experimental osmotic pressure across the membrane. This pressure depends not only on the concentrations on both sides of the membrane but also on the concentration profile in the membrane. Practical equations are given allowing the determination of the average reflection coefficient and of the solute permeabilities of the selective skin and the supporting layer from observed pressure-time curves. The influence of the volume flow history on the initial concentration profile is taken into account. Special attention is paid to the occurrence of asymmetry pressures (osmotic pressures at zero concentration difference over the membrane, which are induced by the initial volume flow).