Diffusion Through a Membrane

Abstract

An exact solution is obtained for the problem of diffusion through a membrane separating two stirred solutions of different concentrations. For a diffusion cell in which the two liquid containers have the same volume and for which the ratio λ (``effective'' volume of membrane : volume of liquid) is small compared with unity, the solution gives explicit expressions for the concentrations at any time in terms of the initial distribution of concentration in the membrane. Two cases are treated: (1) zero initial concentration in the membrane and in one of the liquids; (2) an initial linear concentration gradient connecting the concentrations in the two containers. The usual assumption of a linear gradient across the membrane during the whole course of diffusion will not lead to an appreciable error in a determination of a diffusion constant unless λ exceeds 0.1 or the time of diffusion is much shorter than in the usual practice. Since λ is about 0.02 in the usual type of diffusion cell the use of the simple expression based on a linear gradient cannot be in error. If, however, the preliminary treatment of the membrane fails to yield an initial linear gradient in it, an appreciable error will be made even with λ less than 0.02.