A GENERAL EXPRESSION FOR THE TOTAL RELEASE OF DIFFUSANT THROUGH HETEROGENEOUS MEMBRANES

Abstract

An expression for the total amount of diffusant Q(t) released into a receiver by diffusion through a heterogeneous membrane is rigorously derived for time-dependent boundary conditions and a position-dependent initial condition. The heterogeneity of the membrane is characterized by a position-dependent diffusivity and partition coefficient. Two examples are given to demonstrate the utility of this general expression. It is shown that the expression for Q(t) proposed by Keister [ J. Membrane Sci., 29 (1986) 333-3441 is only valid when the asymptotic concentration of the diffusant within the membrane is zero.