Diffusion in heterogeneous media: properties of a laminated slab

Abstract

A theoretical study has been made of diffusion through a laminated membrane in the form of sheets of alternating phases A and B. In the laminates considered the diffusion coefficients are constant in each phase and in each the diffusant dissolves according to Henry's law. For a fixed volume fraction of each component the steady-state flux normal to the laminae is independent of the state of sub-division characterized by the number n of pairs of laminates A, B. The total quantity of diffusant in the membrane in the steady state has been calculated and employed to define an overall diffusion coefficient for the membrane. The time lag L characteristic of the transient state, has been evaluated and some of its properties investigated. Particular interest attaches to a maximum observed in the variation of the time lag with the volume fraction of one phase. Only for media in which n is large do steady-state and time-lag methods give the same overall diffusion coefficient. Some attention has also been given to the time lag-permeability product.