Diffusion in inhomogeneous films and membranes

In a number of different contexts one is interested in the diffusion of a penetrant into an inhomogeneous film or membrane. We review exact results in the theory of permeation through membranes containing fixed inhomogeneities. We also present the available exact results on permeation, time lag, and sorption for a sufficiently dilute penetrant in an inhomogeneous slab or film. We discuss and compare the kind of information provided by permeation and sorption studies using a variety of examples of simple types of inhomogeneities.