Exact Analytic Solutions for Diffusion Impeded by an Infinite Array of Partially Permeable Barriers

We give an exact solution for the macroscopic diffusion of particles in one dimension impeded by any set of plane, parallel partially permeable barriers. Explicit results are given for one barrier, and for an infinite system of uniformly spaced barriers, for any initial position of the particles. This model can be generalized from slits to square tubes, to cubic pores, etc., and is proposed as a convenient model, with disposable parameters, for fitting to experiment. Various convenient and physically illuminating approximations are discussed. An alternative, and sometimes more convenient, way of computing the exact solution for complicated systems of pores is also given.