Green's functions for a system with a thin membrane

A procedure to determine concentration profiles of solute in a system with a thin membrane is presented. We assume that the permeability of the membrane is described by a set of general coefficients without the need to investigate its internal structure. This procedure is based on the Smoluchowski equation, but the boundary condition on the membrane is given in a new form. The membrane permeability coefficients are given separately with respect to the diffusion, convection, and migration phenomena. The procedure, relative to existing procedures, considerably reduces the calculations necessary to determine concentration profiles.