Theoretical analysis of time-dependent diffusion, reaction and electromigration in membranes

The transport of material through a membrane of finite thickness via the process of diffusion is examined theoretically. The membrane is assumed to be sandwiched between a donor and a receptor compartment and it is assumed that infinite source and sink conditions pertain. The effect of an externally applied electric field and concurrent first-order chemical reaction of the diffusant species with sites in the membrane on the diffusion rate is examined via the formulation of a time-dependent differential equation and its subsequent solution via the technique of Laplace transformation. Closed form expressions for the diffusant lag time and permeability are derived and compared with expressions previously presented in the literature.