Time and spatial concentration profile inside a membrane by means of a memory formalism

In this note, the profile concentration of diffusing particles inside a membrane has been calculated on the basis of the Fick diffusion equation modified by introducing a memory formalism. In highly heterogeneous systems, such as biological membranes, the intrinsic structural complexity of the medium restricts the applicability of continuum diffusion models and suggests that diffusion parameters could depend at a certain time or position on what happens at preceding times (diffusion with memory). Here, we deal with two particular cases, the diffusion of glucose across an erythrocyte membrane, when the concentration at both sides of the membrane are assigned, and the permeation transport of small molecular weight solute through an artificial hydrogel polymeric membrane. However, the present procedure can be easily extended to more general conditions. The knowledge of the concentration profile within a membranous structure, which is usually not easily experimentally accessible, completes the description of the rather complex phenomenon of the transport across a highly structured confined medium and can also lead to an improvement in controlled drug-delivery systems.