Conductive transport through a mixed-matrix membrane

Conductive transport through an infinite homogeneous medium across a layer of finite thickness, a planar array of infinite cylinders, or a planar array of three-dimensional particles with arbitrary conductivity is considered as a model of mixed-matrix membrane separation. The boundary distribution of the transported scalar field on the interior side of the layer, cylinders, or particles is proportional to that on the exterior side according to a linear sorption/desorption kinetics law, while the conductive flux is continuous across the interface. In the case of cylinders and particles, the solution of Laplace’s equation for the transported field is represented by an interfacial distribution of point sources expressed in terms of the periodic Green’s function of Laplace’s equation in two dimensions or the doubly periodic Green’s function of Laplace’s equation in three dimensions. Analytical solutions for small circular cylinders and small spherical particles are derived based on the integral representation, and numerical solution of integral equations arising from the interfacial conditions are computed by boundary-element methods. The results document the displacement of the linear profile of the transported field far from the interfacial layer or array with respect to that prevailing in the absence of membrane. Expressions for the effective diffusivity of the mixed-matrix membrane are derived.