A special case of spatial averaging of the diffusion coefficient

TLDR: In this article, it is shown that if the coordinate dependence of the diffusion coefficient is described by the product of functions depending on different coordinates, then the surfaces of equal concentration coincide with the coordinate planes.

Abstract: Steady-state mass transfer through a heterogeneous layer formed by coordinate planes of an orthogonal coordinate system is considered under the assumption that the boundary conditions at both layer boundaries are independent of coordinates. It is established that, if the coordinate dependence of the diffusion coefficient is described by the product of functions depending on different coordinates, then the surfaces of equal concentration (isohalines) coincide with the coordinate planes. It is shown that, in this case, the diffusion problem has an exact solution and the averaging of the diffusion coefficient is performed by elementary methods.