Diffusion transfer in a spherical granule with ideal contact of two consecutive multi-permeable axisymmetric areas under boundary conditions of the first kind

The unsteady transfer of a substance through diffusion mechanism in an axisymmetric two-layer spherical granule with different permeability with ideal contact is represented by a system of parabolic equations in the format of 1D spherical coordinates. On the outer surface of the granule a constant concentration of diffusing medium is maintained, and at the interface between the layers a boundary condition of the fourth kind is applied. An attempt to solve a similar problem posed by the method of one-sided semi-bounded integral Laplace transform does not lead to a physically justified solution, since for small values of time, the solution is not stable and does not satisfy the criterion of convergence with an increase in the number of terms of the resulting series. However, if the classic method of separation of variables to integrate the original system is applied, the resulting solution satisfies each equation of the system and identically fulfills the initial-boundary conditions. The examined problem has an important practical application for estimating the kinetic coefficient of the Gluckauf postulate of the transfer rate of a single-species medium in a bidisperse granular material in the approximation of a hypothetical linear model with lumped parameters.