Mathematical Modeling of the Mean Concentration Field in Random Stratified Structures with Regard for the Jumps of Sought Function on the Interfaces

Abstract

We study the diffusion processes of an admixture in a two-phase stratified strip of randomly inhomogeneous structure with regard for the jumps of the concentration function and its derivative on the contact boundaries of the phases. A new representation of the operator of equation of mass transfer for the entire body is proposed. We formulate an equivalent integrodifferential equation whose solution is constructed in the form of a Neumann integral series. The obtained solution is averaged over the ensemble of phase configurations with uniform distribution function. It is shown that the computational formula for the mean concentration with explicit account of its jumps on the interfaces contains an additional term. It is demonstrated that the ratios of the diffusion coefficients, the concentration dependences of the chemical potentials in different phases, and their relationships affect the sign of this term. We find the ranges of parameters of the problem for which this term is negligibly small.