Modeling random diffusion mass flow in a two-phase strip with a stochastically disposed sublayer of random thickness

Abstract

The flow of admixture substance is studied in a layer with stochastically disposed layered inclusion,
which thickness is of random magnitude too. The initial-boundary value problem of diffusion
is formulated for the function of admixture particle flow under constant value of the flow on one
body boundary and zero concentration on the other one. The solution is constructed in the form of
Neumann series. Procedures for averaging are performed over the ensemble of phase configurations
and over the random thickness of the sublayer. Calculation formulae for the averaged mass
flow are obtained under zero and nonzero initial concentrations for the cases where the sublayer
thickness is a random variable with uniform or triangular distribution on certain interval. Dependence
of the flow on physical and geometric parameters of the inclusion is analyzed.