Mathematical modeling diffusion of admixture particles in a strip with randomly located spherical inclusions of different materials with commensurable volume fractions of phases

Abstract

The process of diffusion of admixture particles in a multiphase randomly nonhomogeneous body with spherical inclusions of different materials with commensurable volume fractions of phases is investigated. According to the theory of binary systems, a mathematical model of admixture diffusion in a multiphase body with spherical randomly disposed inclusions of different radii is constructed. The dense packing of spheres with different radii is used to modeling the skeleton of the body. The contact initial-boundary value problem is reduced to the mass transfer equation for the whole body. Its solution is constructed in the form of Neumann series. On the basis of the obtained calculation formula, a quantitative analysis of the mass transfer of admixture in the body with spherical inclusions, which are filled with materials of fundamentally different physical nature, but commensurable volume fractions, is carried out. It is shown that in modeling skeleton by spheres of one characteristic radius averaged concentration values coincide for different cases of radius, such as when characteristic radius equals to the average value of the radii of inclusions; or to the radius corresponding the smallest spherical inclusion; or to the radius of an order of magnitude smaller than this value.