EQUATION OF DIFFUSION OF A COMPOSITE MIXTURE INTO A COMPOSITE MEDIUM

The equation of diffusion of a composite mixture into a composite medium has been obtained for the fi rst time. The assumption used is that the macropoint of the medium, i.e., an elementary macrovolume, in which the statistical parameters of distribution of inhomogeneities coincide with the corresponding values assigned for the medium as a whole, is small compared to the geometric dimensions of the volume considered. The ″Reuss–Voigt fork″ has been obtained for determining the limits of the change in the diffusion coeffi cient. Thereafter the fork is narrowed to the ″Kravchuk–Tarasyuk fork.″ Effective diffusion coeffi cients are obtained as an arithmetic mean value of the Kravchuk–Tarasyuk fork. The found averaged physical parameters can be used in solving specifi c physical problems
for inhomogeneous media.
The equation of diffusion of a composite mixture into a composite medium has been obtained for the fi rst time. The assumption used is that the macropoint of the medium, i.e., an elementary macrovolume, in which the statistical parameters of distribution of inhomogeneities coincide with the corresponding values assigned for the medium as a whole, is small compared to the geometric dimensions of the volume considered. The ″Reuss–Voigt fork″ has been obtained for determining the limits of the change in the diffusion coeffi cient. Thereafter the fork is narrowed to the ″Kravchuk–Tarasyuk fork.″ Effective diffusion coeffi cients are obtained as an arithmetic mean value of the Kravchuk–Tarasyuk fork. The found averaged physical parameters can be used in solving specifi c physical problems
for inhomogeneous media.
Author:  A. S. Kravchuk, A. I. Kravchuk, and T. S. Popova
Keywords:  lamellar, structurally inhomogeneous composite material, macropoint of composite material, discrete random quantity, averaging, effective characteristics of a medium, Voigt hypothesis, Reuss hypothesis, Hill′s approximation, Kravchuk–Tarasyuk fork
Page:  1041