UDC 517. 958:532.72 This paper is devoted to the mathematical modeling of admixture diffusion in a two-phase stratified strip of randomly inhomogeneous structure with regard for the conditions of nonideal mass contact on the interfaces. We formulate an equivalent integro-differential equation and construct its solution in the form of a Neumann integral series. We perform averaging of the solution obtained over the ensemble of phase configurations with a uniform distribution function. We also determine the influence of material characteristics on the behavior and level of averaged field of concentration of admixture particles.Natural and artificial materials with complex, in particular, multiphase, structure are widely used in engineering practice. Their application requires estimating the distribution and behavior of temperature and diffusion fields depending on the conditions of internal interphase contact, external actions, and possible spatial realizations of the structure [15,16]. As a rule, data on the specific spatial disposition of separate phases for such materials are unknown, but sufficient information on their volume fractions and main physicochemical properties is available [13,18].Along with the methods of homogenization of the inhomogeneous structure of a body [10, 14, 17], which use the ratio of the sizes of inhomogeneities to the distance of substantial change in the fields under study (temperature, concentration) as a small parameter, new approaches have been developed in recent years. They are based on the apparatus of the theory of generalized functions and averaging over the ensemble of admissible spatial realizations of the phase disposition [11]. In the latter case, in formulating the equation of transfer of the admixture substance for the multiphase body as a whole, it is customary to use the diffusion equation where the diffusion coefficient is considered as a random function. However, information on separate phases often contains data on their density and the kinetic characteristics of migrating particles.In the present work, we solve the contact initial boundary-value problem of diffusion in a two-phase randomly inhomogeneous multilayer strip. Here, we formulate the diffusion equation in contacting domains with the use of kinetic diffusion coefficients, which, in the reduction of our problem to the equivalent integrodifferential equation, leads to taking into account the time derivative in its operator.
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