Mathematical Modelling and Research for Diffusion Processes in Multilayer and Nanoporous Media

Abstract

The problem of mass transfer for diffusion and adsorption in non-regular disperse and porous multilayer media with no stationary regimes of mass exchange processes on the mass exchanged surfaces, which is described by systems of differential equations with boundary conditions and contact conditions, is introduced. The exact analytical solution of the problem by the application of Laplace, Fourier and Bessel integral transforms and the fundamental function method of Cauchy is established. Models were selected in accordance with component distribution in the multilayer media Me-MeO area. The solution of equation systems for different models as well as the investigation of the functions made it possible to find the effective meaning of the diffusion coefficient. The investigations will allow to correct multilayer chemical composition, to understand better the high-temperature oxidation mechanism and adsorption mechanism in nanoporous n-component structures.

Identifying kinetic parameters of mass transfer in components of multicomponent heterogeneous nanoporous media of a competitive diffusion system

“…In the present paper, we will employ mathematical models of competitive diffusion in heterogeneous nanoporous media and methods of deriving analytical solutions with the use of integral transforms [12][13][14][15][16][17][18][19] and experimental results [9,11] to obtain an analytical and numerical solution of a model that describes a nanoporous system. Based on the optimal control theory developed for multicomponent distributed systems [20][21][22] and following [13,[23][24][25][26], we will substantiate the formulations of the direct and conjugate boundary-value coefficient identification problems, implement the gradient procedure of parameter identification of internal transfer kinetics, and obtain the distributions of coefficients of competitive diffusion for intraparticle transfer in a heterogeneous nanoporous medium.…”