Mathematical modeling admixture diffusion processes in a two-phase semispace with the erlang distribution of inclusions
Abstract
Admixture diffusion processes are studied in a two-phase semispace of randomly nonhomogeneous stratified structure, taking into account the conditions of non-ideal mass contact on interphases. Layered inclusions are disposed by the Erlangian distribution. A mass transfer equation for whole body is obtained, considering the jumps of both desired function and its derivative on the interphases. An equivalent integrodiffential equation is formulated and its solution is constructed in terms of Neumann series. Averaging the obtained solution is carried out over the ensemble of phase configurations with the Erlangian distribution function. Material characteristics influence on behaviour and values of the averaged of admixture particle concentration is established.References
Keller J.B. Flow in random porous media // Transport in Porous Media. — 2001. — 43. — P. 395–406.
Zhu Y., Fox P.J. Smoothed particle hydrodynamics model for diffusion through porous media // Transport in Porous Media. — 2001. — 43. — P. 441–471.
Mikdam A., Makardi A., Ahzi S., Garmestani H, Li D.S., Remond Y. Effective conductivity in isotropic heterogeneous media using a strong-contrast statistical continuum theory // J. Mech. and Phys. of Solids. — 2009. — 57. — P. 76–86.
Королюк В.С., Портенко Н.И., Скороход А.В., Турбин А.Ф. Справочник по теории вероятности и математической статистике. — М.: Наука, 1985. — 640 с.
Мюнстер А. Химическая термодинамика. М.: Мир, 1971. — 295 с.
Чапля Є.Я., Чернуха О.Ю. Математичне моделювання дифузійних процесів у випадкових і регулярних структурах. — Київ: Наукова думка, 2009. — 302 с.
Краснов М.Л. Интегральные уравнения. — М.: Наука, 1975. — 300 с.
Владимиров В.С. Уравнения математической физики. — М.: Наука, 1976. — 527 с.
Рытов С.М., Кравцов Ю.А., Татарский В.И. Введение в статистическую радио-физику. Ч. ІІ, Случайные поля. — М.: Наука, 1978. — 436 с.
Справочник по специальным функциям / Под ред. М. Абрамовица и И. Стиган. — М.: Мир, 1979. — 830 с.
Лыков А.В. Теория теплопроводности. — М.: Высшая школа, 1978. — 463 с.
