Modeling of the Flows of Admixtures in a Random Layered Strip with Probable Arrangement of Inclusions Near the Boundaries of the Body
- 4 Downloads
We study the random flow of admixtures in a two-phase stochastically inhomogeneous strip with the most probable arrangement of inclusions in the vicinity of the surfaces of the body. A mathematical model is formulated for the function of diffusion flow with nonzero constant initial concentration. A random diffusion flow is represented in the form of a Neumann series. The procedure of averaging of the random mass flow over the ensemble of phase configurations with arcsine distribution function is performed. The influence of the characteristics of the medium on the distribution of mass flow is analyzed. It is shown that if the diffusion coefficient of admixtures in the inclusion is higher than for the matrix, then the increase in the characteristic thickness of the layers causes a decrease in the value of the diffusion flow, whereas the mass flow in the entire body increases with the volume fraction of the inclusions.
Unable to display preview. Download preview PDF.
- 1.A. E. Davydok, “Simulation and investigation of the pairwise mutual influence of layered inclusions and the mass flow in a randomly inhomogeneous strip with beta-distribution of the phases,” Prikl. Probl. Mekh. Mat., Issue 12, 146–153 (2014).Google Scholar
- 4.M. L. Krasnov, Integral Equations. Introduction to the Theory [in Russian], Nauka, Moscow (1975).Google Scholar
- 7.E. Ya. Chaplya and O. Yu. Chernukha, Mathematical Modeling of Diffusion Processes in Random and Regular Structures [in Ukrainian], Naukova Dumka, Kiev (2009).Google Scholar
- 8.O. Yu. Chernukha, Yu. I. Bilushchak, and A. E. Chuchvara, Modeling of Diffusion Processes in Stochastically Inhomogeneous Layered Structures [in Ukrainian], Rastr-7, Lviv (2016).Google Scholar
- 9.Ch. Bergins, S. Crone, and K. Strauss, “ Multiphase flow in porous media with phase change. Part II: Analytical solutions and experimental verification for constant pressure stream injection,” Transp. Porous Media, 60, No. 3, 275–300 (2005), https://doi.org/ https://doi.org/10.1007/s11242-004-5740-5
- 10.Y. Chaplya, O. Chernukha, and A. Davydok, “Mathematical modeling of random diffusion flows in two-phase multilayered stochastically nonhomogeneous bodies,” Task Quarter., 19, No. 3, 297–320 (2015).Google Scholar