Determination of the concentration and absorption of impurity microparticles during movement of liquid in a porous body

Authors

  • Богдан Гера

DOI:

https://doi.org/10.15407/fmmit2025.41.93

Keywords:

концентрація мікрочастинок, абсорбція, дифузія, адвекція

Abstract

The formulation of the problem of determining the concentration function of impurity components during their convective transfer in a homogeneous porous body and the distribution density of absorbed microparticles until the maximum permissible limit is reached is proposed. Using operational methods, a solution to the one-dimensional initial-boundary value problem in the half-space region is obtained at a given constant concentration of microparticles at the boundary. The results of calculations of the concentration and density of microparticles absorbed by the body matrix at small values of the diffusion coefficient, as well as in its absence, are presented. The obtained results are analyzed

References

M.Th. van Genuchten, Convective-dispersive transport of solutes involved in sequential first-order decay reactions, Comput. Geosci. 11 (2) (1985) 129-147. https://doi.org/10.1016/0098-3004(85)90003-2

J.S. Pérez Guerrero, L.C.G. Pimentel, T.H. Skaggs, M.Th. van Genuchten. Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique // Int. Journal of Heat and Mass Transfer 52 (2009) 3297-3304 https://doi.org/10.1016/j.ijheatmasstransfer.2009.02.002

Cristhian R. Quezada, T. Prabhakar Clement, Kang-Kun Lee. Generalized solution to multi-dimensional multi-species transport equations coupled with a first-order reaction network involving distinct retardation factors // Advances in Water Resources, Volume 27, Issue 5, May 2004, Pages 507-520 https://doi.org/10.1016/j.advwatres.2004.02.013

Chaplya Y., Chernukha O., Bilushchak Y. et al. Advanced approach to mathematical modeling of the impurities diffusion in the process of water softening with limited particles sorption. Sci Rep 15, 5269 (2025). https://doi.org/10.1038/s41598-025-88735-5

Carslaw H.S., Jaeger J.C. Conduction of heat in solids. Oxford university press, 1959. - 517 p.

Harry Bateman. Tables of integral transforms, Vol. 1, New York: McGraw-Hill Book Company, 1954 - 401 p

Ogata A., Banks R.B. A solution of the differential equation of longitudinal dispersion in porous mediums, US Geological Survey, Professional Paper 411-A, 1961. 13 p https://doi.org/10.3133/pp411A

Stanley J.Farlow. Partial differential equation for scientists and engineers. Wiley, 1982. - 402 p.

Published

2025-12-26

How to Cite

Гера, Б. (2025). Determination of the concentration and absorption of impurity microparticles during movement of liquid in a porous body. PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, (41), 93–102. https://doi.org/10.15407/fmmit2025.41.93