We propose a mathematical model of convective diffusion of impurity particles accompanied by sorption processes in a body formed by three contacting porous layers with different physical and chemical characteristics under the conditions of imperfect contact for the concentration on the interfaces. The analytic solution of the contact initial-boundary value problem of convective diffusion of impurity substances in a composite layer is obtained with the help of integral transformations over the spatial variable applied in each contacting layer separately. A system of integral equations for the functions of concentration of migrating particles on the interfaces is obtained and solved. The formulas for finding the concentrations of impurity particles sorbed on the skeleton of the three-layered porous body are obtained.
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Ya. Yo. Burak, B. P. Galapats, and E. Ya. Chaplya, “Deformation of electrically conducting solids taking into consideration heterodiffusion of charged impurity particles,” Fiz.-Khim. Mekh. Mater., 16, No. 5, 8–14 (1980); English translation: Sov. Mater. Sci., 16, No. 5, 395–400 (1981); https://doi.org/10.1007/BF00724467.
Ya. Yo. Burak, B. P. Galapats, and E. Ya. Chaplya, “Input equations for the process of deformation of electrically conducting solid solutions with regard for various ways of diffusion of impurity particles,” Mat. Met. Fiz.-Mekh. Polya, Issue 11, 60–66 (1980).
Ya. Yo. Burak, E. Ya. Chaplya, and O. Yu. Chernukha, Continual Thermodynamic Models of the Mechanics of Solid Solutions [in Ukrainian], Nauk. Dumka, Kyiv (2006).
T. A. Butina and V. M. Dubrovin, “On modeling of the behavior of porous materials in elements of multilayer structures under short-term loads,” Inzh. Zhurn.: Nauka Innov., No. 7 (19) (2013); https://doi.org/10.18698/2308-6033-2013-7-844.
V. A. Ditkin and A. P. Prudnikov, Integral Transformations and Operational Calculus [in Russian], Fizmatgiz, Moscow (1961).
M. Zhurba, Foundations of Tertiary Treatment Processes by Filtration, in: Heat and Mass Transfer in Capillary-Porous Bodies [in Russian], Nauka Tekh., Minsk (1965), pp. 60–73.
V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and Its Applications [in Russian], Nauka, Moscow (1978).
N. A. Martynenko and L. M. Pustylnikov, Finite Integral Transformations and Their Application to the Study of Systems with Distributed Parameters [in Russian], Nauka, Moscow (1986).
On the Direction of Normal for Surfaces and Shells; http://support.ptc.com/help/creo/creo_pma/russian/index.html#page/simulate/simulate/modstr/idealizations/reference/dir_surfshell.html.
M. G. Okhrimenko, I. D. Fartushnyi, and A. B. Kulyk, Ill-Posed Problems and Methods for Their Solution, Politekhnika, Kyiv (2016).
N. S. Sinyukov and T. I. Matviyenko, Topology [in Ukrainian], Vyshcha Shkola, Kyiv (1984).
I. Sneddon, Fourier Transforms, McGraw-Hill, New York (1951).
A. N. Tikhonov and V. Ya. Arsenin, Methods for the Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1979).
Ye. Ya. Chaplya and O. Yu. Chernukha, Mathematical Modeling of Diffusion Processes in Random and Regular Structures [in Ukrainian], Nauk. Dumka, Kyiv (2009).
B. S. Chernov, M. N. Bazlov, and A. I. Zhukov, Hydrodynamic Methods for Studying Wells and Reservoirs [in Russian], Gostoptekhizdat, Moscow (1960).
E. C. Aifantis and J. M. Hill, “On the theory of diffusion in media with double diffusivity. I. Basic mathematical results”, Quart. J. Mech. Appl. Math., 33, No. 1, 1–21 (1980); https://doi.org/10.1093/qjmam/33.1.1.
O. Chernukha, Yu. Bilushchak and B. Pakholok, “System approach to mathematical description of transport processes with chemical reaction in multiphase multicomponent body”, Proc. 2020 IEEE, 2nd Internat. Conf. on Systems Analysis & Intelligent Computing (SAIC), October 5–9, 2020, Kyiv, Ukraine (2020), pp. 144–149; https://doi.org/10.1109/SAIC51296.2020.9239181.
O. Chernukha, Yu. Bilushchak, N. Shakhovska, and R. Kulhanek, “A numerical method for computing double integrals with variable upper limits,” Mathematics, 10, No. 1, Article 108, 26 (2022); https://doi.org/10.3390/math10010108.
A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton (1998).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 64, No. 4, pp. 107–116, October–December, 2021.
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Chernukha, O.Y., Bilushchak, Y. Mathematical Modeling of the Processes of Convective Diffusion and Sorption in a Three-Layer Porous Body. I. Mass Transfer of Impurity Particles with a Porous Solution. J Math Sci 279, 247–259 (2024). https://doi.org/10.1007/s10958-024-07008-0
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DOI: https://doi.org/10.1007/s10958-024-07008-0