This paper presents a mathematical model of solute transport in a soil with account for nonisothermal moisture transfer. The model is based on the equations of convective diffusion, sorption kinetics, and two-phase filtration, on the isotherms of water sorption by the soil, and on the thermodynamic laws. A numerical analysis of the influence of various physical mechanisms on the process of mass transfer in the soil has been performed.
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References
C. W. Fetter, Contaminant Hydrogeology, Prentice-Hall Publishing Company (1998).
J. Bear and A. Verruijt, Modeling Groundwater Flow and Pollution, D. Reidel Publishing Co (1987).
J. Simunek, M. Th. van Genuchten, and M. Sejna, The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat and Multiple Solutes in Variably-Saturated Media, Version 3.0. Department of Environmental Sciences, University of California, Riverside (2005).
A. V. Luikov, Theory of Drying [in Russian], Énergiya, Moscow (1968).
A. S. Shubin, Influence of Temperature and Moisture Parameters on the Moisture Transfer [in Russian], Profizdat, Moscow (1958).
K. Bunzl, W. Kracke, and W. Schimmack, Vertical migration of 239,240Pu, 241Am, and 137Cs. Fallout in a forest soil under spruce, Analyst, No. 117, 469–473 (1992).
V. A. Knatko, A. G. Skomorokhov, V. D. Asimova, et al., Characteristics of 90Sr, 137Cs and 239,240Pu migration in undisturbed soils of southern Belarus after the Chernobyl accident, J. Environ. Radioactivity, 30, No 2, 185–196 (1996).
V. M. Nikolaevskii, Motion of Hydrocarbon Mixtures in a Porous Medium [in Russian], Nedra, Moscow (1968).
R. A. Poluéktov, A. G. Topazh, and V. Mirshel’, Comparison of empirical and theoretical approaches in mathematical modeling of agroecosystems using as an example photosynthesis, Mat. Modelir., 10, No. 7, 25–36 (1998).
E. V. Shtein, A Course in the Physics of Soils: Textbook [in Russian], Izd. MGU, Moscow (2005).
T. M. Roshchina, Adsorption phenomena and surface, Sorosovsk. Obrazov. Zh., No. 2, 89–94 (1998).
N. V. Pavlyukevich, Introduction to the Theory of Heat and Mass Transfer in Porous Media [in Russian], ITMO, Minsk (2001).
G. P. Brovka, Heat-and Mass Transfer in Freezing Natural Disperse Systems [in Russian], Nauka i Tekhnika, Minsk (1991).
G. P. Brovka, Calculation of convective transfer in water-soluble compounds with account for the sorption kinetics, Inzh.-Fiz. Zh., 74, No. 3, 25–29 (2001).
I. I. Lishtvan, G. P. Brovka, I. V. Dedyulya, and E. N. Rovdan, The characteristics of the sorption and migration of the radionuclides Cs-137 and Sr-90 in natural disperse systems, Vestsi Akad. Navuk Belarusi, Ser. Khim. Navuk, No. 4, 79–83 (1996).
V. M. Prokhorov (R. M. Aleksakhin Ed.), Migration of Radioactive Contaminants in Soils. Physicochemical Mechanisms and Modeling [in Russian], Énergiya, Moscow (1981).
G. Z. Serebryanyi and M. L. Zhemzhurov, Analytical model of migration of radionuclides in porous media, Inzh.-Fiz. Zh., 76, No. 6, 146–150 (2003).
A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii, et al. (I. S. Grigor’ev and E. Z. Meilikhov Eds.), Physical Quantities: Handbook [in Russian], Énergoatomizdat, Moscow (1991).
S. P. Kundas, N. N. Grinchik, and I. A. Gishkelyuk, A mathematical model of the migration of radionuclides in the soil, Vest. Polotsk. Gos. Univ., No. 3, 56–60 (2005).
S. Kundas, N. Grinchik, and I. Gishkeluk, Computer simulation of non-isothermal water and solute transport in soil, J. University Appl. Sci. Mittweida (Germany), No. 13, 27–30 (2005).
N. N. Grinchik, Processes of Transfer in Porous Media, Electrolytes, and Membranes [in Russian], ITMO, Minsk (1991).
M. P. Vukalovich, Tables of the Thermophysical Properties of Water and Steam [in Russian], Izd. Standartov, Moscow (1969).
O. Zenkevich and K. Morgan, Finite Elements and Approximation [in Russian], Mir, Moscow (1986).
Femlab 3.0. User’s Guide, Comsol, Los Angeles (2004).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 924–935, September–October, 2008.
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Gishkelyuk, I.A., Kundas, S.P. & Grinchik, N.N. Mathematical modeling of convective diffusion of soluble compounds in the soil at nonisothermal moisture transfer. J Eng Phys Thermophy 81, 963–975 (2008). https://doi.org/10.1007/s10891-009-0117-9
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DOI: https://doi.org/10.1007/s10891-009-0117-9