Geodesic
Development of mathematical model of component mass transfer of water-salt solution in heaving soils based on the kinetic theory of liquids
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 10 (2018) no. 1, pp. 37-44
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The reliability of engineering structures mostly depends on the possibility to resist adverse environmental factors. One of the most dangerous geological processes is frost heaving of soils, which is capable to develop a huge pressure and significant irregular vertical deformations. This processes is especially dangerous for non-rigid structures with a negative average annual temperature ($-6\dots-0,5^\circ$ C), for example, for underground gas and condensate pipelines. Pipelines has a strong bends in short sections under the influence of frost heaving pressure, that often leads to emergency incidents. To predict the frost heaving it is necessary to solve the problem of mass transfer of water-salt solution from thawed to frozen soil. Using the kinetic theory of fluid, the authors of the article developed a mathematical model of the mass transfer of water and salt in thawed, freezing and frozen soils. The model allow to determine in an explicit form the contribution of different mechanisms of mass transfer: thermal diffusion, concentration diffusion, and filtration. The equations of diffusion transport allow to take into account the unequal mobility of molecules in an adsorbed film. In addition, it was shown that the classical expression for the diffusion flux density is valid only in the particular case of equality of the diffusion coefficients of each com-ponent in accordance with the kinetic theory of the liquid.
Keywords: kinetic theory of liquids, mass transfer, matrix potential
Mots-clés : diffusion flow. 
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     title = {Development of mathematical model of component mass transfer of water-salt solution in heaving soils based on the kinetic theory of liquids},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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E. V. Markov; S. A. Pulnikov; A. D. Gerber. Development of mathematical model of component mass transfer of water-salt solution in heaving soils based on the kinetic theory of liquids. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 10 (2018) no. 1, pp. 37-44. http://geodesic.mathdoc.fr/item/VYURM_2018_10_1_a4/

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