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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2023, Volume 64, Issue 3, Pages 161–173
DOI: https://doi.org/10.15372/PMTF202215138 (Mi pmtf1315) 		 
Filtration of highly miscible liquids based on two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations

V. V. Shelukhina, V. V. Krut'kob, K. V. Trusovc

a Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Gazpromneft NTT, St. Petersburg, Russia
c Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.15372/PMTF202215138
Abstract: This paper presents the results of numerical analysis of the filtration equations for highly miscible liquids obtained by two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations for two-dimensional flows. It is shown that the permeability tensor is generally anisotropic. For one-dimensional flows, the miscibility dynamics is investigated, and it is shown that the displacement of one phase by injection of another phase can occur even in the absence of a pressure gradient in the sample.
Keywords: Navier–Stokes equations, Cahn–Hilliard equations, filtration of miscible liquids, two-scale homogenization.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FZMW-2020-0008
Received: 12.05.2022
Revised: 15.10.2022
Accepted: 28.11.2022
English version:
Journal of Applied Mechanics and Technical Physics, 2023, Volume 64, Issue 3, Pages 499–509
DOI: https://doi.org/10.1134/S0021894423030161
Bibliographic databases:
Document Type: Article
UDC: 532.546
Language: Russian
Citation: V. V. Shelukhin, V. V. Krut'ko, K. V. Trusov, “Filtration of highly miscible liquids based on two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations”, Prikl. Mekh. Tekh. Fiz., 64:3 (2023), 161–173; J. Appl. Mech. Tech. Phys., 64:3 (2023), 499–509
Citation in format AMSBIB
\Bibitem{SheKruTru23}
\by V.~V.~Shelukhin, V.~V.~Krut'ko, K.~V.~Trusov
\paper Filtration of highly miscible liquids based on two-scale homogenization of the Navier--Stokes and Cahn--Hilliard equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2023
\vol 64
\issue 3
\pages 161--173
\mathnet{http://mi.mathnet.ru/pmtf1315}
\crossref{https://doi.org/10.15372/PMTF202215138}
\elib{https://elibrary.ru/item.asp?id=53804239}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2023
\vol 64
\issue 3
\pages 499--509
\crossref{https://doi.org/10.1134/S0021894423030161}
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