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Matematicheskoe modelirovanie, 2001, Volume 13, Number 1, Pages 3–25 (Mi mm663)  

This article is cited in 8 scientific papers (total in 8 papers)

The generalized Darcy law of filtration as inquest of Stefan–Maxwell relations for heterogeneous medium

A. V. Kolesnichenkoa, V. M. Maksimovb

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
b Russian Academy of Science Oil and Research Institute
Abstract: The methods of non-equilibrium thermodynamics give Stefan–Maxwell relations for a heterogeneous medium and adjusted expression for a full flow of heat. Filtration movement of a multiphase mixture in a pore space of a rigid body are analysed on the basis of these relations (with capillary properties), provided that the pressure in phases do not coincide, and the generalized Darcy law of a filtration, spreading the classic theory of two-phase flow on a common case, is received. The algebraic equations are offered permitting to define factors of relative permeability of phases (for which there are no systematic experimental data in the literature) through binary factors of interphase friction.
Received: 02.03.2000
Bibliographic databases:
Language: Russian
Citation: A. V. Kolesnichenko, V. M. Maksimov, “The generalized Darcy law of filtration as inquest of Stefan–Maxwell relations for heterogeneous medium”, Mat. Model., 13:1 (2001), 3–25
Citation in format AMSBIB
\Bibitem{KolMak01}
\by A.~V.~Kolesnichenko, V.~M.~Maksimov
\paper The generalized Darcy law of filtration as inquest of Stefan--Maxwell relations for heterogeneous medium
\jour Mat. Model.
\yr 2001
\vol 13
\issue 1
\pages 3--25
\mathnet{http://mi.mathnet.ru/mm663}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1862302}
\zmath{https://zbmath.org/?q=an:1091.80500}
Linking options:
  • https://www.mathnet.ru/eng/mm663
  • https://www.mathnet.ru/eng/mm/v13/i1/p3
  • This publication is cited in the following 8 articles:
    1. Knyazeva A.G., Nazarenko N.N., “Coupled Model of a Biological Fluid Filtration Through a Flat Layer With Due Account For Barodiffusion”, Transp. Porous Media, 141:2 (2022), 331–358  crossref  mathscinet  isi
    2. A. V. Kolesnichenko, “Primenenie geterogennoi mekhaniki dlya modelirovaniya gazopylevogo ekzoplanetnogo diska. II. Turbulentnaya stadiya obrazovaniya subdiska”, Preprinty IPM im. M. V. Keldysha, 2021, 091, 43 pp.  mathnet  crossref
    3. A. V. Kolesnichenko, “Primenenie geterogennoi mekhaniki dlya modelirovaniya gazopylevogo protoplanetnogo diska. I. Laminarnaya stadiya obrazovaniya subdiska”, Preprinty IPM im. M. V. Keldysha, 2020, 039, 44 pp.  mathnet  crossref
    4. A. V. Kolesnichenko, “Kineticheskii vyvod novoi formy sootnoshenii Stefana–Maksvella i anizotropnykh koeffitsientov perenosa dlya chastichno ionizovannykh gazov vo vneshnem magnitnom pole”, Preprinty IPM im. M. V. Keldysha, 2017, 045, 35 pp.  mathnet  crossref
    5. Kobchikova P.P., Doroginitskii M.M., Fattakhov A.V., Kosarev V.E., Murzakaev V.M., “The Study of Water Saturation Process of Dolomite Core Under Atmospheric Pressure By Mri Method”, Uchenye Zap. Kazan. Univ.-Ser. Estestvennye Nauki, 159:4 (2017), 618–628  isi
    6. Knyazeva A.G., Demidov V.N., “Koeffitsienty perenosa dlya trekhkomponentnogo deformiruemogo splava”, Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2011, no. 3, 84–99  elib
    7. Kolesnichenko, AV, “Fundamentals of the mechanics of heterogeneous media in the circumsolar protoplanetary cloud: The effects of solid particles on disk turbulence”, Solar System Research, 40:1 (2006), 1  crossref  adsnasa  isi  elib  scopus
    8. Kolesnichenko, AV, “A synergetic approach to the description of advanced turbulence”, Solar System Research, 36:2 (2002), 107  crossref  mathscinet  adsnasa  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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