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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2020, Volume 22, Number 2, Pages 208–224
DOI: https://doi.org/10.15507/2079-6900.22.202002.208-224
(Mi svmo770)
 

Mathematical modeling and computer science

Viscous fluid microflows in cells of a porous medium in the presence of a gradient pressure

M. S. Deryabinaa, S. I. Martynovb

a Yugra State University, Khanty-Mansiysk
b Surgut State University
References:
Abstract: A simulation of the flow of a viscous fluid with a given pressure gradient through a porous structure, which was represented as a system of fixed particles, was carried out. Inside the porous structure there are moving particles, which are markers of microflows in the cells. The viscous fluid flows along a flat wall bounding the porous structure on one side. The calculations take into account the hydrodynamic interaction of all particles, both moving and stationary between themselves and with the plane. Computer simulations of this kind of flows through model structures formed, respectively, of 441, 567 periodically and 478 randomly located motionless particles of effective size and different positions of the flat wall, were carried out. The size of the moving particles placed in a viscous liquid was 0.2 of the size of the effective particles. The results of numerical simulation showed that microflows with an opposite direction of velocity are realized inside the structure, which follows from Darcy's law. Such a complex dynamics of the flow inside the porous structure means that the use of averaged equations of fluid filtration gives an incorrect picture of the flow at the pore size and can serve as an explanation of the nonlinear dependence of the average filtration rate on the applied pressure gradient.
Keywords: numerical simulation, viscous fluid, porous structure, hydrodynamic interaction of particles, microflows.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-0007
Document Type: Article
UDC: 532.529:541.182
MSC: Primary 76D07; Secondary 76D09, 76D17
Language: Russian
Citation: M. S. Deryabina, S. I. Martynov, “Viscous fluid microflows in cells of a porous medium in the presence of a gradient pressure”, Zhurnal SVMO, 22:2 (2020), 208–224
Citation in format AMSBIB
\Bibitem{DerMar20}
\by M.~S.~Deryabina, S.~I.~Martynov
\paper Viscous fluid microflows in cells of a porous medium in the presence of a gradient pressure
\jour Zhurnal SVMO
\yr 2020
\vol 22
\issue 2
\pages 208--224
\mathnet{http://mi.mathnet.ru/svmo770}
\crossref{https://doi.org/10.15507/2079-6900.22.202002.208-224}
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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