MSC2020 76D07, 76D09, 76D17
Viscous fluid microflows in cells of a porous medium in the presence of a gradient pressure
M. S. Deryabina1, S. I. Martynov2
| Annotation | 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. |
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| Keywords | numerical simulation, viscous fluid, porous structure, hydrodynamic interaction of particles, microflows |
1Member of the grant team of the Russian Foundation for Basic Research at Ugra State University (16 Chekhova st., Khanty-Mansiysk 628000, Russia), ORCID: https://orcid.org/0000-0003-4331-3675
2Chief Researcher, Surgut State University (1 Lenina av., Surgut 628412, Russia), Doctor of Physical and Mathematical Sciences, ORCID: https://orcid.org/0000-0001-6420-3315, martynovsi@mail.ru
Citation: M. S. Deryabina, S. I. Martynov, "[Viscous fluid microflows in cells of a porous medium in the presence of a gradient pressure]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:2 (2020) 208–224 (In Russian)
DOI 10.15507/2079-6900.22.202002.208-224
