Authors: Daria Yu. HANUKAEVA graduated from MIPT in 1999. She is Ph.D. in Physical and Mathematical Sciences, Associate Professor of the Department of Mathematics. She is author of more than 30 scientific papers in the field of mechanics and mathematics.
E-mail: knanuk@yandex.ru
Anatoly N.FILIPPOV was born in 1960, graduated from the M.V. Lomonosov Moscow State University in 1982. He is Doctor of Physical and Mathematical Sciences, Professor of the Department of Mathematics. He is author of over 250 scientific papers in the field of physical-chemical mechanics, colloid chemistry and mathematics.
E-mail filippov.a@gubkin.ru
Abstract: The flow of viscous incompressible fluid under constant pressure gradient in the long flat fissure and cylindrical channel filled with porous material is considered. The qualitative and quantitative analysis of analytical solutions of the cor-responding boundary value problems is carried out. The size of the near wall flow, where the law of Darcy is violated, is estimated. The conclusion about the appropriateness of the Brinkman approach in a number of practically important cases is made.
Index UDK: УДК 532.546.2
Keywords: filtration of viscous fluid, Brinkman media
Bibliography:
1. Nield D.A., Bejan A. Convection in porous media. — 3rd ed. — New York: Springer, 2006. — 654 p.
2. Brinkman H.C. A calculation of the viscous force exerted by a flowing fluid in a dense swarm of particles. App. Sci. Res. (London), 1947, vol. A1, р. 27–34.
3. Ochoa-Tapia J.A., Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid I. Theoretical development. Int. J. Heat Mass Transfer, 1995, vol. 38, р. 2635–2646.
4. Starov V.M., Zhdanov V.G. Effective properties of suspensions/emulsions, porous and composite materials. Advances Colloid and Interface Sci, 2008, vol. 137, p. 2–19.
5. Barenblatt G.I., Entov V.M., Ryzhik V.M. Theory of fluid flows through natural rocks. Dordrecht: Kluwer Academic Publishers, 1990, 395p. (Russ. ed.: Barenblatt G.I., Entov V.M., Ryzhik V.M. Dvizhenie zhidkostej i gazov v prirodnyh plastah. Moscow, Nedra, 1984. 211 p.)
6. Auriault J.-L. On the domain of validity of Brinkman’s equation. Transp. Porous Med., 2009, vol. 79, p. 215–223.
7. Kumar S., Zimmerman R.W., Bodvarsson G.S. Permeability of fractures with cylindrical asperities. Fluid Dynam. Res., 1991, vol. 7, p. 131.
8. Brinkman H.C. Problems of fluid flows through swarms of particles and through macro-molecules in solution. Research (London), 1949, vol. 2, p. 190–194.
9. Vasin S.I. and Filippov A.N. Permeability of Complex Porous Media. Colloid Journal, 2009, vol. 71, p. 31–45.
10. Carman P.C. Flow of gases through porous media. New York: Academic Press, 1956, 182 p.
11. Filippov A.N., Khanukaeva D.Yu., Vasin S.I., Sobolev V.D., Starov V.M. Liquid Flow inside a Cylindrical Capillary with Walls Covered with a Porous Layer (Gel). Colloid Journal, 2013, vol. 75, no. 2, pp. 214-225.