Scientific and technical journal

«Proceedings of Gubkin University»

ISSN 2073-9028

Proceedings of Gubkin University

UDC: 532.546.2
DOI: -


Hanukaeva Daria Yu.1,
Filippov Anatoly N.1

1 Gubkin Russian State University of Oil and Gas

Keywords: filtration of viscous fluid, Brinkman media


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.


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. Баренблатт Г.И., Ентов В.М., Рыжик В.М. Движение жидкостей и газов в природных пластах. — М.: Недра, 1984. — 211 с.
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 macromolecules in solution. Research (London), 1949, vol. 2, p. 190–194.
9. Васин С.И., Филиппов А.Н. Проницаемость сложнопористых сред//Коллоидный журнал. — 2009. — Т. 71. — С. 149–163.
10. Carman P.C. Flow of gases through porous media. New York: Academic Press, 1956, 182 p.
11. Течение жидкости внутри цилиндрического капилляра, стенки которого покрыты пористым слоем (гелем)/А.Н. Филиппов, Д.Ю. Ханукаева, С.И. Васин, В.Д. Соболев, В.М. Старов//Коллоидный журнал. — 2013. — Т. 75. — С. 237–249.