Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-28T20:07:55.233Z Has data issue: false hasContentIssue false

Darcy's law for slow viscous flow past a stationary array of bubbles

Published online by Cambridge University Press:  14 November 2011

Robert Lipton
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A.
Marco Avellaneda
Affiliation:
Courant Institute of Mathematical Sciences, New York, NY 10012, U.S.A.

Synopsis

We examine slow viscous flow past a concentrated bed of small stationary viscous bubbles of a second fluid, and derive Darcy's law relating the average fluid velocity to the overall pressure gradient and body force.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Allaire, G.. Homogenization of Stokes flow in a connected porous medium. Asymptotic Analysis (to appear).Google Scholar
2Bensoussan, A., Lions, J. L. and Papanicolaou, G.. Asymptotic Analysis for Periodic Structures (Amsterdam: North-Holland, 1978).Google Scholar
3Cox, R. G.. The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 37(3) (1969), 601623.CrossRefGoogle Scholar
4Keller, J. B., Rubenfield, L. A. and Molyneux, J. E.. Extremum principles for slow viscous flows with application to suspensions. J. Fluid Mech. 30 (1967), 97125.CrossRefGoogle Scholar
5Schowalter, W. R., Chaffey, C. E. and Brenner, H.. Rheological behavior of a dilute emulsion. J. Colloid Interface Sci. 26 (1968), 152160.CrossRefGoogle ScholarPubMed
6Tartar, L.. Appendix. In Nonhomogeneous Media and Vibration Theory, ed. Sanchez-Palencia, E., Lecture Notes in Physics 127 (Berlin: Springer-Verlag, 1980).Google Scholar
7Taylor, G. I.. The viscosity of a fluid containing small drops of another fluid. Proc. Roy. Soc. London Ser. A. 138 (1932), 4148.Google Scholar
8Temam, R.. Navier–Stokes Equations (Amsterdam: North-Holland, 1984).Google Scholar