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Creeping flow in two-dimensional networks

Published online by Cambridge University Press:  20 April 2006

Joel Koplik
Joel Koplik
Affiliation:
Schlumberger-Doll Research, P.O. Box 307, Ridgefield, Connecticut 06877, U.S.A.
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Abstract

We discuss creeping incompressible fluid flow in two-dimensional networks consisting of regular lattice arrays of variable-sized channels and junctions. The intended application is to low-Reynolds-number flow in models of porous media. The flow problem is reduced to an analogue linear-network problem and is solved by numerical matrix inversion. It is found that ‘effective-medium theory’ provides an excellent approximation to flow in such networks. Various qualitative features of such flows are discussed, and an elegant general form for the absolute permeability is derived. The latter, and the effective-medium approximation, are equally applicable to three-dimensional networks.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 219 - 247
Copyright
© 1982 Cambridge University Press

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