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Parallel flow in Hele-Shaw cells

Published online by Cambridge University Press:  26 April 2006

M. Zeybek  and
Y. C. Yortsos
M. Zeybek
Affiliation:
Petroleum Engineering Program, Department of Chemical Engineering. University of Southern California, Los Angeles, CA 90089-1211, USA
Y. C. Yortsos
Affiliation:
Petroleum Engineering Program, Department of Chemical Engineering. University of Southern California, Los Angeles, CA 90089-1211, USA
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Abstract

We consider the parallel flow of two immiscible fluids in a Hele-Shaw cell. The evolution of disturbances on the fluid interfaces is studied both theoretically and experimentally in the large-capillary-number limit. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by a set of KdV and Airy equations. The waves are dispersive provided that the fluids have unequal viscosities and that the space occupied by the inner fluid does not pertain to the Saffman-Taylor conditions (symmetric interfaces with half-width spacing). Experiments conducted in a long and narrow Hele-Shaw cell appear to validate the theory in both the symmetric and the non-symmetric cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 421 - 442
Copyright
© 1992 Cambridge University Press

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