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Viscous fingering in Hele-Shaw cells

Published online by Cambridge University Press:  21 April 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Applied Mathematics, 217-50, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (Hele-Shaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a less-viscous fluid drives a more-viscous one. The status of the problem is reviewed and progress with the thirty-year-old problem of explaining the shape and stability of the fingers is described. The paradoxes and controversies are both mathematical and physical. Theoretical results on the structure and stability of steady shapes are presented for a particular formulation of the boundary conditions at the interface and compared with the experimental phenomenon. Alternative boundary conditions and future approaches are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 73 - 94
Copyright
© 1986 Cambridge University Press

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