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Viscous fingering in Hele-Shaw cells

Saffman, P. G. (1986) Viscous fingering in Hele-Shaw cells. Journal of Fluid Mechanics, 173 . pp. 73-94. ISSN 0022-1120. doi:10.1017/S0022112086001088.

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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.

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Additional Information:© 1986 Cambridge University Press. Reprinted with permission. (Received 24 March 1986) It is a pleasure to thank Dr. John McLean, Dr. Dan Meiron, Dr. Douglas Reinelt and Dr. Saleh Tanveer for many discussions on different aspects of Hele-Shaw fingering and dendritic pattern formation, and for their interest and contributions oft the understanding of a 30-year old problem. I wish to thank Professor L. Kadanoff for bringing the argument about limits on the value of the surface tension to my attention. This work was supported by the Department of Energy, Office of Basic Energy Sciences (DE-AT03-76ER72012). I also wish to thank the Exxon Educational Foundation for valuable support.
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Department of Energy (DOE) Office of Basic Energy ScienceDE-AT03-76ER72012
Exxon Education FoundationUNSPECIFIED
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ID Code:10133
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Deposited On:14 Apr 2008
Last Modified:08 Nov 2021 21:05

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