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Bubbles and Fingers in Hele-Shaw Cells

Saffman, P. G. (1990) Bubbles and Fingers in Hele-Shaw Cells. In: Nonlinear Structures in Physical Systems. Woodward Conference. Springer New York , New York, NY, pp. 3-10. ISBN 9781461280132.

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The phenomena of viscous fingering in the flow of immiscible fluids in Hele-Shaw cells is discussed. Early work is reviewed and the present state of the theory is examined. It appears that the selection mechanisms by which small surface tension effects choose a particular solution from the continuum of solutions which exist when surface tension is neglected are now basically well understood. There are some uncertainties with respect to anomalously thin fingers, but there is good evidence that three-dimensional effects on the boundary conditions at the interface will resolve these questions and perturbation theories have been developed to handle these cases. Good progress has been made with regard to the stability of fingers, but questions remain with respect to the nature of finite amplitude instabilities. The theory for bubble selection and stability has been carried out but significant disagreements exist here between theory and experiment, which are probably caused by uncertainty about the boundary conditions for a retreating interface.

Item Type:Book Section
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Additional Information:© Springer-Verlag New York, Inc. 1990.
Subject Keywords:Porous Medium; Capillary Number; Perturbation Expansion; Immiscible Fluid; Proper Boundary Condition
Series Name:Woodward Conference
Record Number:CaltechAUTHORS:20201008-131242243
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105934
Deposited By: George Porter
Deposited On:09 Oct 2020 14:12
Last Modified:16 Nov 2021 18:47

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