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The effect of surface tension on the shape of fingers in a Hele Shaw cell

McLean, J. W. and Saffman, P. G. (1988) The effect of surface tension on the shape of fingers in a Hele Shaw cell. In: Dynamics of Curved Fronts. Academic Press , San Diego, CA, pp. 175-189. ISBN 978-0-12-550355-6. http://resolver.caltech.edu/CaltechAUTHORS:20170802-083427552

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Abstract

The experimental results of Saffman & Taylor (1958) and Pitts (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed as the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions are compared with experimental results. The shapes of the profiles are very well predicted, but the dependence of finger width on surface tension is not quantitatively accurate, although the qualitative behaviour is correct. A conflict between the numerics and a formal singular perturbation analysis is noted but not resolved. The stability of the steady finger to small disturbances is also examined. Linearized stability analysis indicates that the two-dimensional fingers are not stabilized by the surface-tension effect, which disagrees with the experimental observations. A possible reason for the discrepancy between theory and experiment is suggested.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/B978-0-08-092523-3.50018-6DOIArticle
http://www.sciencedirect.com/science/article/pii/B9780080925233500186PublisherArticle
Additional Information:© 1988 Academic Press, Inc. Published by Elsevier Inc.
Record Number:CaltechAUTHORS:20170802-083427552
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170802-083427552
Official Citation:J.W. McLEAN and P.G. SAFFMAN, The effect of surface tension on the shape of fingers in a Hele Shaw cell, In Dynamics of Curved Fronts, edited by Pierre Pelcé,, Academic Press, San Diego, 1988, Pages 175-189, ISBN 9780125503556, https://doi.org/10.1016/B978-0-08-092523-3.50018-6. (http://www.sciencedirect.com/science/article/pii/B9780080925233500186)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79738
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Aug 2017 17:32
Last Modified:02 Aug 2017 17:32

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