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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. (1981) The effect of surface tension on the shape of fingers in a Hele Shaw cell. Journal of Fluid Mechanics, 102 . pp. 455-469. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120718-151352644

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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:Article
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http://dx.doi.org/10.1017/S0022112081002735DOIUNSPECIFIED
http://journals.cambridge.org/abstract_S0022112081002735PublisherUNSPECIFIED
Additional Information:© 1981 Cambridge University Press. Received 24 June 1980; Published online 20 April 2006. This work was supported by the Department of Energy (Office of Basic Energy Sciences). We also wish to thank Control Data Corporation for the granting of time on their CYBER 203 computer at the C.D.C. Service Center, Arden Hills, Minnesota, which enabled us to implement Newton’s method for large matrices.
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Department of Energy (DOE) Office of Basic Energy SciencesUNSPECIFIED
Record Number:CaltechAUTHORS:20120718-151352644
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120718-151352644
Official Citation: J. W. McLean and P. G. Saffman (1981). The effect of surface tension on the shape of fingers in a Hele Shaw cell. Journal of Fluid Mechanics, 102 , pp 455-469 doi:10.1017/S0022112081002735
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32567
Collection:CaltechAUTHORS
Deposited By: Aucoeur Ngo
Deposited On:18 Jul 2012 22:34
Last Modified:26 Dec 2012 15:37

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