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Singular effects of surface tension in evolving Hele-Shaw flows

Published online by Cambridge University Press:  26 April 2006

Michael Siegel ,
Saleh Tanveer  and
Wei-Shen Dai
Michael Siegel
Affiliation:
Mathematics Department, New Jersey Institute of Technology, Newark, NJ 07102, USA
Saleh Tanveer
Affiliation:
Mathematics Department, Ohio State University, Columbus, OH 43210, USA
Wei-Shen Dai
Affiliation:
Electrotechnical Laboratory, Supermolecular Section, Tsubcuba, Ibaraki 305, Japan
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Abstract

In this paper, we present evidence to show that a smoothly evolving zero-surface tension solution of the Hele-Shaw equations can be singularly perturbed by the presence of arbitrarily small non-zero surface tension in order-one time. These effects are explained by the impact of ‘daughter singularities’ on the physical interface, whose formation was suggested in a prior paper (Tanveer 1993). For the case of finger motion in a channel, it is seen that the daughter singularity effect is strong enough to produce the transition from a finger of arbitrary width to one with the selected steady-state width in O(1) time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 323 , 25 September 1996 , pp. 201 - 236
Copyright
© 1996 Cambridge University Press

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