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Surprises in viscous fingering

Published online by Cambridge University Press:  25 April 2000

S. TANVEER
Affiliation:
Mathematics Department, The Ohio State University, Columbus, OH 43210, USA

Abstract

In this paper, we review some aspects of viscous fingering in a Hele-Shaw cell that at first sight appear to defy intuition. These include singular effects of surface tension relative to the corresponding zero-surface-tension problem both for the steady and unsteady problem. They also include a disproportionately large influence of small effects like local inhomogeneity of the flow field near the finger tip, or of the leakage term in boundary conditions that incorporate realistic thin-film effects. Through simple explicit model problems, we demonstrate how such properties are not unexpected for a system approaching structural instability or ill-posedness.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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