Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell |
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Authors: | D Crowdy H Kang |
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Institution: | (1) Department of Mathematics, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London, SW7 2BZ, U. K. e-mail: d.crowdy@ic.ac.uk, UK |
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Abstract: | Summary. The theory of algebraic curves and quadrature domains is used to construct exact solutions to the problem of the squeeze
flow of multiply-connected fluid domains in a Hele-Shaw cell. The solutions are exact in that they can be written down in
terms of a finite set of time-evolving parameters. The method is very general and applies to fluid domains of any finite connectivity.
By way of example, the evolution of fluid domains with two and four air holes are calculated explicitly. For simply connected
domains, the squeeze flow problem is well posed. In contrast, the squeeze flow problem for a multiply connected domain is
not necessarily well-posed and solutions can break down in finite time by the formation of cusps on the boundaries of the
enclosed air holes.
Received September 20, 2000; accepted September 10, 2001 Online publication November 5, 2001 |
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