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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(3):455-482; doi:10.1093/qjmam/56.3.455
© 2003 by Oxford University Press
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Extinction Behaviour of Contracting Bubbles in Porous Media

S. W. Mccue1, J. R. King1 and D. S. Riley1

( 1 Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD )

This paper is concerned with bubble contraction in porous media otherwise filled with viscous fluid. We suppose that an external pressure is applied to the (fixed) boundary of a porous medium, forcing a bubble to contract towards a point. By using the Baiocchi transform, we are able to give a rather complete asymptotic description of the process at times just before the bubble vanishes. The application of time-reversal to the results leads to implications for bubble nucleation.

Received 30 January 2002. Revised 10 February 2003.


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