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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(3):361-379; doi:10.1093/qjmam/56.3.361
© 2003 by Oxford University Press
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Mushy Regions in Negative Squeeze Films

J. R. Ockendon1, S. D. Howison1 and A. A. Lacey2

( 1 Mathematical Institute, Oxford University, 24–29 St Giles', Oxford OX1 3LB 2 Department of Mathematics, Heriot–Watt University, Riccarton, Edinburgh EH14 4AS )

An elegant experiment described by Hayes and Feiten in 1964 suggests a novel free boundary model for the evolution of a mushy region in a negative squeeze film. The mushy region nucleates when the plates enclosing the film are pulled apart sufficiently rapidly for the pressure to drop to a critical value at some point of the film. On the basis of an earlier one-dimensional analysis, a complementarity model is proposed for quite general mush evolutions and a regularization of this model is studied analytically and numerically.

Received 17 November 2001. Revised 19 November 2002.


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