The Mathematical Institute, University of Oxford, Eprints Archive

The selection of Saffman-Taylor fingers by kinetic undercooling

Chapman, S. J. and King, J. R. (2003) The selection of Saffman-Taylor fingers by kinetic undercooling. Journal of Engineering Mathematics, 46 (1). pp. 1-32. ISSN 0022-0833


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The selection of Saffman-Taylor fingers by surface tension has been widely studied. Here their selection is analysed by another regularisation widely adopted in studying otherwise ill-posed Stefan problems, namely kinetic undercooling. An asymptotic-beyond-all-orders analysis (which forms the core of the paper) reveals for small kinetic undercooling how a discrete family of fingers is selected; while these are similar to those arising for surface tension, the asymptotic analysis exhibits a number of additional subtleties. In Appendix 1 a description of some general features of the Hele-Shaw problem with kinetic undercooling and an analysis of the converse limit in which kinetic undercooling effects are large are included, while Appendix 2 studies the role of exponentially small terms in a simple linear problem which clarifies the rather curious behaviour at the origin of Stokes lines in the Hele-Shaw problem with kinetic undercooling.

Item Type:Article
Subjects:O - Z > Partial differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:300
Deposited By: Jon Chapman
Deposited On:04 Oct 2006
Last Modified:29 May 2015 18:19

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