Journal of Engineering Mathematics

, Volume 46, Issue 1, pp 1–32 | Cite as

The selection of Saffman-Taylor fingers by kinetic undercooling

  • S.J. Chapman
  • J.R. King


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.

asymptotics beyond-all-orders finger selection Hele-Shaw kinetic undercooling 


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© Kluwer Academic Publishers 2003

Authors and Affiliations

  • S.J. Chapman
    • 1
  • J.R. King
    • 2
  1. 1.OxfordUnited Kingdom
  2. 2.Department of Theoretical MechanicsUniversity of NottinghamNottinghamUnited Kingdom

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