Journal of Engineering Mathematics
, Volume 46, Issue 1, pp 132
First online:
The selection of SaffmanTaylor fingers by kinetic undercooling
 S.J. ChapmanAffiliated with
 , J.R. KingAffiliated withDepartment of Theoretical Mechanics, University of Nottingham
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The selection of SaffmanTaylor fingers by surface tension has been widely studied. Here their selection is analysed by another regularisation widely adopted in studying otherwise illposed Stefan problems, namely kinetic undercooling. An asymptoticbeyondallorders 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 HeleShaw 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 HeleShaw problem with kinetic undercooling.
 Title
 The selection of SaffmanTaylor fingers by kinetic undercooling
 Journal

Journal of Engineering Mathematics
Volume 46, Issue 1 , pp 132
 Cover Date
 200305
 DOI
 10.1023/A:1022860705459
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 asymptotics
 beyondallorders
 finger selection
 HeleShaw
 kinetic undercooling
 Industry Sectors
 Authors

 S.J. Chapman ^{(1)}
 J.R. King ^{(2)}
 Author Affiliations

 1. 24–29 St. Giles', Oxford, OX1 3LB, United Kingdom
 2. Department of Theoretical Mechanics, University of Nottingham, Nottingham, NG7 2RD, United Kingdom