Evolution of flat crystallisation front in forced hydrodynamic flow - some explicit solutions

L. J. Cummings, K. Kornev

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider the two-dimensional solidification/melting (one problem being the time-reversal of the other) of dendrites in an imposed hydrodynamic flow with a stagnation point. Complex variable methods are used, and a new class of solutions is presented (neglecting surface effects at the interface). These solutions can exhibit the interesting phenomenon of transient singularity formation in the dendrite boundary; a cusp forms in the boundary, but then instantly smooths and the solution can be continued.

Original languageEnglish (US)
Pages (from-to)33-47
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume127
Issue number1-2
DOIs
StatePublished - Mar 1 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Crystallisation
  • Dendrite
  • Hydrodynamic flow
  • Melting

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