On small-time similarity-solution behaviour in the solidification shrinkage of binary alloys

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Abstract

In the one-dimensional solidification of a binary alloy undergoing shrinkage, there is a relative motion between solid and liquid phases in the mushy zone, leading to the possibility of macrosegregation; thus, the problem constitutes an invaluable benchmark for the testing of numerical codes that model these phenomena. Here, we revisit an earlier obtained solution for this problem, that was posed on a semi-infinite spatial domain and valid for the case of low superheat, with a view to extending it to the more general situation of a finite spatial domain, arbitrarily large superheat and both eutectic and non-eutectic solidification. We find that a similarity solution is available for short times which contains a boundary layer on the liquid side of the mush-liquid interface; this solution is believed to constitute the correct initial condition for the subsequent numerical solution of the full non-similar problem, which is deferred to future work.

Original languageEnglish
JournalEuropean Journal of Applied Mathematics
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • Dimensional analysis and similarity
  • Dynamics of phase boundaries
  • Key words:
  • Moving boundary problems

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