TY - JOUR

T1 - On small-time similarity-solution behaviour in the solidification shrinkage of binary alloys

AU - Assunção, M.

AU - Vynnycky, M.

AU - Mitchell, S. L.

N1 - Publisher Copyright:
© The Author(s) 2020. Published by Cambridge University Press.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Dimensional analysis and similarity

KW - Dynamics of phase boundaries

KW - Key words:

KW - Moving boundary problems

UR - http://www.scopus.com/inward/record.url?scp=85083885560&partnerID=8YFLogxK

U2 - 10.1017/S0956792520000091

DO - 10.1017/S0956792520000091

M3 - Article

AN - SCOPUS:85083885560

SN - 0956-7925

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

ER -