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Solid–mush interface conditions for mushy layers

Published online by Cambridge University Press:  16 November 2011

Nicholas R. Gewecke  and
Tim P. Schulze
Nicholas R. Gewecke*
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Tim P. Schulze
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-0614, USA
*
†Email address for correspondence: ngewecke@math.udel.edu
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Abstract

A subtle issue in the study of mushy zones which form during the solidification of binary alloys is that there are two distinct types of solid–mush interfaces which may occur. One of these is a eutectic front and the other is a front which separates the mushy layer and, assuming complete solute rejection, a layer of pure solid. For semi-infinite-domain configurations that admit similarity solutions, such as those at a uniform initial temperature and concentration with an imposed cold temperature at the lower boundary, only one of the two types appears, and the type of front is determined by the various parameters of the system. In a finite domain, it is possible for each type of front to appear at different times. Specifically, the advance of the eutectic front is restricted by the isotherm associated with the eutectic temperature, and the other front type will appear over a longer time scale. Leading up to the time when the front changes type, the concentration being frozen into the solid decreases. This process writes a history of the system into the solid.

JFM classification

Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 689 , 25 December 2011 , pp. 357 - 375
Copyright
Copyright © Cambridge University Press 2011

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