Hostname: page-component-76d6cb85b7-lcgwf Total loading time: 0 Render date: 2026-07-23T20:45:21.384Z Has data issue: false hasContentIssue false
  • English
  • Français

The rapid advance and slow retreat of a mushy zone

Published online by Cambridge University Press:  25 March 2011

NICHOLAS R. GEWECKE  and
TIM P. SCHULZE
NICHOLAS R. GEWECKE*
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-0614, USA
TIM P. SCHULZE
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-0614, USA
*
†Email address for correspondence: gewecke@math.utk.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss a model for the evolution of a mushy zone which forms during the solidification of a binary alloy cooled from below in a tank with finite height. Our focus is on behaviours of the system that do not appear when either a semi-infinite domain or negligible solute diffusion is assumed. The problem is simplified through an assumption of negligible latent heat, and we develop a numerical scheme that will permit insights that are critical for developing a more general procedure. We demonstrate that a mushy zone initially grows rapidly, then slows down and eventually retreats slowly. The mushy zone vanishes after a long time, as it is overtaken by a slowly growing solid region at the base of the tank.

JFM classification

Phase change: Solidification/melting

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 227 - 243
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Anderson, D. M. 2003 A model for diffusion-controlled solidification of ternary alloys in mushy layers. J. Fluid Mech. 483, 165–197.CrossRefGoogle Scholar
Davis, S. H. 2001 Theory of Solidification. Cambridge University Press.CrossRefGoogle Scholar
Evans, L. C. 1998 Partial Differential Equations. American Mathematical Society.Google Scholar
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1990 Solidification of an alloy cooled from above. Part 1. Equilibrium growth. J. Fluid Mech. 216, 323–342.CrossRefGoogle Scholar
Langer, J. S. 1980 Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52, 1–28.CrossRefGoogle Scholar
Peppin, S. S. L., Aussillous, P., Huppert, H. E. & Worster, M. G. 2007 Steady-state mushy layers: experiments and theory. J. Fluid Mech. 570, 69–77.CrossRefGoogle Scholar
Peppin, S. S. L., Huppert, H. E. & Worster, M. G. 2008 Steady-state solidification of aqueous ammonium chloride. J. Fluid Mech. 599, 465–476.CrossRefGoogle Scholar
Schulze, T. P. & Worster, M. G. 1999 Weak convection, liquid inclusions and the formation of chimneys in mushy layers. J. Fluid Mech. 388, 197–215.CrossRefGoogle Scholar
Schulze, T. P. & Worster, M. G. 2005 A time-dependent formulation of the mushy-zone free-boundary problem. J. Fluid Mech. 541, 193–202.CrossRefGoogle Scholar
Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.CrossRefGoogle Scholar
Worster, M. G. 1991 Natural convection in a mushy layer. J. Fluid Mech. 224, 335–359.CrossRefGoogle Scholar
Worster, M. G. 1997 Convection in mushy layers. Annu. Rev. Fluid Mech. 29, 91–122.CrossRefGoogle Scholar
Supplementary material: PDF

Gewecke and Schulze supplementary material

Appendix

Download Gewecke and Schulze supplementary material(PDF)
PDF 55.1 KB