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Solidification of an alloy cooled from above Part 1. Equilibrium growth

Published online by Cambridge University Press:  26 April 2006

Ross C. Kerr ,
Andrew W. Woods ,
M. Grae Worster  and
Herbert E. Huppert
Ross C. Kerr
Affiliation:
Department of Applied Mathematics and Theoretical Physics Present address: Research School of Earth Sciences, ANU, GPO Box 4, Canberra, ACT 2601, Australia.
Andrew W. Woods
Affiliation:
Department of Applied Mathematics and Theoretical Physics Institute of Theoretical Geophysics, University of Cambridge, Silver Street, Cambridge CB3 9EW. UK
M. Grae Worster
Affiliation:
Department of Applied Mathematics and Theoretical Physics Present address: Departments of Engineering Sciences and Applied Mathematics, and Chemical Engineering, Northwestern University, Evanston, IL 60208, USA.
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics Institute of Theoretical Geophysics, University of Cambridge, Silver Street, Cambridge CB3 9EW. UK
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Abstract

The interaction between the solidification and convection that occurs when a melt is cooled from above is investigated in a series of three papers. In these papers we consider a two-component melt that partially solidifies to leave a buoyant residual fluid. The solid forms a mushy layer of dendritic crystals, the interstices of which accommodate the residual fluid. The heat extraction through the upper boundary, necessary to promote solidification, drives convection at high Rayleigh numbers in the melt below the mushy layer. The convection enhances the heat transfer from the melt and alters the rate of solidification. In this paper the various phenomena are studied in a series of laboratory experiments in which ice is frozen from aqueous solutions of isopropanol. The experiments are complemented by the development of a general theoretical model in which the mush is treated as a continuum phase with thermodynamic properties that are functions of the local solid fraction. The model, which is based upon principles of equilibrium thermodynamics and local conservation of heat and solute, produces results in good agreement with the experimental data. Careful comparisons between this theory and experiments suggest the need to explore non-equilibrium effects, which are investigated in Parts 2 and 3.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 216 , July 1990 , pp. 323 - 342
Copyright
© 1990 Cambridge University Press

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