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Solidification of an alloy cooled from above Part 2. Non-equilibrium interfacial kinetics

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 model developed in Part 1 for the solidification and convection that occurs when an alloy is cooled from above is extended to investigate the role of disequilibrium at the mush–liquid interface. Small departures from equilibrium are important because in a convecting system an interfacial temperature below its equilibrium value can drive the bulk temperature of the melt below its liquidus. This behaviour is observed in experiments and can result in crystallization within and at the base of the convecting melt. The additional crystals formed in the interior can settle to the base of the fluid and continue to grow, causing the composition of the melt to change. This ultimately affects the solidification at the roof. The effects of disequilibrium are explored in this paper by replacing the condition of marginal equilibrium at the interface used in the model of Part 1 with a kinetic growth law of the form $\dot{h}_1 = {\cal G}\delta T$, where $\dot{h}_1$ is the rate of advance of the mush–liquid interface, δT is the amount by which the interfacial temperature is below the liquidus temperature of the melt and [Gscr ] is an empirical constant. This modification enables the model to predict very accurately both the growth of the mushy layer and the development of supersaturation in the isopropanol experiments described in Part 1. An additional series of experiments, using aqueous solutions of sodium sulphate, is presented in which the development of supersaturation leads to the internal nucleation and growth of crystals. A further extension of the model is introduced which successfully accounts for this internal crystal growth and the changing composition of the melt. We discuss the implications of this work for geologists studying the formation of igneous rocks. Important conclusions include the facts that cooling the roof of a magma chamber can lead to crystallization at its floor and that vigorous convection can occur in a magma chamber even when there is no initial superheat.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 331 - 348
Copyright
© 1990 Cambridge University Press

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References

Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids. Oxford University Press.
Chen, C. F. & Turner, J. S. 1980 Crystallization in a double-diffusive system. J. Geophys. Res. 85, 2573–2593.Google Scholar
Denton, R. A. & Wood, I. R. 1979 Turbulent convection between two horizontal plates. Intl J. Heat Mass Transfer 22, 1339–1346.Google Scholar
Flood, S. C. & Hunt, J. D. 1987 A model of a casting. Appl. Sci. Res. 44, 27–42.Google Scholar
Glicksman, M. E. & Voorhees, P. W. 1984 Ostwald ripening and relaxation in dendritic structures. Metall. Trans. 15, 995–1001.Google Scholar
Huppert, H. E. & Worster, M. G. 1985 Dynamic solidification of a binary melt. Nature 314, 703–707.Google Scholar
Kaye, G. W. C. & Laby, T. H. 1973 Tables of Physical and Chemical Constants and some Mathematical Functions. Longman.
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1989 Disequilibrium and macrosegregation during the solidification of a binary melt. Nature 340, 357–362.Google Scholar
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1990a Solidification of an alloy from above. Part 1. Equilibrium growth. J. Fluid Mech. 216, 323–342.Google Scholar
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1990b Solidification of an alloy from above. Part 3. Compositional stratification within the solid. J. Fluid Mech. 218, 337–354.Google Scholar
Kurz, W. & Fisher, D. J. 1986 Fundamentals of Solidification. Trans. Tech. Publications.
Turcotte, D. L. & Schubert, G. 1982 Geodynamics. John Wiley & Sons.
Turner, J. S., Huppert, H. E. & Sparks, R. S. J. 1986 Komatiites II: Experimental and theoretical investigations of post-emplacement cooling and crystallization. J. Petrol. 27, 397–437.Google Scholar
Washburn, E. W. (ed.) 1926 International Critical Tables of Numerical Data: Physics, Chemistry and Technology. National Academic Press.
Weast, R. C. (ed.) 1971 CRC Handbook of Chemistry and Physics. The Chemical Rubber Co.
Woods, A. W. & Huppert, H. E. 1989 The growth of compositionally stratified solid above a horizontal boundary. J. Fluid Mech. 199, 29–53.Google Scholar
Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.Google Scholar