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Solidification of an alloy cooled from above. Part 3. Compositional stratification within the solid

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, Australian National University, GPO Box 4, Canberra, 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: Department of Engineering Sciences and Applied Mathematics and Department of 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

This is the third of a series of papers which investigates the evolution of a binary alloy that is cooled from above and releases buoyant residual fluid as one component of the alloy is preferentially incorporated within the solid. This paper focuses on the compositional zonation that is produced when the melt is completely solidified. Parts 1 and 2 considered the temperature of the cooled boundary to be greater than the eutectic temperature of the alloy so that only partial solidification of the alloy could occur. Here we extend the study by investigating the effects that arise when the cooling temperature is less than the eutectic temperature. The formation of a completely solid layer results, which extends from the cooling plate down to a mushy zone of dendritic crystals and interstitial melt. The melt below this mushy layer is convectively unstable because it is cooled from above. This generates vigorous thermal convection. Eventually the melt becomes completely solidified and a compositionally zoned solid is formed. The solid below the cooling plate is shown to be of fixed bulk composition until it reaches the depth that the interface between the mushy layer and melt occupied when the melt first became saturated. Below this level, the composition of the solid decreases with depth until it merges into the solid growing from the floor, whose composition is nearly equal to that of the heavier component of the alloy. Results of laboratory experiments with aqueous solutions of sodium sulphate are in good agreement with our quantitative predictions. The model is used to give an interpretation of profiles of the composition of magnesium oxide found within solidified komatiite lavas.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 337 - 354
Copyright
© 1990 Cambridge University Press

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References

Ames, W. F.: 1977 Numerical Methods for Partial Differential Equations (2nd edn). Academic.
Arndt, N. T.: 1986 Differentiation of komatiite flows. J. Petrol. 27, 279–301.Google Scholar
Batchelor, G. K.: 1974 Transport properties of two phase materials with random structure. Ann. Rev. Fluid. Mech. 6, 227–255.Google Scholar
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
Donaldson, C. H.: 1982 Spinifex textured komatiites: a review of compositions and layering. In Komatiites (ed. N. T. Arndt & E. G. Nisbet), Chap. 16, pp. 213–244. Allen and Unwin.
Doremus, R. H.: 1985 Rates of Phase Transformations. Academic.
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. & Sparks, R. S. J. 1986 Komatiites I: eruption and flow. J. Petrol. 26, 694–725.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988 Melting the roof of a chamber containing a hot, turbulently convecting fluid. J. Petrol. 29, 559–624.Google Scholar
Huppert, H. E., Sparks, R. S. J., Wilson, J. R., Hallworth, M. A. & Leitch, A. M., 1987 Laboratory experiments with aqueous solutions modelling processes in a magma chamer II. Cooling and crystallization along inclined planes. In Origins of Igneous Layering (ed. I. Parsons), pp. 539–568. Reidel.
Huppert, H. E. & Worster, M. G., 1985 Dynamic solidification of a binary melt. Nature 314, 703–707.Google Scholar
Kerr, R. C. & Tait, S., 1986 Crystallisation and convection in a porous medium with application to layered igneous intrusions. J. Geophys. Res. 91, 3591–3608.Google Scholar
Kerr, R. C. & Turner, J. S., 1982 Layered convection and crystal layers in multi-component systems. Nature 298, 731–733.Google Scholar
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E., 1990a Solidification of an alloy cooled from above. Part 1. Equilibrium model. 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 cooled from above. Part 2. Non-equilibrium interfacial kinetics. J. Fluid Mech. 217, 331–348.Google Scholar
Kurz, W. & Fisher, D. J., 1986 Fundamentals of Solidification. Trans Tech Publications.
Martin, D. & Nokes, I., 1988 Crystal settling in a vigorously convecting magma chamber. Nature 332, 534–536.Google Scholar
Martin, D. & Nokes, R. I., 1989 A fluid-dynamical study of crystal settling in convecting magma chambers. J. Petrol. 30, 1471–1500.Google Scholar
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 (herein referred to as THS).Google Scholar
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 by cooling a binary alloy from below. J. Fluid Mech. 199, 29–55.Google Scholar
Worster, M. G.: 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.Google Scholar
Worster, M. G., Huppert, H. E. & Sparks, R. S. J. 1990 Convection and crystallization in magma cooled from above. Earth Planet. Sci. Lett. (in press).Google Scholar