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Melting and dissolving

Published online by Cambridge University Press:  26 April 2006

Andrew W. Woods
Andrew W. Woods
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

The diffusion-governed melting that occurs when a binary melt is placed in contact with a pure solid is described. It is shown that if the melt superheat is much greater than the solid supercooling, the melt composition at the interface equals that of the solid and so the solid will melt at a rate determined by the thermal diffusivity. However, as the liquid superheat decreases, chemical disequilibrium may lower the interface temperature and so the melt composition at the interface increases above that of the solid, according to the liquidus relation. In this case the solid will dissolve into the liquid at a rate determined by the solutal diffusivity. These diffusion-governed solutions are used to infer the different modes of convection which may rise when the interface between the solid and the melt is horizontal.

The theory is generalized to investigate the diffusion-governed melting of a binary solid solution placed in contact with a binary melt. If the melt superheat is sufficient then the rate of phase change is again determined by the thermal diffusivity. In this case, owing to the very small solutal diffusivity in both the solid and the liquid, the melt composition at the interface is nearly equal to that of the solid. This corresponds to the melting regime. As the liquid superheat decreases, the rate of phase change decreases to values determined by the solutal diffusivity in the liquid, and the melt composition at the interface evolves towards that of the far-field liquid. This corresponds to the dissolving regime. As the melt superheat decreases further, with the solid still changing phase into liquid, then the melt composition at the interface remains approximately equal to that of the far-field melt. In each case, a compositional boundary layer develops in the solid, just ahead of the interface, in order to restore the solid at the interface to thermodynamic equilibrium. These different phase change regimes may arise if the composition of the solid is either higher or lower than that of the liquid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 429 - 448
Copyright
© 1992 Cambridge University Press

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