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Solidification of a binary alloy of variable viscosity from a vertical boundary

Published online by Cambridge University Press:  26 April 2006

Richard A. Jarvise  and
Herbert E. Huppert
Richard A. Jarvise
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present address: Laboratoire de Dynamique des Systèmes Géologiques, Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cedex 05, France.
Herbert E. Huppert
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

We analyse the complete solidification from a side boundary of a finite volume of a binary alloy. Particular emphasis is placed upon the compositional stratification produced in the solid, the structure of which is determined by the competition between the rates of solidification and of laminar box filling by the fractionated fluid released at the solid/liquid interface. It is demonstrated by scaling arguments that numerical calculations performed at relatively low values of the Rayleigh and Lewis numbers may be used to describe equally well laboratory experiments previously performed at moderate Rayleigh and Lewis numbers and the high-Rayleigh-number, high-lewis-number convective regime expected during the solidification of a large magmatic body, provided that the balance between solidification and laminar box filling is maintained. This balance can be represented by a single dimensionless group of parameters. The boundary-layer analysis is extended to fluids whose viscosity is strongly dependent upon temperature and composition, and an effective viscosity is derived which may be used to describe both the magnitude and pattern of compositional stratification in the solid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 303 , 25 November 1995 , pp. 103 - 132
Copyright
© 1995 Cambridge University Press

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