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J. Fluid Mech. (2003), vol. 483, pp. 165197. c 2003 Cambridge University Press DOI: 10.1017/S0022112003004129 Printed in the United Kingdom
 

Summary: J. Fluid Mech. (2003), vol. 483, pp. 165197. c 2003 Cambridge University Press
DOI: 10.1017/S0022112003004129 Printed in the United Kingdom
165
A model for diffusion-controlled solidification of
ternary alloys in mushy layers
By D. M. ANDERSON
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
(Received 30 July 2002 and in revised form 26 December 2002)
We describe a model for non-convecting diffusion-controlled solidification of a ternary
(three-component) alloy cooled from below at a planar boundary. The modelling
extends previous theory for binary alloy solidification by including a conservation
equation for the additional solute component and coupling the conservation equations
for heat and species to equilibrium relations from the ternary phase diagram. We
focus on growth conditions under which the solidification path (liquid line of descent)
through the ternary phase diagram gives rise to two distinct mushy layers. A primary
mushy layer, which corresponds to solidification along a liquidus surface in the ternary
phase diagram, forms above a secondary (or cotectic) mushy layer, which corresponds
to solidification along a cotectic line in the ternary phase diagram. These two mushy
layers are bounded above by a liquid layer and below by a eutectic solid layer. We
obtain a one-dimensional similarity solution and investigate numerically the role of

  

Source: Anderson, Daniel M. - Department of Mathematical Sciences, George Mason University
Huppert, Herbert - Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Worster, M. Grae - Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

 

Collections: Geosciences; Mathematics