Journal of Fluid Mechanics

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

Ross C.  Kerr a1p1, Andrew W.  Woods a1a2, M. Grae  Worster a1p2 and Herbert E.  Huppert a1a2
a1 Department of Applied Mathematics and Theoretical Physics.
a2 Institute of Theoretical Geophysics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK

Article author query
kerr rc   [Google Scholar] 
woods aw   [Google Scholar] 
worster mg   [Google Scholar] 
huppert he   [Google Scholar] 


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 [script G] 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.

(Published Online April 26 2006)
(Received June 22 1989)

p1 Present address: Research School of Earth Sciences, ANU, GPO Box 4. Canberra, ACT 2601, Australia.
p2 Present address: Departments of Engineering Sciences and Applied Mathematics, and Chemical Engineering, Northwestern University, Evanston, IL 60208, USA.