We investigate interactions between interfacial disequilibrium and compositional convection during the freezing of an alloy from below to form a mushy layer. A theoretical model is developed in which a stagnant mushy layer underlies a melt that is convecting vigorously, driven by compositional gradients associated with undercooling at the mush-liquid interface. In a series of laboratory experiments, we measure the interfacial undercooling in aqueous solutions of ammonium chloride contaminated to varying degrees by copper sulphate. It has recently been found (Huppert & Hallworth 1993) that a small amount of copper sulphate added to a solution of ammonium chloride significantly inhibits the formation of chimneys in the mushy layer that forms when the solution is cooled below its liquidus. It is our thesis that this phenomenon can be explained in large part by the consequences of the interactions between compositional convection and interfacial undercooling that are investigated herein. The measured undercooling is a function of the rate of advance of the interface and is found to be a very strong, increasing function of the concentration of copper sulphate in solution. The theoretical model is evaluated using parameter values appropriate to the experimental system and it is found that the transient development of the mushy layer depends significantly on the level of interfacial disequilibrium. In particular, it is predicted that the time taken for the Rayleigh number associated with the mushy layer to reach any particular value increases enormously as the level of interfacial disequilibrium increases and that the Rayleigh number can have an upper bound that is less than the critical value needed for the onset of convection within the mushy layer. This suggests that the formation of chimneys in the mushy layer can be similarly delayed or prohibited, in agreement with the experimental findings of Huppert & Hallworth (1993). Additionally, the model predicts that under certain conditions the solid fraction can increase away from the cooled boundary leading to trapping of the interstitial liquid. The model also describes a mechanism for macrosegregation of alloys cooled and solidified from below.
Linear Stability of Compositional Convection in a Mushy Layer during Solidification of Ammonium Chloride Solution