Solid-mush interface conditions for mushy layers

A subtle issue in the study of mushy zones which form during the solidification of binary alloys is that there are two distinct types of solid-mush interfaces which may occur. One of these is a eutectic front and the other is a front which separates the mushy layer and, assuming complete solute rejection, a layer of a pure solid. For semi-infinite domain configurations that admit similarity solutions, such as those at a uniform initial temperature and concentration with an imposed cold temperature at the lower boundary, only one of the two types appears and the type of front is determined by the various parameters of the system. In a finite domain, it is possible for each type of front to appear at different times. Specifically, the advance of the eutectic front is restricted by the isotherm associated with the eutectic temperature, and the other front type will appear over a longer time-scale. Leading up to the time when the front changes type, the concentration being frozen into the solid decreases. This process writes a history of the system into the solid.