A generalized Scheil-Pfann equation for a dynamical theory of a mushy zone
This paper develops a thermodynamically consistent theory of the freezing of a binary alloy in a region of mixed liquid and solid phase, possibly in relative motion. Attention is focussed on the cases when the liquid has the composition of the equilibrium liquidus, but in which the diffusion of one constituent through the other in the solid phase is negligible. An isolated system can not then attain complete thermodynamic equilibrium in a finite time, only a state of quasi-equilibrium in which the composition of the solid phase is not that of the solidus and, in general, is not even uniform in space. The complete theory must admit these quasi-equilibria as the steady final states of isolated systems. This is found to be so stringent a requirement that it almost completely decides the form that the theory must take. A simple physical situation is solved: one-dimensional freezing of a stagnant material. The Scheil- Pfann solution is recovered.
scientific article; zbMATH DE number 4068377