Solute redistribution and growth velocity response in directional solidification process

Based on the principle of solute conservation during directional solidification of binary alloys, the solute redistribution equations are obtained. A differential equation to evaluate the actual growth velocity is derived and the equation is solved by the method of matched asymptotic expansions. The solution shows the effect of kinematic supercooling and the coupling of thermal and mass transportation on the real growth of a planar interface. Numerical results indicate that there exists not only a hysterical effect of the solid-liquid interface during solidification but also a transient zone of growth velocity in the initial transient process. The growth velocity response to the externally imposed velocity sharply increases at the very beginning of solidification, then develops successively and progressively during the transient zone.