Modeling of micro-macrosegregation in solidification processes

The purpose of the note is to establish the average continuity equation of solute which describes micro-macrosegregation phenomena in real alloy systems, i.e., where solute diffusion in the solid phase is almost zero (Scheil equation) and convection in the mushy region is present. Such a model can be directly incorporated into numerical codes for solidification. The physical consequences of such a nonequilibrium model are discussed in terms of equilibrium conditions at the solid-liquid interface during local solidification and remelting. The continuity equations for heat, mass, and momentum are briefly summarized for background.