Numerical simulation of freckle formation in directional solidification of binary alloys

A mathematical model of solidification is presented which simulates the formation of segregation models known as `freckles´ during directional solidification of binary alloys. The growth of the two-phase or dendritic zone is calculated by solving the coupled equations of momentum, energy, and solute transport, as well as maintaining the thermodynamic constraints dictated by the phase diagram of the alloy. Calculations for lead-tin alloys show that the thermosolutal convection in the dendritic zone during solidification can produce heavily localized inhomogeneities in the composition of the final alloy