SEGREGATION AND FLOW DURING THE SOLIDIFICATION OF ALLOYS

The crystallization of a binary alloy from a cooled boundary is analysed and the structure of the resulting solid product examined. The analysis includes effects due to differences in densities between solid and liquid phases and due to a non-zero segregation coefficient of the alloy. We determine the general conditions under which the solidification takes place either at a planar interface or throughout a mushy layer of solid dendrites bathed in interstitial fluid. We are able to make significant analytical progress by finding appropriate similarity solutions of the governing differential equations, and then simplifying these solutions in the asymptotic limit of practical interest wherein the compositional diffusivity is very much less than the thermal diffusivity. Thereby we determine a simple criterion that distinguishes between the solidification at a planar front being controlled mainly by the transport of the rejected component away from the phase boundary rather than by the associated thermal transports. We also calculate the solid fraction and the degree of micro-segregation in the mushy layer. In addition, the density difference between the liquid and solid phases is shown to induce a flow of the liquid phase during solidification, which causes macro-segregation of the resulting solid product.