The prediction of tip radius during rapid dendritic growth under coupled thermo-solutal control: What value sigma

A phase-field model for dendritic growth under coupled thermo-solutal control model is presented. Constructed in the quantitatively valid thin-interface limit the model uses advanced numerical techniques such as mesh adaptivity, multigrid and implicit time-stepping to solve the non-isothermal alloy solidification problem for materials parameters that are realistic for metals. Using this model we demonstrate that the dendrite radius selection parameter, σ*, shows a complex dependence on a number of materials properties including undercooling, Lewis number, alloy concentration and partition coefficient, in addition to the known dependence on anisotropy strength. Consequently, we argue that as a predictive tool, at least for non-isothermal alloy solidification away from the limits of vanishing concentration and Peclet number, the concept of σ* probably retains little intrinsic value.