A free dendritic growth model accommodating curved phase boundaries and high Peclet number conditions

A steady-state free dendrite growth model accommodating nonlocal equilibrium tip conditions and curved liquidus and solidus has been developed. The developed model assumes a dendrite tip of a paraboloid of revolution and is applicable to dendrite growth in dilute binary alloys for all values of P-c, and reduces to the BCT model for linear liquidus and solidus. The marginal stability criterion of Trivedi and Kurz is shown to apply even in the presence of kinetic undercooling and curved phase boundaries when used with an appropriate concentration-dependent liquidus slope. The model is applied to Sn-Pb alloys to predict the tip velocity, tip radius, solute trapping, and four components of undercooling in the quasi-solutal, solutal-to-thermal transition and quasi-thermal regions.