Effect of convective flow on stable dendritic growth in rapid solidification of a binary alloy

A model for anisotropic growth of a dendritic crystal in a binary mixture under non-isothermal conditions is presented. A criterion for a stable growth mode is given for the dendrite tip as a function of the thermal Péclet number and the ratio between the velocities of dendrite growth and solute diffusion in the liquid bulk. Limiting cases of known criteria for anisotropic dendrite growth at low and high growth Péclet numbers are provided. The inclusion of forced convective flow extends the range of theoretical predictions, especially to low growth velocities, thus eliminating systematic discrepancies between earlier models and observed experimental data, as shown by a comparison of model predictions with measured growth velocities in Ti-55 at% Al alloys solidified under electromagnetic levitation.