Effect of Soret diffusion on the growth of spherical crystals in supercooled alloy melts under oscillatory flow

The growth of spherical crystals in binary alloy melts with thermal diffusion effects under oscillatory flow is investigated analytically. Using the multiple scale method, we derive approximate analytical solutions for both the crystal interface growth rate and the solute concentration. Our results demonstrate that the Soret effect significantly influences both the solute concentration near the crystal interface and the crystal growth rate. Specifically, with a positive Soret coefficient, the growth rate of spherical crystals in a binary dilute alloy melt decreases as the coefficient increases, while the solute concentration near the interface increases. In contrast, with a negative Soret coefficient, the growth rate of the spherical crystals increases as the coefficient decreases, and the solute concentration near the interface decreases. Additionally, the presence of oscillatory flow markedly promotes the grain refinement induced by the Soret effect.