Diffusion-stress coupling in liquid phase during rapid solidification of binary mixtures

• We propose the diffusion-stress coupling model for binary solidification.
• The coupling arises at deep undercooling.
• With diffusive dynamics, the models result in parabolic transfer equations.
• With the wavelike dynamics, the models lead to hyperbolic transfer equations.
• The coupling strongly affects the solute partition coefficient.

An analytical model has been developed to describe the diffusion-viscous stress coupling in the liquid phase during rapid solidification of binary mixtures. The model starts with a set of evolution equations for diffusion flux and viscous pressure tensor, based on extended irreversible thermodynamics. It has been demonstrated that the diffusion-stress coupling leads to non-Fickian diffusion effects in the liquid phase. With only diffusive dynamics, the model results in the nonlocal diffusion equations of parabolic type, which imply the transition to complete solute trapping only asymptotically at an infinite interface velocity. With the wavelike dynamics, the model leads to the nonlocal diffusion equations of hyperbolic type and describes the transition to complete solute trapping and diffusionless solidification at a finite interface velocity in accordance with experimental data and molecular dynamic simulation.