The role of incoming flow on crystallization of undercooled liquids with a two-phase layer

Motivated by important applications of crystallization phenomena, we consider a directional solidification process for a binary melt with a two-phase (mushy) layer in the presence of weak melt flow. We consider the steady-state solidification scenario, so that the two-phase layer filled with solid and liquid material keeps its thickness. In addition, we consider that the melt flows onto the two-phase layer slowly in the opposite direction to directional crystallization and solidifies there. A complete analytical solution to non-linear two-phase layer equations is constructed in a parametric form, where the solid phase fraction represents a decision variable. The temperature and solute concentration distributions, mushy layer permeability and average interdendritic spacing as well as solidification velocity and mushy layer thickness are analytically determined. We show that incoming melt flow plays a decisive role on mushy layer parameters and internal structures. The solid phase fraction within the two-phase layer and its thickness essentially grow while the mushy layer permeability and average interdendritic spacing decrease with increasing intensity of incoming melt flow.