The Effect of Convection Motion on Dendritic Growth

Abstract

In the past several years, we have extensively studied the problems of dendrite growth with no convection, from a pure melt, as well as from a binary mixture. An interfacial wave theory has been established for selecting the tip-velocity and determining the formation of micro-structure at the later stage of growth. The theoretical predictions agree with the available experimental data very well (see Figure 1). In the present work, we turn to investigate the effect of convection in melt. Assume that a single dendrite growing into an undercooled pure melt in the negative z-axis direction with a constant average velocity U. At the far field, a uniform external flow against the dendrite with the velocity (U ∞)D may be applied. We assume that the mass density of the liquid phase is ρ, while the mass density of the solid phase is ρs. Due to the external flow and/or the change of density in solidification, a convective motion in melt is produced. The fluid motion will affect the heat transport process and change the temperature distribution. We consider the melt as an incompressible Newtonian fluid. Then system involves the following parameters: $$ {T_\infty };\,\,\varepsilon \, = \,{{\sqrt \Gamma } \over {\eta _0^2}};\,\,\alpha \, = \,{{\rho s - \rho } \over \rho };\,{U_\infty };\,\,Pr = {\nu \over {{\kappa _T}}}{\rm{.}} $$ (1.1)