Thermo-solutal and kinetic regimes of an anisotropic dendrite growing under forced convective flow

A thermo-diffusional problem of a free dendrite growing in a binary mixture is considered analytically. Effects of the anisotropy and convective flow on the stable mode of the dendrite with four-fold crystal symmetry are studied. Special analysis is given for the parabolic dendrite growing at arbitrary Péclet numbers and with small anisotropy of surface energy and atomic kinetics. The stable growth mode is analyzed through the solvability condition giving the stability criterion for the dendrite tip velocity V and dendrite tip diameter ρ as a function of growth Péclet number, Pg, flow Péclet number, Pf, and Reynolds number, Re. Using the obtained criterion of stability, a complete sequence of transitions in growth regimes (namely, from solute diffusion-limited to thermally controlled and further to kinetically-limited regimes) of the anisotropic dendrite is derived and revealed. Limiting cases to known criteria for small and high growth Péclet numbers of the solidifying system with and without convective fluid flow are found. Two-dimensional solidification regimes and scalings obtained are discussed for their extension to three-dimensional dendritic growth.