Selected mode for rapidly growing needle-like dendrite controlled by heat and mass transport

The boundary integral method is developed for fast anisotropic interfaces. A general integro-differential equation for curved interfaces controlled by heat and mass transport is derived and applied to the problem of rapid dendritic growth. A selection criterion for the steady-state mode of growing parabolic interfaces is obtained and, in common solution with the undercooling balance, it is compared with experimental data on rapid dendritic solidification of deeply supercooled liquid droplets. In this comparison, transitions from solute diffusion-limited to thermo-solutal regime and, finally, to pure thermally controlled regime of the anisotropic dendrite are discussed and revealed. Limiting cases of known selection criteria for anisotropic dendrites growing at small and high growth Péclet numbers are provided.

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