Selection criteria for n-fold symmetry of dendrite growth in the presence of convective flow

Abstract

A model for the n-fold symmetric dendrites growing under convective flow is formulated for the convective-type heat and mass balance conditions at the dendritic interface. Using the linear stability analysis and solvability theory, the selection criteria in the case of n-fold symmetry for thermally and solutally controlled growth of the dendrite is derived. The obtained selection criteria determines the stable mode of dendritic growth, i.e. it gives an additional relation connecting the dendrite tip velocity and dendrite tip diameter in the case of intensive convective heat and mass transfer near a growing dendritic tip. The theory under consideration transforms to the previously known analytic dependence for selection criteria in the case of four-fold symmetry of crystal growth.