Theory of dendritic growth—III. Effects of surface tension☆

Abstract The linear stability analysis of a dendrite tip, presented in the preceding paper, is generalized to include effects of surface tension. The equations of motion are studied numerically by both a forward integration method and an eigenvalue analysis. The most striking result of these computations is the appearance of sidebranching instabilities. For large enough growth velocities, the dendrite tip stabilizes, but the sidebranching instability persists. We argue that the state of dynamic stability proposed in the first paper of this series is achieved by means of a nonlinear coupling between the sidebranching mode and the extended deformations which govern the overall shape and growth velocity of the dendrite.