Effect of stress and interface kinetics on the growth of a cylinder of ternary alloy in contact with its melt

The linear stability analysis of the growth of a cylinder made of a ternary alloy in contact with its melt has been investigated from a theoretical point of view, in presence of stress and interface kinetics. It is found that instability is facilitated as the number of diffusing species increases from two to three. The radii characterizing the different growth regimes of the cylinder and the fluctuation have been determined as a function of the diffusion, elastic and kinetics parameters of the problem. It has been established that unlike interface kinetics that penalizes the growth of the fluctuation, the stress favors its development. In particular, a regime where the growth of the fluctuation is faster than the cylinder one has been identified in the early step of the cylinder development, this regime resulting from a pure elasticity effect.