Diffusion-controlled growth of a solid cylinder into its undercoded melt: Instabilities and pattern formation studied with the phase-field model

Instabilities in the solidification of a cylinder in its undercooled melt are numerically studied within the phase-field model. This growth becomes morphologically unstable when its radius exceeds a critical value R*, that is a decreasing function of the thermodynamic driving force: the circular growth regime should be hardly observable, in practice, except possibly at extremely low values of the dimensionless undercooling Delta. However, the equation for the amplitude of the perturbing modes shows that the response of the growing front to a finite noise is drastically reduced when Delta is increased, so that a more stable growth should be associated to larger undercoolings. This suggestion is confirmed by the numerical simulations, which allow us to fix the onset and the extent of the perturbations. To summarize the results, an effective critical radius is represented as a function of Delta.