Groove instability in cellular solidification

We simulate in two dimensions the cellular solidification of a binary alloy, to focus on the emergence of a secondary instability consisting in the periodic detachment of liquid droplets from the bottom of the intercellular liquid grooves. This phenomenon, observed in the solidification of thin samples, was previously interpreted in terms of an instability of the liquid-jet type; as it should occur only in three-dimensional systems, it was argued that even for thin samples the grooves have a tubelike structure. Recently the droplets detachment has been evidenced also in a two-dimensional simulation, so that a different interpretation should be given. We show that the phenomenon arises as the result of diffusional and capillary effects driven by the strong curvature of the solid-liquid interface. The dependence of the emission frequency and the droplets radius on the growth velocity is also studied.