Growth of a two-phase finger in eutectics systems.

We present a theoretical study of the growth of a two-phase finger in eutectic systems. This pattern was observed experimentally by Akamatsu and Faivre [Phys. Rev. E 61, 3757 (2000)]. We study this two-phase finger using a boundary-integral formulation and we complement our investigation by a phase-field validation of the stability of the pattern. The deviations from the eutectic temperature and from the eutectic concentration provide two independent control parameters, leading to very different patterns depending on their relative importance. We propose scaling laws for the velocity and the different length scales of the pattern.