On the emergence of one-dimensional front instabilities in directional solidification and fusion of binary mixtures

We study, for directional solidification or fusion of binary mixtures, the stability of planar fronts against one-dimensional deformations. We extend the perturbative approach of Wollkind and Segel to the case where solute diffusion in the « daughter » phase in non-negligible. We study the bifurcation diagram and calculate the coefficient of the cubic term in the amplitude equation. From a qualitative analysis of the results, the liquid/ liquid crystal (and, possibly, the liquid/plastic crystal) transition appears to be the most attractive system for systematic experimental investigation.