Capillary-Wave Model for the Solidification of Dilute Binary Alloys

Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The model does not rely on the sharp-interface assumption, and includes non-equilibrium effects, relevant in the rapid-growth regime. In many applications it can be evaluated analytically, culminating in the appearance of an instability which, interfering with the Mullins-Sekerka instability, is similar to that, found by Cahn in grain-boundary motion.