We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial melting of solid alloys. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by diffusion in the liquid film, whereas the process with only one melting front would be controlled by the very slow diffusion in the mother solid phase. The relatively weak coherency strain energy is the effective driving force for LFM. As in the classical dendritic growth problems, also in this case an exact family of steady-state solutions with two parabolic fronts and an arbitrary velocity exists if capillary effects are neglected [5]. We develop a velocity selection theory for this problem, including anisotropic surface tension effects. The strong diffusion interaction and coherency strain effects in the solid near the melting front lead to substantial changes compared to classical dendritic growth.The early observation of liquid film migration (LFM) were made during sintering in the presence of liquid phase [1] or during partial melting of alloys [2] (see [3] for a review). Nowadays LFM is a well established phenomenon of great practical importance. In LFM one crystal is melted and another one is solidified. Both solid-liquid interfaces move together with the same velocity. In the investigated alloys systems the migration velocity is of the order of 10 −6 − 10 −5 cm/s and it is controlled by the solute diffusion through a thin liquid layer between the two interfaces [4]. The migration velocity is much smaller than the characteristic velocity of atomic kinetics at the interfaces. Therefore, both solids should at the interfaces be locally in thermodynamic equilibrium with the liquid phase. On the other hand, these local equilibrium states should be different for the two interfaces to provide the driving force for the process. It is by now well accepted (see, for example, [3,4]) that the difference of the equilibrium states at the melting and solidification fronts is due to the coherency strain energy, important only at the melting front because of the sharp concentration profile ahead the moving melting front (diffusion in the solid phase is very slow and the corresponding diffusion length is very small). Thus, the liquid composition at the melting front, which depends on the coherency strain energy and on the curvature of the front, differs from the liquid composition at the unstressed and curved solidification front. This leads to the necessary gradient of the concentration across the liquid film and the process is controlled by the diffusion in the film.If only the melting front existed, the melting process would be controlled by the very slow diffusion in the mother solid phase and elastic effects would be irrelevant. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by the much faster diffusion in the liquid film. ...
