The onset of solidification: From interface formation to the Stefan regime

The onset of a solidification process is considered in a situation where the free surface of a warm liquid is touched by a sufficiently cold solid. The process is analyzed in terms of a model that takes into account the formation of a liquid-solid interface as the two media are brought in contact and then the appearance of the solidified liquid as a third bulk phase. As is shown, the temperature at the liquid-solid interface and then at the solidification front evolves in a non-monotone way, and when the solidification front appears and starts to move, its velocity is not a function of its temperature. The classical Stefan regime of solidification appears as a limit as the temperature at the solidification front evolves toward the melting temperature.