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

Abstract

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.

Fluids meet solids

“…Some articles focus on model systems to address fundamental questions, such as the study of the effect of the curvature on the solid-fluid interfacial free energy by Martin et al 37 Belozerov and Shikhmurzaev estimate the velocity of solidification when a fluid is brought in contact with a cold solid using theoretical methods. 38 Loche et al investigate the dielectric properties at interfaces of water with graphite and graphene, addressing issues such as the roughness, the effect of metallic properties of the surface, or the presence of ions in water. 39 This collection also includes studies motivated by the desire to address specific practical problems.…”