Solidification of free liquid films

We examine steady longitudinal freezing of a two-dimensional single-component free liquid film. In the liquid, there are thermocapillary and volume-change flows as a result of temperature gradients along the film and density change upon solidification. We examine these flows, heat transfer, and interfacial shapes using an asymptotic analysis which is valid for thin films with small aspect ratios. These solutions depend sensitively on contact conditions at the tri-junctions. In particular, when the sum of the angles formed in the solid and liquid phases falls below a critical value, the existence of steady solutions is lost and the liquid film cannot be continuous, suggesting breakage of the film owing to freezing. The solutions are relevant to the freezing of foams of metals or ceramics, materials unaffected by surface active agents.