Confinement effects in premelting dynamics

When the free surfaces of most solids approach the bulk melting temperature from below, the surfaces are wet by the melt phase. The thin film of the melt phase flows as a viscous fluid when the temperature is sufficiently close to the bulk melting temperature. This phenomenon is called the interfacial premelting when melt phase exists between the bulk solid phase and a foreign substrate. We examine the effects of confinement on the dynamics of premelted films driven by thermomolecular pressure gradient parallel to an interfacially premelted elastic wall. The modification treats the increase in viscosity associated with the thinning of films, studied in a wide variety of materials, using a power law and we examine the consequent evolution of the confining elastic wall. We treat (1) a range of interactions that are known to underlie interfacial premelting and (2) a constant temperature gradient wherein the thermomolecular pressure gradient is constant. The difference between the cases with and without the proximity effects increases the viscosity as the film thickness decreases thereby requiring the thermomolecular pressure driven flux to be accommodated at higher temperatures where the premelted film thickness is the largest. Implications for experiments and observations of frost heave are discussed.