A numerical approach to simulate the dynamics of premelted film around a spherical particle in ice

In this paper, a model for computer simulations of thermal regelation processes has been developed and validated for isolated spherical particles surrounded by a premelted liquid film forming at the interface with the ice matrix, even when the temperature is everywhere below the bulk freezing point. The dynamics of premelted films regulates natural phenomena such as frost heave and glacial movements, combining thermodynamic microscopic and continuum mechanical processes. In real systems, the premelted film thickness is typically only a few tens of nanometres, making direct numerical simulations of these systems infeasible, even for micrometric particles. Nevertheless, exploiting the flexibility of numerical modelling, it has been possible to conceive configurations with an artificially thick premelted layer sufficient to make the numerical simulation possible and yet retain the dynamics of the real physical process. The numerical simulations confirm that, when subjected to an external temperature gradient, the particle translates in the same direction as the temperature gradient with a velocity proportional to the third power of the liquid film thickness δ . The flow within the liquid layer behaves as a lubrication flow and this limit is better approximated the thinner is the liquid film δ . An additional set of simulations has been devoted to the effects of different material properties of the different phases; their results indicate that particles with larger thermal conductivity tend to weaken the local magnitude of the temperature gradient leading to reduced particle velocity. Finally, although the present results have been obtained only for spherical and constant curvature particles and for a limited parameter range investigated, the method is absolutely general and can handle with the same ease and efficiency non-spherical shapes as well as particle clusters; this opens the way to several future applications and developments for the model.