Ice friction: Role of non-uniform frictional heating and ice premelting

The low friction of ice is usually attributed to the formation of a thin water film due to melting of ice by frictional heating. Melting of ice is a first order phase transition where physical quantities like mass density, the elastic modulus or the shear strength changes abruptly at the transition temperature. Thus, one may expect the friction coefficient to change abruptly at some characteristic sliding speed, when the melt water film is produced. We show that taking into account that, due to non-uniform frictional heating, melting does not occur simultaneously in all the ice contact regions, the transition is not abrupt but still more rapid (as a function of sliding speed) than observed experimentally. The slower than expected drop in the friction with increasing sliding speed may be a consequence of the following paradoxical phenomena: before the melt-water film is formed, the friction of ice is high and a large frictional heating occur which may result in the melting of the ice. If a thin (nanometer) water film would form, the friction becomes low which results in small frictional heating and the freezing of the water film. This suggests a region in sliding speed where a thin (nanometer) surface layer of the ice may be in a mixed state with small ice-like and water-like domains, which fluctuate rapidly in space and time. Alternatively, and more likely, heat-softening of the ice may occur resulting in a thin, statistically homogeneous (in the lateral direction) layer of disordered ice, with a shear strength which decreases continuously as the ice surface temperature approaches the bulk melting temperature. This layer could be related to surface premelting of ice. Using a phenomenological expression for the frictional shear stress, I show that the calculated ice friction is in good agreement with experimental observations.