Physics of lubricated impact of a sphere on a plate in a narrow continuum to gaps of molecular dimensions

Abstract

This paper investigates the phenomenon of lubricated impact dynamics of ellipsoidal bodies upon semi-infinite elastic solids, giving rise to Hertzian contact conditions. The analysis conforms to the numerical predictions and experimental findings of others, when the physics of motion of the lubricant can be described through Newtonian continuum mechanics, with the dominant viscous action embodied in the transient solution of Reynolds' equation. The equivalence of squeeze film action under impacting conditions with that of a converging gap in pure entraining motion is shown. This concept is extended to study the accelerative nature of the lubricant film surface, and its concordance with Reynolds' assumption through use of a relativistic frame of reference and hyperbolic geometry.When the investigation is extended to the case of ultra-thin film conjunctions of the order of a few to several molecular diameters of the intervening fluid layer, the physics of fluid film motion through impact involves more complex kinetic interactions. These include the effect of structural force of solvation, as well as that of a meniscus force, formed in such narrow conjunctions. The former, through active dispersion, tends to promote a structureless environment, whilst the latter through wetting action encourages the formation of a coherent film. This paper shows the interplay between these competing kinetics.