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.

A contact model for normal immersed collisions between a particle and a wall

“…The numerical studies by Al-Samieh & Rahnejat (2002) calculated the pressure increase and surface deformation for a particle impacting a surface coated with a thin liquid layer. By coupling the equation for the motion of the liquid layer with the motion of the particle and the elasticity of the solid surfaces, the authors were able to calculate the pressure rise and compared it with the experiments by Safa & Gohar (1986).…”

Effect of lubricant molecular rheology on formation and shear of ultra-thin surface films

“…With this assumption taken into account, it is clear that the cavitated region is governed by a balance between the squeeze film effect (the ultimate term in the last equation) and the drainage of the fluid from the contact on the account of hydrodynamics alone. Separation of the surfaces on account of squeeze; ∂θh/∂t > 0 increases the chance of cavitation, which is the same as an increase in the speed of entraining motion (Al-Samieh and Rahnejat [11]). One should then expect reduced cavitation at lower sliding speeds as an outcome of the analysis, which would encourage better lubricant distribution on the free surface post film reformation.…”

“…Matsuoka and Kato [5], Abd Al-Samieh and Rahnejat [4] and Al-Samieh and Rahnejat [1,11] also assumed the same for the bulk hydrodynamic behaviour of the lubricants such as those described above and used in the current analysis. Clearly, for the cavitated region: ρ = ρ c when p = p c .…”

Boundary Conditions for Elastohydrodynamics of Circular Point Contacts

“…Al-Samieh and Rahnejat [27] showed that the monitored pressure spike could be predicted accurately once these issues were adequately addressed. Their predictions agreed well with the measured pressure distributions for a ball bearing falling freely upon an oily glass plate upon which Safa and Gohar [28] had fabricated a manganin micro-transducer.…”