Squeezing a lubricant with exponential pressure dependence of viscosity: Resolution of a hydrodynamic paradox

It is known that viscosity of most fluids, in particular lubricants, increases with pressure. The most typical dependence used in lubrication applications is a simple exponential law (Barus law). This behavior is of great importance for lubricated systems in highly loaded mechanical parts, such as rolling bearings, gears, or cam followers. In this paper, we are going back to the origins of the theory of elastohydrodynamic lubrication and consider contact of rigid bodies separated by a pressure-dependent lubricant. We consider a long-standing paradox in the theory of pressure-dependent lubrication of rigid partners connected with a pressure singularity in the lubricant at finite external forces. We revisit this theory and suggest a simple solution to this paradox.