Hydrodynamic Pressurization of a Trapped Lubricant Pool Between a Rippled Rigid Indenter and an Elastic Layer: An Investigation Into the Role of Surface Roughness on Cartilage Lubrication

Abstract

In recent studies of articular diarthrodial joint lubrication, it has been proposed that hydrostatic pressurization of the cartilage interstitial fluid upon joint loading contributes significantly to the load support across the articular layers, thus reducing frictional forces and wear [1–3]. This boundary contact mechanism for porous media can explain the observed time-dependent response of the frictional coefficient. Nevertheless, alternative hypotheses have been also proposed which attribute the low friction coefficient to hydrodynamic lubrication [4]. In our recent analysis of a mixed lubrication problem where a lubricant pool is trapped between a rippled rigid indenter and a biphasic cartilage layer [5], it was observed that the hydrostatic pressurization of the trapped lubricant can enhance the fluid load support to a certain extent, but typically for a short duration on the order of 1 s only, until the lubricant is depleted by flowing into the cartilage layer. Furthermore, under steady-state sliding, it was found that a lubricant pool could not be sustained due to lubricant depletion. These analyses employed an inviscid model for the lubricant as they focused on hydrostatic pressurization only. In the current study, we investigate whether lubricant viscosity, which can promote hydrodynamic pressurization, might further enhance the fluid load support mechanism or alter the conclusions gathered from our earlier studies. To investigate these fundamental mechanisms, an elastic layer is used instead of a biphasic layer at first; a more elaborate biphasic analysis could be employed subsequently if warranted by the current findings.