Stokes Flow in Thin Films

Abstract

Present understanding of the mechanisms of lubrication and the load carrying capacity of lubricant films mainly relies on models in which the Reynolds equation is used to describe the flow. The narrow gap assumption is a key element in its derivation from the Navier Stokes equations. However, the tendency in applications is that lubricated contacts have to operate at smaller film thickness levels, and because engineering surfaces are never perfectly smooth, locally in the film this narrow gap assumption may violated. In addition to this geometric limitation of the validity of the Reynolds equation may come a piezoviscous and compressibility related limitation. In this paper the accuracy of the predictions of the Reynolds model in relation to the local geometry of the gap is investigated. A numerical solution algorithm for the flow in a narrow gap has been developed based on the Stokes equations. For a model problem the differences between the pressure and velocity fields according to the Stokes model and the Reynolds equation have been investigated. The configuration entails a lower flat surface together with an upper surface (flat or parabolic) in which a local defect (single asperity) of known geometry has been embedded. It is investigated how the magnitude of the differences develops as a function of the geometric parameters of the film and the feature. Finally, it is discussed to what extend for these problems a perturbation approach can provide accurate corrections to be applied to the Reynolds solution.