Reynolds equation, apparent slip, and viscous friction in a three-layered fluid film

Abstract

Experimental evidence of wall slip in lubricated contacts sometimes leads to reconsider the usual no-slip conditions. The main theoretical slip conditions found in literature depend on parameters (shear stress threshold, slip length, etc.) to which calculated friction is directly related. A different point of view, on which this work is focused, considers that the apparent wall shear rate is only representative of the bulk flow, and assumes the existence of wall layers, which define the actual local shear rate and friction. The aim of this exploratory work is to build a generalized Reynolds model, with no-slip wall conditions, able to simulate situations of either slip or immobile layers. A very simple ‘rheological’ model, consisting of different Newtonian viscosities in the bulk flow and in wall layers is used. By varying the orders of magnitude of the layers’ thicknesses and viscosities, it is possible to capture all possibilities between apparent wall slip and immobile layers. The model is applied to a plane pad bearing at a prescribed load, and revealed two modes of velocity accommodation giving friction forces significantly smaller than those for a mono-layered film: plug flow with apparent wall slip or middle slip layers.