Analytical and numerical solutions of thin lubricating films for differing shear-thinning viscosity models

Abstract

A detailed assessment of thin film lubrication, for shear-thinning fluids, in two benchmark geometries - a classical linear slider-bearing and a converging-diverging gap arrangement - is provided in terms of the associated pressure distribution, flowrate, and variation in friction. Solutions, both analytical and purely numerical are obtained, with three different rheological constitutive relationships, the viscosity being represented via either a power-law or a Moore or an Ellis model. Finite-element simulations, with these rheological models fully integrated within the weak form of the momentum equation, show that the accuracy of the corresponding analytical solutions depends on whether the resulting pressure gradient-flux relationships are derived using either a full or average shear-dependence formulation. Indeed, the analytical results obtained via the latter form reveal significant discrepancies as the shear-thinning effects increase, in that the behaviour of the pressure field is not well captured.