Comparison of Non-Newtonian Constitutive Laws in Hydrodynamic Lubrication

Present day commercial lubricants incorporate a range of additives of long-chain polymers. Such polymers are called Viscosity Index improvers and were originally introduced to limit the decrease of viscosity with temperature. However, in addition, these polymers cause the oil to exhibit non-Newtonian behavior. The most common, and probably the most important, non-Newtonian effect is the reduction of viscosity with shear rate, so-called shear thinning. In rheological terms this is called generalized Newtonian (purely viscous) behavior. In this study, several ‘true’ non-Newtonian models (as opposed to generalized Newtonian) are compared. There is some experimental evidence that such non-Newtonian effects are favorable to lubrication. The models studied include time-dependent effects—a linear and nonlinear viscoelastic Maxwell model; and they include the effect of particles within the fluid—the Finitely Extensible Nonlinear Elastic (FENE) dumbbell model, and the Stokes couple stress model. The Maxwell and FENE models show a small decrease in load capacity, while the Stokes model shows a significant increase.