A new approach for modeling viscoelastic thin film lubrication

Abstract

Lubricants can exhibit significant viscoelastic effects due to the addition of high molecular weight polymers. The overall behavior of the mixture is vastly different from a simpler Newtonian fluid. Therefore, understating the influence of viscoelasticity on the load carrying capacity of the film is essential for lubricated contacts. A new modeling technique based on lubrication theory is proposed to take into account viscoelastic effects. As a result, we obtain a modified equation for the pressure, i.e. the viscoelastic Reynolds (VR) equation. We have first examined a parabolic slider to mimic a roller bearing configuration. An increase of the load carrying capacity is observed when polymers are added to the lubricant. Furthermore, our results are compared with existing models based on the lubrication approximation and direct numerical simulations (DNS). For small Weissenberg number (), i.e. the ratio between the polymer relaxation time and the residence time scale, VR predicts the same pressure of the linearized model, in which is the perturbation parameter ( is the ratio between the vertical length scale and the horizontal length scale). However, the difference grows rapidly as viscoelastic effects become stronger. Excellent quantitative and qualitative agreement is observed between DNS and our model over small to moderate Weissenberg number. While DNS is numerically unstable at high values of the Weissenberg number, VR does not have the same issue allowing to capture the evolution of the stress and pressure also when the viscoelastic effects are strong. It is shown that even in high shear flows, normal stresses have the largest impact on load carrying capacity and thus cannot be neglected. Furthermore, the additional pressure due to viscoelasticity comprises two components, the first one due to the normal stress and the second one due to the shear stress. Afterwards, the methodology used for the parabolic slider is extended to a plane slider where, instead, the load decreases by adding polymers to the fluid. In particular, under the effect of the polymers surface slopes enhance the rate at which pressure gradients increase, whereas curvature opposes this along the contact. Therefore, the increase of the load carrying capacity observed for viscoelastic lubricants is due to its shape close to the inlet, which is steeper than the plane slider.