The effect of fluid viscoelasticity in soft elastohydrodynamic lubrication

Abstract

Lubrication is crucial across various industries and natural environments to prevent direct contact between solid surfaces. Elastohydrodynamic lubrication specifically addresses situations where solid surfaces are likely to deform. Viscoelastic additives in fluids can alter lubrication characteristics significantly. Reduced models available today efficiently solve viscoelastic equations numerically in thin film contacts, surpassing direct numerical computations in efficiency. Employing numerical techniques, viscoelastic fluids within the linear elastic regime are successfully analyzed. Further investigations into contraction geometries aim to elucidate findings on soft lubrication. An elementary experimental study was conducted to demonstrate the effect of viscoelasticity on load-carrying capacity. A comprehensive literature review provided the necessary mathematical foundation for understanding viscoelasticity and solid deformation. Concepts such as the upper convected time derivative and polymeric constitutive equations were summarized. Reynolds equation, incorporating polymeric elastic stress, is combined under the thin film lubrication approximation. Viscoelasticity is characterized by the non-dimensional number De, which represents the ratio of polymer relaxation time to observation time t/to . In the context of lubrication, the observation time t/to is defined as L/U, where L is the length of the channel and U is the speed of flow. The reduced numerical methods are based on finite differencing schemes and linearization of the flow with respect to De. The linearized flow using the Oldroyd-B constitutive model forms the basis for a more complex numerical model that is compatible with direct numerical solvers. A unique semi-implicit method has been developed to solve nonlinear stress equations. The coupling between solid and fluid solvers is fully explained with schematics, and the boundary element method is integrated with the finite difference method. Prior to presenting results, the developed numerical methods were validated against previous outcomes published in journal articles. Elastohydrodynamic lubrication results indicate that the friction coefficient decreases with increasing De at high deformabilities. To further illustrate EHL cases, step-like channels were studied. Finally, experimental data is provided for future use, concluding with remarks to contextualize our findings.