Rheological properties of liquids under conditions of elastohydrodynamic lubrication

Abstract: There is an ongoing debate concerning the best rheological model for liquid flows in elastohydrodynamic lubrication (EHL). Due to the small contact area and high relative velocities of bounding solids, the lubricant experiences pressures in excess of 500 MPa and strain rates that are typically $10^5 -10^7$ $\textrm{s}^{-1}$. The high pressures lead to a dramatic rise in Newtonian viscosity $\eta_{N}$ and the high rates lead to large shear stresses and pronounced shear-thinning. This paper presents detailed simulations of a model EHL fluid, squalane, using nonequilibrium molecular dynamics methods to extract the scaling of its viscosity with shear rate ($10^5 - 10^{10}$ $\textrm{s}^{-1}$) over a wide range of pressure $P$ (0.1 MPa to 1.2 GPa), and temperature $T$ ($150 - 373$ K). Simulation results are consistent with a broad range of equilibrium and nonequilibrium experiments. At high $T$ and low $P$, where $\eta_{N}$ is low, the response can be fit to a power-law, as in the common Carreau model. Shear-thinning becomes steeper as $\eta_{N}$ increases, and for $\eta_{N}\gtrsim 1$ Pa-s, shear-thinning is consistent with the thermally activated flow assumed by another common model, Eyring theory. Simulations for a bi-disperse Lennard-Jones (LJ) system show that the transition from Carreau to Eyring is generic. For both squalane and the LJ system, the viscosity decreases by only about a decade in the Carreau regime, but may fall by many orders of magnitude in the Eyring regime. Shear thinning is often assumed to reflect changing molecular alignment, but the alignment of squalane molecules saturates after the viscosity has dropped by only about a factor of three. In contrast, thermal activation describes shear thinning by six or more decades in viscosity. Changes in the diagonal elements of the stress tensor with rate and shear stress are also studied.