  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.
