Scaling of viscosity with rate, pressure, and temperature: Linking simulations to experiments

Elastohydrodynamic lubrication (EHL) is important in many practical devices and produces extreme pressures ($>1$ GPa) and shear rates ($10^5-10^7$ s$^{-1}$). This makes EHL fluids ideal candidates for bridging the gap between experimental and simulation studies of viscosity. There is an ongoing debate about whether the high-rate response of simple molecules like squalane follows a power-law Carreau model or a thermal activation based Eyring model. We use molecular dynamics simulations to investigate the rheological response of squalane for a wide range of rates ($10^5-10^{10}$ s$^{-1}$), pressures (0.1 MPa to 3 GPa), and temperatures ($100-313$ K). We find that experimental and theoretical results can be collapsed onto a master curve consistent with Eyring theory over more than 20 orders of magnitude in rate. Extrapolating Eyring fits to simulations at $10^7$ s$^{-1}$ and above yields Newtonian viscosities $\eta_0$ that are consistent with available low-rate experiments, and allows predictions to much higher pressures and lower temperatures. There is no indication of a diverging viscosity at finite stress, since log $\eta_0$ rises sublinearly with pressure up to 6 GPa and $\eta_0 > 10^{12}$ Pa-s. Correlations between chain conformations and Eyring parameters are also presented.