A Scaling Parameter and Function for the Accurate Correlation of Viscosity With Temperature and Pressure Across Eight Orders of Magnitude of Viscosity

Quantitative calculations of film thickness and friction in elastohydrodynamic lubrication will require that the low-shear viscosity, $μ$⁠, be described with far greater accuracy than it is today. The free volume model has the advantage, over those currently used, of reproducing all of the trends that were known $80years$ ago, although not necessarily to experimental accuracy. A scaling parameter, $φ∝TVγ$⁠, based on the repulsive intermolecular potential having exponent $−3γ$ allows the viscosity to be written as a function of temperature, $T$⁠, and volume, $V$⁠, only, as $μ=F(φ)$⁠. The appropriate function for lubricants appears to be a Vogel-like form, $μ∝exp(BFφ∞∕(φ−φ∞))$⁠. Parameters are presented here for seven liquids. When the dynamic crossover is present, two such functions are required. A low molecular weight dimethyl silicone having high compressibility is an exception.