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Research Papers: Lubricants

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

[+] Author and Article Information
Scott Bair1

Center for High-Pressure Rheology, George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

Riccardo Casalini

Chemistry and Biochemistry Department, George Mason University, Fairfax, VA, 22030; Chemistry Division, Naval Research Laboratory, Washington, DC 20375-5342

1

Corresponding author.

J. Tribol 130(4), 041802 (Aug 07, 2008) (7 pages) doi:10.1115/1.2959116 History: Received April 01, 2008; Revised June 17, 2008; Published August 07, 2008

## Abstract

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.

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## Figures

Figure 1

The difference between viscosity measurements and the portrayal of the pressure dependence of viscosity in the EHL literature (9-14)

Figure 2

Top: the viscosity of L23699 versus the reciprocal of the scaling parameter for pressures up to 1.4GPa and indicated temperatures for γ=3.228. Bottom: the derivative Stickel analysis for the scaling parameter applied to the viscosity of the jet oil.

Figure 3

Top: the viscosity of DIIDP and PGLY versus the reciprocal of the scaling parameter. Bottom, the derivative Stickel analysis for the scaling parameter.

Figure 4

Top: the viscosity of LVI 260 and PC versus the reciprocal of the scaling parameter. Bottom: the derivative Stickel analysis for the scaling parameter.

Figure 5

The new VTF-like model presented in terms of temperature and pressure in comparison with the measured values

Figure 6

Top: the viscosity of MCS418 versus the inverse of the scaling parameter φ for γ=5.690. A dynamic crossover is evident at μB=90Pas. Curves are the best fits above and below the crossover to Eqs. 10,11. Bottom: the derivative Stickel analysis for MCS418. Lines: the Stickel analysis of the best fits to Eqs. 10,11.

Figure 7

Top: the viscosity of the inorganic liquid DMTS having a high compressibility versus the inverse scaling variable φ for γ=4.164. The solid line is the best fit to Eq. 10. Bottom: the derivative Stickel analysis. The line is the Stickel analysis of the best fit to Eq. 10.

## Errata

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