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


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

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, φTVγ, 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, μexp(BFφ(φφ)). 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.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
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.

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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.

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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.

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Figure 5

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

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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.

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Figure 1

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

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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.




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