Normalized Ashurst-Hoover Scaling and a Comprehensive Viscosity Correlation for Compressed Liquids

[+] Author and Article Information
Scott Bair1

 George W. Woodruff School of Mechanical Engineering, Center for High-Pressure Rheology, Georgia Institute of Technology, Atlanta, GA 30332-0405scott.bair@me.gatech.edu

Arno Laesecke

 Thermophysical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305-3328Arno.Laesecke@Boulder.NIST.Gov


Corresponding author.

This work is in part a work of the US Government. ASME disclaims all interest in the US Government’s contributions.

J. Tribol 134(2), 021801 (Mar 06, 2012) (8 pages) doi:10.1115/1.4005374 History: Received July 13, 2011; Accepted September 12, 2011; Published March 06, 2012; Online March 06, 2012

The recent move toward physics-based elastohydrodynamics promises to yield advances in the understanding of the mechanisms of friction and film generation that were not possible a few years ago. However, the accurate correlation of the low-shear viscosity with temperature and pressure is an essential requirement. The Ashurst-Hoover thermodynamic scaling, which has been useful for thermal elastohydrodynamic simulation, is normalized here in a manner that maps the viscosity of three widely different liquids onto a master Stickel curve. The master curve can be represented by a combination of two exponential power law terms. These may be seen as expressions of different molecular interaction mechanisms similar to the two free-volume models of Batschinski-Hildebrand and Doolittle, respectively. The new correlation promises to yield more reasonable extrapolations to extreme conditions of temperature and pressure than free-volume models, and it removes the singularity that has prevented wide acceptance of free-volume models in numerical simulations.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

The materials considered in this work in terms of their electrostatic potential color-mapped onto the isoelectron density surfaces at 0.002 electron•au−3 with a color scale ranging from red (negative charge) to blue (positive charge)

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Figure 2

(a) Master curve for R134a, 1,1,1,2-Tetrafluoroethane for pressure to 400 MPa and (b) master curve for DIDP, Diisodecyl Phthalate for pressure to 1000 MPa

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Figure 3

The βV-Stickel analysis for R134a, 1,1,1,2-Tetrafluoroethane and DIDP, Diisodecyl Phthalate. Temperature increases to the left, pressure to the right.

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Figure 4

The Stickel function versus the logarithm of viscosity scaling parameter for all six experimental materials. Temperature increases to the left, pressure to the right.

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Figure 5

The new correlation, Eq. 7, applied to the viscosities of R134a, DMP and squalane. Temperature increases to the left, pressure to the right.

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Figure 6

Viscosity master curves for three diverse materials described with the same d(lnμ)/dβV

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Figure 7

The Stickel plot of the new model, Eq. 7, for DMTS. Data points are from measured viscosities.

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Figure 8

The Stickel plot for viscosity of PC measured to 1.0 GPa (open data points) and the dielectric relaxation times [31] at pressures to 1.3 GPa and temperatures from 171 to 314 K. The new model was fitted to the viscosities; however, it extrapolates well to the dielectric data at greater pressure.



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