Tribology Letters

, 68:7 | Cite as

Viscous Heating in Compressed Liquid Films

  • Scott BairEmail author
Original Paper


The greatest challenge in high-shear viscometry is the recognition of the difference between constitutive behavior and thermal feedback. The failure to realize this distinction was the cause of a serious mistake which has had a profound effect upon the EHL field for four decades. A traction curve is not a rheological flow curve. The classical approach to EHL has ignored the measurement of viscosity in viscometers at elevated pressures. As a consequence, the field has not benefitted from the understanding gained from directly observing the thermal softening effects of viscous heating. The Eyring sinh-law appears in high-shear viscometry when viscous heating causes thermal softening. The thermal limit of pressurized thin film Couette viscometers with high thermal conductivity cylinders is well-defined by the Nahme–Griffith number. The Spikes and Jie equation overcorrects at low values of the Nahme–Griffith number and undercorrects at high values. The viscous heating in a shear-thinning liquid may cause an apparent transition from power-law to sinh-law above some viscous power. Surprisingly, the sinh-law in this instance extrapolates back to the correct low-shear viscosity. The same response has been observed in one set of NEMD simulations.


Quantitative EHL Rheology Thermal EHL 

List of Symbols


Yasuda parameter


Heat capacity of the solid (J/kg K)




Heat flux (W/m2)


Effective shear modulus or critical shear stress for shear-thinning (Pa)


Film thickness (m)


Thermal conductivity of liquid (W/m K)


Thermal conductivity of the solid (W/m K)


Pressure (Pa)


Nahme–Griffith number


Power-law exponent


Temperature (K or  °C)


Time (s)


Half of the width of the shear zone (m)


Dimensionless coordinate in the flow direction of a contact


Coordinate in the axial direction of a cylinder pair (m)

\(\dot{\beta }\)

Temperature-viscosity coefficient (K−1)

\(\dot{\gamma }\)

Shear rate (s−1)


Generalized (non-Newtonian) viscosity (Pa s)


Low-shear viscosity (Pa s)


Mass density of the solid (kg/m3)


Shear stress (Pa)


Eyring stress (Pa)



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Regents’ Researcher, Georgia Institute of Technology, Center for High-Pressure RheologyGeorge W. Woodruff School of Mechanical EngineeringAtlantaUSA

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