Tribology Letters

, 67:91 | Cite as

Polymer-Thickened Oil Rheology When There Is No Second Newtonian

  • Scott BairEmail author
Original Paper


The recent development of quantitative elastohydrodynamics makes the accurate description of the temperature, pressure, and shear dependence of viscosity extremely important. It has been customary for tribologists to expect a second Newtonian plateau to appear in any flow curve for a polymer-blended lubricant and, since viscometers at ambient pressure cannot reach such a plateau, procedures have been suggested to extrapolate to a second Newtonian from commercial high-shear viscometer data. Two examples of oils, characterized in pressurized thin-film Couette viscometers, are presented for which there is no second Newtonian. Extrapolation from ambient-pressure high-shear viscometer data, by fixing the second Newtonian viscosity at the viscosity of the base oil, is not useful. Apparently, the second Newtonian will not appear when the base oil begins to shear thin at the shear stress for which the second Newtonian inflection might appear.


Shear thinning Time–temperature–pressure superposition Second Newtonian 

List of Symbols

\(a0,\,a1,\,a2,\,b0,\,b1,\,c0,\,c1,\,\hat{\alpha }\)

Temperature modifying parameters for the hybrid model (various units)


Pressure-fragility parameter




Temperature-fragility parameter


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


Newtonian limit stress of the ith-modified Carreau term (Pa)


Molecular mass kg/kmol


Pressure (Pa)

\(p_{\infty }\)

Divergence pressure (Pa)


McEwen exponent


Universal gas constant, 8314 J/kmol/K


First normal stress difference (Pa)


Power-law exponent of the ith-modified Carreau term


Temperature (K or °C)

\(T_{\infty }\)

Divergence temperature (K or °C)


ith Yasuda parameter


Initial pressure–viscosity coefficient (Pa−1)

\(\dot{\gamma }\)

Shear rate (s−1)


Generalized (non-Newtonian) viscosity (Pa s)


Characteristic time (s)


Low-shear (first Newtonian) viscosity (Pa s)


Low-shear viscosity at \(p\, = \,0\) (Pa s)


Second Newtonian viscosity (Pa s)


Low-shear viscosity of base oil (Pa s)

\(\mu_{\infty }\)

Low-shear viscosity at \(p\, = \,0\) for unbounded temperature (Pa s)


Mass density of the liquid (kg/m3)


Shear stress (Pa)


Eyring stress (Pa)



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Copyright information

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

Authors and Affiliations

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

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