Tribology Letters

, 64:25 | Cite as

Rheology of an Ionic Liquid with Variable Carreau Exponent: A Full Picture by Molecular Simulation with Experimental Contribution

  • Nicolas Voeltzel
  • Philippe Vergne
  • Nicolas Fillot
  • Nathalie Bouscharain
  • Laurent Joly
Original Paper


The rheological behavior of an ionic liquid was investigated by means of molecular dynamics simulations with experimental contribution, under conditions close to those found in the elastohydrodynamic and the very-thin film lubrication regimes. The molecular model was applied to nearly 200 temperature–pressure–shear rate cases, without any parameter adjustment. Experiments were conducted on a rheometer and a high-pressure falling-body viscometer. This unique combination of numerical and experimental tools has enabled the full description of the ionic liquid rheological response to extreme conditions of temperature, pressure and shear rate. In the linear domain, a very good consistency between the two computational approaches (nonequilibrium molecular dynamics, equilibrium molecular dynamics via the Green–Kubo formalism) and the experiments was obtained on the Newtonian viscosity. Reliable values of the pressure–viscosity coefficient, another rheological characteristic necessary for predicting film thickness in the regimes of interest in this work, were inferred. Compared with a conventional lubricant of almost identical Newtonian viscosity, the pressure–viscosity coefficient of the ionic fluid is much lower, its variations with temperature remaining, however, very similar. The application of the time–temperature–pressure superposition principle and the regression to the Carreau equation for describing the nonlinear domain have revealed, for the first time, significant variations in the exponent of the Carreau model which have been correlated with the changes in temperature and pressure.


Ionic liquids Lubrication Rheology Molecular dynamics High pressure High shear rate Nonlinear regime Carreau model Relaxation time Time–temperature–pressure superposition 

List of symbols


Viscosity shift factor for the application of the time–temperature–pressure superposition

\(a_{{\dot{\gamma }}}\)

Shear-rate shift factor for the application of the time–temperature–pressure superposition


Typical ion size (m)


Average self-diffusion coefficient (m2 s−1)


Fragility parameter (VFT model)


Exponent of the Carreau law (−)


Pressure (Pa)


Pressure at the reference state (Pa)


Coefficient of correlation from data regression (−)


Relaxation time (s)


Temperature (K)


Glass transition temperature at pressure p (K)


Temperature at the reference state (K)

\(T_{\infty }\)

Vogel temperature at which the viscosity diverges (VFT model, K)


Pressure–viscosity coefficient (GPa−1)


Reciprocal asymptotic isoviscous pressure coefficient, as proposed by Blok (GPa−1)


Viscosity (Pa s)


Viscosity at the glass transition (=1012 Pa s)


Newtonian viscosity (Pa s)


Reduced viscosity (Pa s)

\(\eta_{\infty }\)

Viscosity extrapolated to infinite temperature (VFT model, Pa s)

\(\dot{\gamma }\)

Shear rate (s−1)

\(\dot{\gamma }_{\text{c}}\)

Critical shear rate, at the onset of the nonlinear behavior (s−1)

\(\dot{\gamma }^{*}\)

Reduced shear rate (s−1)


Density (kg m−3)


Density at the reference state (kg m−3)


  1. 1.
    Gupta, S.A., Cochran, H.D., Cummings, P.T.: Shear behavior of squalane and tetracosane under extreme confinement. III. Effect of confinement on viscosity. J. Chem. Phys. 107(23), 10335–10343 (1997)CrossRefGoogle Scholar
  2. 2.
    McCabe, C., Cui, S., Cummings, P.T., Gordon, P.A., Saeger, R.B.: Examining the rheology of 9-octylheptadecane to giga-pascal pressures. J. Chem. Phys. 114(4), 1887–1891 (2001)CrossRefGoogle Scholar
  3. 3.
    McCabe, C., Manke, C.W., Cummings, P.T.: Predicting the Newtonian viscosity of complex fluids from high strain rate molecular simulations. J. Chem. Phys. 116(8), 3339–3342 (2002)CrossRefGoogle Scholar
  4. 4.
    Kioupis, L.I., Maginn, E.J.: Rheology, dynamics, and structure of hydrocarbon blends: a molecular dynamics study of n-hexane/n-hexadecane mixtures. Chem. Eng. J. 74, 129–146 (1999)CrossRefGoogle Scholar
  5. 5.
    Kioupis, L.I., Maginn, E.J.: Impact of molecular architecture on the high-pressure rheology of hydrocarbon fluids. J. Phys. Chem. B 104, 7774–7783 (2000)CrossRefGoogle Scholar
  6. 6.
    Bair, S., McCabe, C., Cummings, P.T.: Comparison of nonequilibrium molecular dynamics with experimental measurements in the nonlinear shear-thinning regime. Phys. Rev. Lett. 88(5), 058302-1–058302-4 (2002)CrossRefGoogle Scholar
  7. 7.
    Bair, S., McCabe, C., Cummings, P.T.: Calculation of viscous EHL traction for squalane using molecular simulation and rheometry. Tribol. Lett. 13(4), 251–254 (2002)CrossRefGoogle Scholar
  8. 8.
    Ramasamy, U.S., Bair, S., Martini, A.: Predicting pressure–viscosity behavior from ambient viscosity and compressibility: challenges and opportunities. Tribol. Lett. 57(2), 11 (2015)CrossRefGoogle Scholar
  9. 9.
    Blok, H.: Inverse problems in hydrodynamic lubrication and design directives for lubricated flexible surfaces. In: Proceedings International Symposium on Lubrication and Wear, Houston. McCutchan Publishing Corp., Berkeley (1963)Google Scholar
  10. 10.
    Liu, P., Yu, H., Ren, N., Lockwood, F.E., Wang, Q.J.: Pressure–viscosity coefficient of hydrocarbon base oil through molecular dynamics simulations. Tribol. Lett. 60(3), 34 (2015)CrossRefGoogle Scholar
  11. 11.
    Ye, C., Liu, W., Chen, Y., Yu, L.: Room-temperature ionic liquids: a novel versatile lubricant. Chem. Commun. 21, 2244–2245 (2001)CrossRefGoogle Scholar
  12. 12.
    Minami, I.: Ionic liquids in tribology. Molecules 14(6), 2286–2305 (2009)CrossRefGoogle Scholar
  13. 13.
    Maginn, E.J.: Molecular simulation of ionic liquids current status and future opportunities. J. Phys. Condens. Matter 21(37), 373101 (2009)CrossRefGoogle Scholar
  14. 14.
    Zhou, F., Liang, H., Liu, W.: Ionic liquid lubricants: designed chemistry for engineering applications. Chem. Soc. Rev. 38, 2590–2599 (2009)CrossRefGoogle Scholar
  15. 15.
    Palacio, M., Bhushan, B.: A review of ionic liquids for green molecular lubrication in nanotechnology. Tribol. Lett. 40(2), 247–268 (2010)CrossRefGoogle Scholar
  16. 16.
    Tokuda, H., Hayamizu, K., Ishii, K., Susan, M.A.B.H., Watanabe, M.: Physicochemical properties and structures of room temperature ionic liquids. 2. Variation of alkyl chain length in imidazolium cation. J. Phys. Chem. B 109(13), 6103–6110 (2005)CrossRefGoogle Scholar
  17. 17.
    Tokuda, H., Tsuzuki, S., Susan, M.A.B.H., Hayamizu, K., Watanabe, M.: How ionic are room-temperature ionic liquids? An indicator of the physicochemical properties. J. Phys. Chem. B 110(39), 19593–19600 (2006)CrossRefGoogle Scholar
  18. 18.
    Voeltzel, N., Gulliani, A., Vergne, P., Fillot, N., Joly, L.: Nanolubrication by ionic liquids: molecular dynamics simulations reveal an anomalous effective rheology. Phys. Chem. Chem. Phys. 35(17), 23226–23235 (2015)CrossRefGoogle Scholar
  19. 19.
    Electronic Supplementary Information: ESI. Phys. Chem. Chem. Phys. 35(17), 23226–23235 (2015)Google Scholar
  20. 20.
    Canongia Lopes, J.N., Deschamps, J., Pádua, A.A.H.: Modeling ionic liquids using a systematic all-atom force field. J. Phys. Chem. B 108, 2038–2047 (2004)CrossRefGoogle Scholar
  21. 21.
    Salanne, M.: Simulations of room temperature ionic liquids: from polarizable to coarse-grained force fields. Phys. Chem. Chem. Phys. 17, 14270–14279 (2015)CrossRefGoogle Scholar
  22. 22.
    Schroder, C.: Comparing reduced partial charge models with polarizable simulations of ionic liquids. Phys. Chem. Chem. Phys. 14, 3089–3102 (2012)CrossRefGoogle Scholar
  23. 23.
    Chaban, V.: Polarizability versus mobility: atomistic force field for ionic liquids. Phys. Chem. Chem. Phys. 13, 16055–16062 (2011)CrossRefGoogle Scholar
  24. 24.
    Müller-Plathe, F.: Reversing the perturbation in nonequilibrium molecular dynamics: an easy way to calculate the shear viscosity of fluids. Phys. Rev. E 59, 4894–4898 (1999)CrossRefGoogle Scholar
  25. 25.
    Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, Oxford (1989)Google Scholar
  26. 26.
    Bair, S., Vergne, P., Querry, M.: A unified shear-thinning treatment of both film thickness and traction in EHD. Tribol. Lett. 18(2), 145–152 (2005)CrossRefGoogle Scholar
  27. 27.
    Bair, S.: A routine high-pressure viscometer for accurate measurements to 1 GPa. Tribol. Trans. 47(3), 356–360 (2004)CrossRefGoogle Scholar
  28. 28.
    Angell, C.A.: Formation of glasses from liquids and biopolymers. Science 276, 1924–1935 (1995)CrossRefGoogle Scholar
  29. 29.
    Ahosseini, A., Scurto, A.M.: Viscosity of imidazolium-based ionic liquids at elevated pressures: cation and anion effects. Int. J. Thermophys. 29, 1222–1243 (2008)CrossRefGoogle Scholar
  30. 30.
    Bair, S., Mary, C., Bouscharain, N., Vergne, P.: An improved Yasutomi correlation for viscosity at high pressure. Proc. Inst. Mech. Eng. J J. Eng. Tribol. 227(9), 1056–1060 (2013)CrossRefGoogle Scholar
  31. 31.
    Hamrock, B.J., Dowson, D.: Isothermal elastohydrodynamic lubrication of point contacts, part III—fully flooded results. Trans. ASME J. Lubr. Technol. 99(2), 264–276 (1977)CrossRefGoogle Scholar
  32. 32.
    Chaomleffel, J.P., Dalmaz, G., Vergne, P.: Experimental results and analytical predictions of EHL film thickness. Tribol. Int. 40(10–12), 1543–1552 (2007)CrossRefGoogle Scholar
  33. 33.
    Bair, S.: High-Pressure Rheology for Quantitative Elastohydrodynamics. Elsevier, Amsterdam (2007)Google Scholar
  34. 34.
    Pensado, A.S., Comuñas, M.J.P., Fernández, J.: The pressure-viscosity coefficient of several ionic liquids. Tribol. Lett. 31(2), 107–118 (2008)CrossRefGoogle Scholar
  35. 35.
    Harris, K.R., Kanakubo, M., Woolf, L.A.: Temperature and pressure dependence of the viscosity of the ionic liquids 1-hexyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. J. Chem. Eng. Data 52, 1080–1085 (2007)CrossRefGoogle Scholar
  36. 36.
    Vergne, P.: Comportement Rhéologique des Lubrifiants et Lubrification : Approches Expérimentales. Habilitation Thesis (in French), INSA de Lyon, Lyon, France. 28 March 2002Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Univ LyonINSA Lyon, CNRS, LaMCoS - UMR5259VilleurbanneFrance
  2. 2.Univ LyonUniversité Claude Bernard Lyon 1, CNRS, ILM - UMR5306VilleurbanneFrance

Personalised recommendations