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

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Abstract

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.

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Abbreviations

a η :

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

d :

Typical ion size (m)

D :

Average self-diffusion coefficient (m2 s−1)

\(D_{\text{F}}\) :

Fragility parameter (VFT model)

N :

Exponent of the Carreau law (−)

p :

Pressure (Pa)

\(p_{\text{Ref}}\) :

Pressure at the reference state (Pa)

R 2 :

Coefficient of correlation from data regression (−)

t rel :

Relaxation time (s)

T :

Temperature (K)

T g(p):

Glass transition temperature at pressure p (K)

T Ref :

Temperature at the reference state (K)

\(T_{\infty }\) :

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

α :

Pressure–viscosity coefficient (GPa−1)

\(\alpha^{*}\) :

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

η :

Viscosity (Pa s)

η g :

Viscosity at the glass transition (=1012 Pa s)

η 0 :

Newtonian viscosity (Pa s)

\(\eta^{*}\) :

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)

ρ :

Density (kg m−3)

ρ Ref :

Density at the reference state (kg m−3)

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Acknowledgments

The authors, in particular N. Voeltzel, P. Vergne, N. Fillot and N. Bouscharain are grateful to the SKF company for its funding through the Research Chair “Lubricated Interfaces for the Future,” signed with LaMCoS and INSA-Lyon Foundation. They are grateful to Professor Josefa Fernández, from the Universidade de Santiago de Compostela (Spain), for her interest in the topic and for sharing some results on ionic liquids, which have contributed to this work. Our last thanks go to the Fédération Lyonnaise de Modélisation et Sciences Numériques (FLMSN) for providing computing resources via the P2CHPD facility.

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Authors and Affiliations

  1. Univ Lyon, INSA Lyon, CNRS, LaMCoS - UMR5259, 69621, Villeurbanne, France

    Nicolas Voeltzel, Philippe Vergne, Nicolas Fillot & Nathalie Bouscharain

  2. Univ Lyon, Université Claude Bernard Lyon 1, CNRS, ILM - UMR5306, 69622, Villeurbanne, France

    Laurent Joly

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  1. Nicolas Voeltzel
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  2. Philippe Vergne
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  4. Nathalie Bouscharain
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Correspondence to Philippe Vergne.

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Voeltzel, N., Vergne, P., Fillot, N. et al. Rheology of an Ionic Liquid with Variable Carreau Exponent: A Full Picture by Molecular Simulation with Experimental Contribution. Tribol Lett 64, 25 (2016). https://doi.org/10.1007/s11249-016-0762-z

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