A molecular simulation study of shear and bulk viscosity and thermal conductivity of simple real fluids

doi:10.1016/j.fluid.2004.05.011

Fluid Phase Equilibria

Volume 221, Issues 1–2, 30 July 2004, Pages 157-163

https://doi.org/10.1016/j.fluid.2004.05.011 Get rights and content

Abstract

Shear and bulk viscosity and thermal conductivity for argon, krypton, xenon, and methane and the binary mixtures argon + krypton and argon + methane were determined by equilibrium molecular dynamics with the Green–Kubo method. The fluids were modeled by spherical Lennard–Jones pair-potentials with parameters adjusted to experimental vapor liquid-equilibria data alone. Good agreement between the predictions from simulation and experimental data is found for shear viscosity and thermal conductivity of the pure fluids and binary mixtures. The simulation results for the bulk viscosity show only poor agreement with experimental data for most fluids, despite good agreement with other simulation data from the literature. This indicates that presently available experimental data for the bulk viscosity, a property which is difficult to measure, are inaccurate.

Introduction

Transport properties play an important role in many technical and natural processes. With the rapid increase of available computing power, molecular simulation in combination with molecular modeling is becoming an interesting option for describing transport properties in regions where experimental data are not available or difficult to obtain. The calculation of transport coefficients by molecular simulation can be achieved by non-equilibrium molecular dynamics (NEMD) or equilibrium molecular dynamics (EMD). In NEMD, transport coefficients are calculated as the ratio of a flux to an appropriate driving force, extrapolating to the limit of zero driving force [1]. In EMD transport coefficients are often calculated by the Green–Kubo formalism [2], [3]. The choice between EMD and NEMD is largely a matter of taste and inclination, see, e.g. [4], [5], [6]. There are numerous contributions in the literature in which both methods were applied for the calculation of shear viscosity [4], [7], [8], [9], [10], [11], [12], bulk viscosity [13], [14], [15], and thermal conductivity [7], [10], [11], [16], [17] with comparable performance. To our knowledge the most comprehensive study on transport coefficients of the spherical Lennard–Jones (LJ) fluid is reported in [18], [19]. Despite of the large number of publications on simulation of transport properties with the spherical Lennard–Jones potential, not much effort seems to have been spent on a comparison of simulation results with experimental data of real fluids. Exceptions are the works of Michels et al. [20] and Heyes and coworkers [10], [11]. Michels and Trappeniers [20] compared the self-diffusion coefficient to the Chapman-Enskog theory and experimental data for krypton and methane at high densities, but thermodynamic properties were not considered. Heyes et al. [10], [11] simulated both transport and thermodynamic properties of argon + krypton, argon + methane, and methane + nitrogen, but properties of pure fluids were not considered. In other cases [21], [22] more complex molecules like ethylene, carbon dioxide, phenol, alkanes, or carbon tetrachloride were modeled by the spherical Lennard–Jones potential, which surely is an oversimplification. Simulation data on transport properties were compared there to experimental data, but not the thermodynamic properties.

The interest here lies in the quantitative evaluation of the performance of Lennard–Jones models [23], which have been optimized for the accurate prediction of thermodynamic properties, in the description of transport properties. In this work EMD is used to carry out a comprehensive comparison, of shear and bulk viscosity and thermal conductivity of pure fluids and binary mixtures of noble gases and methane. The molecular models are taken from [23]. These models were adjusted only to vapor-liquid equilibria and yield accurate descriptions of static thermodynamic properties over a wide range of temperatures and densities. Furthermore, they were recently applied for the prediction of diffusion coefficients of pure and binary mixtures of simple fluids over a wide range of temperatures and densities with good results [24].

Section snippets

Theoretical background

Transport coefficients are associated to irreversible processes, however, it is possible to describe irreversible processes in terms of reversible microscopic fluctuations, through the fluctuation dissipation theory [25]. In that theory, it is shown that transport coefficients can be calculated as integrals of time-correlation functions of appropriate quantities [2], [3]. There are different methods to relate transport coefficients to time-correlation functions; a good review can be found in

Results and discussion

In this section the prediction of shear and bulk viscosity and thermal conductivity are compared pointwise with experimental data. For the shear viscosity the correlation of Rowley and coworkers [8], [9], which is based on molecular simulation results, was also used.

Fig. 2 shows the results for the shear viscosity of argon, krypton, xenon and methane in comparison with experimental data. The data are reported at different temperatures and were taken from Vargaftik et al. [42] for the noble

Conclusion

In the present work, the Green–Kubo formalism was used to calculate transport properties for pure and binary mixtures of four noble gases and methane. The molecular interactions of the fluids were modeled by the spherical Lennard–Jones pair potential with parameters adjusted to vapor-liquid equilibrium only. A comprehensive comparison with available experimental data shows good agreement for pure fluids and binary mixtures for shear viscosity and thermal conductivity. On the other hand, for the

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^☆: Dedicated to Professor Friedrich Kohler, Ruhr-Universität Bochum, on the occasion of his 80th birthday.

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A molecular simulation study of shear and bulk viscosity and thermal conductivity of simple real fluids☆

Abstract

Introduction

Section snippets

Theoretical background

Results and discussion

Conclusion

Physica A

Fluid Phase Equilib.

Chem. Phys. Lett.

J. Chem. Phys.

J. Phys. Soc. Jpn.

J. Chem. Phys.

Phys. Rev. A

Mol. Phys.

Mol. Phys.

Int. J. Thermophys.

Phys. Chem. Liq.

J. Chem. Phys.

Mol. Phys.

Phys. Rev. A

J. Chem. Soc. Faraday Trans. II

Phys. Rev. A

J. Chem. Phys.

Phys. Rev. A

Int. J. Thermophys.

J. Chem. Phys.

J. Phys. Chem. B

Int. J. Thermophys.

Rpts. Progr. Phys.

Ann. Rev. Phys. Chem.