The strain rate dependence of shear viscosity, pressure and energy from two-body and three-body interactions
Introduction
Recent non-equilibrium molecular dynamics simulation (NEMD) results for argon, using the Barker–Fisher–Watts (BFW) and Axilrod–Teller (AT) intermolecular potentials, indicate that both pressure and energy vary linearly with the square of the strain rate [1], [2], [3]. In contrast, mode-coupling theory [4] predicts a non-analytic three-halves power dependence on the strain rate. Most earlier molecular simulation studies [5], [6], [7] using effective multi-body intermolecular potentials such as the Lennard–Jones or Weeks–Chandler–Anderson (WCA) intermolecular potentials appear to support the predictions of mode-coupling theory. Other results [8], [9] for argon using the BFW and AT potentials also indicate a three-halves dependence on strain rate. Ryckaert et al. [10] reported a strain rate-squared dependence of the shear viscosity but the significance of these results is unclear because of the high strain rates and large statistical uncertainties in the data [11] and the possible influence of string-phases [12], [13]. In contrast, our results [1] for argon were obtained with greater statistical accuracy and no string-phases or other sources of error were observed.
It is of considerable interest to determine whether or not our results for argon are also valid for other atoms. In this work, we report NEMD calculations for the shear viscosity of xenon. Xenon was chosen because it is considerably larger than argon; an accurate two-body potential [14] is available in the literature and the non-additive coefficient is known accurately [15]. To the best of our knowledge, the shear viscosity of xenon has not been reported previously using accurate two- and three-body intermolecular potentials. The results reported here indicate that both energy and pressure have an unambiguous dependence of the strain rate-squared.
Section snippets
Theory
The simulation method has been discussed extensively elsewhere [1]. Therefore, only an outline of the main details is given here.
Results and discussion
The results of NEMD simulations for the pressure, energy and shear viscosity of xenon at different strain rates are reported in Table 1. The normal convention was adopted for the reduced density (), temperature (/ε), energy (/ε), pressure (/ε), viscosity () and strain rate (). Unless otherwise stated, all quantities quoted in this work are in terms of these reduced quantities and the superscript “∗” will be omitted. All simulations were performed at the
Conclusions
The NEMD simulations are reported for the shear viscosity of xenon using accurate intermolecular two- and three-body potentials. The data indicate that both the pressure and energy of the fluid vary linearly with the square of the strain rate. This is consistent with earlier work [1] for the strain rate dependence of argon.
Acknowledgements
GM thanks the Australian Government for an International Postgraduate Research Award (IPRA). Generous allocations of computer time on the Fujitsu VPP300 and NEC SX-4/32 computers were provided by the Australian National University Supercomputer Centre and the CSIRO High Performance Computing and Communications Centre, respectively.
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