Abstract:Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, separated by 22 years, one valid in the dilute gas, and another in the liquid phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate reference correlations for the transport properties of the Lennard-Jones 12-6 flu… Show more
Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for singlecomponent quasiuniversality.
Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for singlecomponent quasiuniversality.
“…For a new treatment of the entropy scaling characteristics of the transport coefficients of the LJ fluid over the whole density range, see Ref. 56. It has been found that the scaled self-diffusion coefficient and shear viscosity of the LJ fluids are to a very good approximation invariant along an isomorph for densities above approximately the critical value.…”
Molecular dynamics simulations have been carried out along four Lennard-Jones (LJ) fluid isomorphs close to the freezing line, covering a temperature, T, in the range of 0.8-350 and a number density, ρ, in the range of 1.1-3.0 in LJ units. Analysis of the transport coefficients is via the Green-Kubo time correlation function method. The radial distribution function, percolation threshold connectivity distance, self-diffusion coefficient, and shear viscosity are shown to be invariant along an isomorph to a very good approximation when scaled with Rosenfeld's macroscopic units, although there are some small departures for T ≃ 1 and lower temperatures. The thermal conductivity is shown for the first time also to be isomorph invariant. In contrast, the Einstein and moment-based frequencies, and especially the bulk viscosity, η b , show poor isomorphic collapse at low T but not surprisingly tend to an "inverse power" potential limiting value in the high T limit. In the case of the bulk viscosity, the significant departures from invariance arise from oscillations in the pressure autocorrelation function at intermediate times, which scale for inverse power potential systems but not for the LJ case, at least in part, as the pressure and bulk elastic moduli are not isomorph invariant.
“…For the calculation of viscosities of real fluids, this approach was primarily used in connection with semi-empirical equations such as the PCP-SAFT [42][43][44] or the CPA [45] equation of state. After introducing a modified approach with a dimensionless residual entropy per unit volume as the independent scaling variable and a suitable choice of a reference fluid for refrigerants [46], the approach was first applied to model fluids in conjunction with accurate Helmholtz-energy equations of state [47]. Subsequently, comprehensive studies on pure hydrocarbons were carried out by Bell [48,49].…”
A literature review on experimental data for binary mixtures of methane and carbon dioxide with hydrocarbons up to n-hexadecane is presented. Based on these data, the extended corresponding states method, two entropy scaling approaches, and the friction theory are analyzed with respect to their capability of calculating viscosity values with increasing asymmetry of the binary mixture. It is shown that not only the viscosity model but also the underlying thermodynamic equation of state has a significant influence on the result of such calculations. Shortcomings are identified both in the experimental data and in the modeling approaches.
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