Transport coefficients of hard-sphere mixtures. III. Diameter ratio 0.4 and mass ratio 0.03 at high fluid density.

Abstract

The equation of state and the transport coefficients of shear viscosity, thermal conductivity, thermal diffusion, and mutal diffusion are estimated for a binary, equimolar mixture of hard spheres having a diameter ratio of 0.4 and a mass ratio of 0.03 at volumes in the range 1.7${\mathit{V}}_{0}$ to 3${\mathit{V}}_{0}$ (${\mathit{V}}_{0}$=1/2 \ensuremath{\surd}2 N${\mathit{tsum}}_{\mathit{a}}$${\mathit{x}}_{\mathit{a}}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{a}}^{3}$, where ${\mathit{x}}_{\mathit{a}}$ are the mole fractions, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{a}}$ are the diameters, and N is the number of particles), complementing and, in some cases, improving earlier low-density results through Monte Carlo, molecular-dynamics calculations using the Green-Kubo formulas. Calculations are reported for 108 to 2048 particles, so that both finite-system and, in the case of the transport coefficients, long-time tail corrections can be applied to obtain accurate estimates of the pressure and the transport coefficients in the thermodynamic limit. Corrections of both types are found to be increasingly important at higher densities, for which the pressure is observed to become nonlinear in 1/N over the range covered. The Mansoori-Carnahan-Starling-Leland (MCSL) equation is found to account for the pressure with considerable accuracy for V\ensuremath{\ge}1.7${\mathit{V}}_{0}$; the difference between the observed (infinite-system) pressure and the MCSL prediction increases monotonically with density, reaching 0.4% at V=1.7${\mathit{V}}_{0}$. For volumes below 2${\mathit{V}}_{0}$ the pressure in excess of the MCSL prediction is found to ``soften'' slightly in its dependence on the density.The pressure is also compared with the known virial series (${\mathit{B}}_{2}$ and ${\mathit{B}}_{3}$) and the difference is fitted to a rational polynomial from which estimates for ${\mathit{B}}_{4}$ and ${\mathit{B}}_{5}$ are derived. The transport coefficients are compared with the predictions of the revised Enskog theory, evaluated using the MCSL equation of state. The shear viscosity coefficient is found to lie within about 5% of the theory over much of the range of densities, exceeding the Enskog prediction at both high and low densities and rising sharply at the highest densities. The thermal conductivity drops to about 94% of the Enskog value at about 2.5${\mathit{V}}_{0}$, but the ratio increases at higher densities. The thermal diffusion and mutal diffusion coefficients, relative to the Enskog values, drop monotonically to roughly 0.75 with increasing density. The pressure estimates vary in accuracy from 0.001% to 0.01% with increasing density. The accuracy of the estimates of the transport coefficients similarly ranges from 0.5% to 3.8%. The magnitude of the 1/N corrections to both the pressure and the transport coefficients increase with density, equaling, for example, 0.3% of the 256-particle pressure at V=1.7${\mathit{V}}_{0}$. At the same density, the combined finite-system and long-time tail correction for the mutual diffusion is 4.3% of the 256-particle result.