Revised Enskog theory and molecular dynamics simulations of the viscosities and thermal conductivity of the hard-sphere fluid and crystal.

Abstract

Hard-sphere (HS) shear, longitudinal, cross, and bulk viscosities and the thermal conductivity are obtained by molecular dynamics (MD) simulations, covering the entire density range from the dilute fluid to the solid crystal near close-packing. The transport coefficient data for the HS crystal are largely new and display, unlike for the fluid, a surprisingly simple behavior in that they can be represented well by a simple function of the density compressibility factor. In contrast to the other four transport coefficients (which diverge), the bulk viscosity in the solid is quite small and decreases rapidly with increasing density, tending to zero in the close-packed limit. The so-called cross viscosity exhibits a different behavior to the other viscosities, in being negative over the entire solid range, and changes sign from negative to positive on increasing the density in the fluid phase. The extent to which the viscosity tensor and thermal conductivity of the HS crystal can be represented by revised Enskog theory (RET) is investigated. The RET expressions are sums of an instantaneous (I), a kinetic (K), and a so-called α part. The I part of the transport coefficients evaluated directly by MD are statistically indistinguishable from those of the corresponding kinetic theory (Enskog and RET) expressions. For the K part the integral over the spatial two-particle distribution function at contact was determined and the α part was estimated using the direct correlation function and density functional theory approximations. All three parts were determined in this work which allowed the accuracy of RET for solid systems to be assessed rigorously. It is found that in the case of the thermal conductivity the predictions of RET are in excellent agreement with the MD results. Also, for the shear viscosity the agreement over the entire solid phase is quite good but is considerably worse for the three remaining viscosities in the solid phase.