Thermodynamics and dynamics of the hard-sphere system: From stable to metastable states

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

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.

A comprehensive study of the thermal conductivity of the hard sphere fluid and solid by molecular dynamics simulation

This work reports a new set of hard sphere (HS) thermal conductivity coefficient, λ, data obtained by Molecular Dynamics (MD) computer simulation, over a density range covering the dilute fluid to near the close-packed solid, and for a large number of particles (up to N = 13 1072) and long simulation times. The N-dependence of the thermal conductivity is shown to be proportional to N-2/3 to a good approximation over a wide range of system sizes, which enabled λ values in the thermodynamic limit to be predicted accurately. The fluid and solid λ can be represented well by the Enskog theory (ET) formula, λE, times a density-dependent correction term, which is close to unity for the fluid and practically constant for the solid. The convergence of the MD λ data back towards ET in the metastable fluid starts just above the freezing density. For the HS solid and dense fluid it was found that the thermal conductivity is nearly linear in pressure, as has been observed experimentally for a number of solids. Simple excess entropy scaling over the higher density fluid phase region was found, and Rosenfeld's exponential relationship can be fitted to the simulation data for the solid to a high degree of accuracy. The simulation analysis has revealed a number of new trends in the behaviour of the HS thermal conductivity which could be useful in building more accurate models for heat conduction in experimental systems.

Simple liquids' quasiuniversality and the hard-sphere paradigm

This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.