Velocity-correlation functions in two and three dimensions. II. Higher density

The short- and long-time behavior of the velocity-correlation functions characteristic for the coefficient of self-diffusion, and the kinetic parts of the coefficient of viscosity, and thermal conductivity, respectively, are computed approximately as a function of the density for a gas of hard disks or hard spheres on the basis of kinetic theory. The results obtained here are a generalization to higher densities of those obtained in an earlier paper, and reduce to them in the low-density limit. The density dependence is obtained by taking into account a larger number of dynamical events than previously considered. It is found that for short times the correlation functions decay exponentially, but that for longer times $t$, the correlation functions decay $\sim {\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\mathrm{}\left(n\right)\mathrm{}{\left(\frac{t}{t_0}\right)}^{\frac{d}{2}}$ where $n$ is the density, $t_0$ the mean free time between collisions, and $d$ is the number of dimensions. The coefficient ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\mathrm{}\left(n\right)\mathrm{}$ is determined by the transport coefficients of the Enskog theory for a dense gas of hard disks or hard spheres and is in very good agreement with existing computer experiments.