Propagation of Density Fluctuations in Dense Monatomic Fluids [Thesis]

The Fourier transform S(K,ω) of the time-dependent density-density correlation function G($\overrightarrow{r}$,t) has been calculated using the linerized Boltzmann equation in the case of dilute gases and the Enskog and the Vlasov equation in the case of dense fluids. The approach consists of solving an initial value problem for a small density disturbance and identifying G($\overrightarrow{r}$,t) as the velocity integral of the distribution function. In the case of Maxwell molecules for a dilute gas, the exact results of S(K,ω) have been compared with those of the Navier-Stokes and Burnett equations of hydrodynamics. The exact numerical solutions of S(K,ω) for Maxwell molecules have also been compared with the experiments on Brillouin scattering from dilute gases. The sound dispersion phenomena in dilute gases are reviewed and extended and it is shown that the observed sound dispersion, even to the lowest order, is very sensitive to the way it is measured. To be able to solve the Enskog equation for S(K,ω), the interactions terms have to be approximated. The calculations have also been done with corrections to the first approximations and the results compared. Its application to Brillouin scattering and neutron scattering has also been discussed. To apply the Vlasov equation to classical fluids, the intermolecular potential in the equation has to be replaced by the direct correlation function. The results are compared with the experimental S(K,ω) observed through neutron scattering in liquid lead and there is seen to be a qualitative agreement. It also predicts the propagation of a collisionless sound at some wave numbers. The effect of including collisions in the Vlasov equation has also been investigated. A numerical comparison, in the structureless regime, between the Enskog equation and the Vlasov equation with collisions has also been made.