Kinetic Theory of Moderately Dense Gases

Abstract

A kinetic equation approach to the kinetic theory of moderately dense gases is developed by asymptotic expansions from a viewpoint independent of Bogoliubov chaos assumptions. The theory is applied to the rigid sphere model where the contributions which determine the Enskog dense gas theory are identified. The existence of divergences in the time integrations for triple collision events in the case of rigid discs and for quadruple collision events in the case of rigid spheres is confirmed by means of variable transformations. A scheme for renormalizing the divergences into an asymptotic density expansion containing nonanalytic logarithmic terms is proposed, illustrated for the case of rigid discs, and employed to deduce the fact that the first density corrections for rigid spheres, being convergent, remain intact as the lead term of the asymptotic density expansion. Numerical studies of the first density corrections to the thermal conductivity and shear viscosity of rigid spheres are performed in order to assess the relative importance of Enskog dense gas contributions and dynamical correlation effects. The results are in substantial agreement with preliminary Monte Carlo calculations of Sengers based upon Bogoliubov theory.