Divergent Transport Coefficients and the Binary-Collision Expansion

Abstract

The binary-collision expansion for the viscosity of a two-dimensional gas of hard disks is discussed. A divergence appears in ${\eta }_1$, the first correction to the Boltzmann-equation result. The calculations presented here are exact and explicitly demonstrate the dynamical origin of the divergence indicated by Kawasaki and Oppenheim. The coefficient of the divergence is computed and found to be precisely the same as that found by Sengers by an entirely different method. The origin of the divergence is shown to be exactly the same as that found by Dorfman and Cohen.