Kinetic Theory of Nonlinear Viscous Flow in Two and Three Dimensions

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form t XI 3j2 for hard spheres, or IX I log[ XI for hard disks. Here Xis proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t -a~2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range of X values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.