Granular Viscosity, Planetary Rings and Inelastic Particle Collisions

The functional dependencies of the viscosity η on temperature and density, derived for granular gases under certain physical environments— force free, and in a central gravitational field— are compared and numerically checked. It is known that different physical conditions lead to different functional dependencies of the viscosity η on the granular temperature T and also the matter density. This is caused by gradients of volume forces which create curvatures in the particle trajectories (epicycles) which bound the free motion and limit the mean free path l to finite values even for vanishing particle density ρ, where in the force free case l α ρ.1 diverges. This results in the known dependence η α √T in the force- free case for nearly elastic collisions. In planetary rings the transport coefficients of momentum and energy are proportionalto T. We check the validity of these expressions with numerical particle simulations. For planetary rings the dependence of the coefficient of restitution e on the impact velocity v imp is crucialfor their stability. Hence, we present models of the dynamics of the particle collisions, which account for the velocity-dependence e(v imp ) by a visco-elastic model for particle collisions, as well as for the sticking at very low impact velocities. The latter is a further improvement of previous models, and the results are in accordance with laboratory measurements.