Particle properties and the large-scale structure of planetary rings: Rebound characteristics and viscosity

In a swarm of particles on Keplerian orbits, like a planetary ring, systematic flow is circular with velocity decreasing with distance from the planet. Viscosity ordinarily transports momentum from a faster to a slower moving region, i.e., outward. But any individual at apocenter of its orbit moves slower, and at pericenter faster, than the mean flow, suggesting a reversed momentum transport or negative viscosity. Resolution of this seeming paradox illuminates the importance of physical properties of particles. A conventional model has uniform, highly elastic, perfectly slippery, spherical particles, with a particular dependence of elasticity on impact velocity. Even slight deviation from that ideal affects viscosity and leads to inconsistencies with observed ring structure. If particles are less elastic they may clump into large temporary agglomerations. The size of the larger bodies in the rings probably determines random velocities, viscosity, and much about ring structure.