Tangential Restitution Research Articles

The dynamics of particle disks: II. Effects of spin degrees of freedom

Thermal equilibria of differentially rotating axisymmetric disks composed of identical hard sphere particles which have spin as well as translational degrees of freedom are investigated. The dynamics of spinning particle disks are described by introducing two new parameters: the tangential restitution coefficient ε t and the dimensionless moment of inertia I ∗ . The former is related to the surface properties of the sphere, while the latter is related to the mass distribution in the sphere. It is found that rings composed of spinning particles can generally be thermally balanced within more restricted ranges of the normal optical depth τ and at higher values of the normal restitution coefficient ε n than spinless rings. It is also found that the ratio of spin to translational random kinetic energy in equilibrium is almost independent of τ but substantially dependent on ε t and I ∗ . The viscous instability in spinning particle rings is also found to occur in more restricted ranges of τ than in spinless rings. Under the present assumption that the finite particle-size effects are completely neglected the mean spin is found to be indefinite. A more consistent theory of spinning particle disks which can determine the mean spin must incorporate the finite particle-size effects.