Low-velocity impact experiments of porous ice balls simulating Saturn's ring particles: Porosity dependence of restitution coefficients and the mechanism of inelastic collision

We investigated the porosity dependence of the restitution coefficient (epsilon) of porous ice balls with porosities of 49.6%, 53.8%, and 60.8% colliding with granite, ice and porous ice plates at a low impact velocity (nu(i) = 0.93-96.9 cm s(-1)) and temperature of -13.8 degrees C. The relationship between the impact velocity and the restitution coefficient was divided into two regions by the critical velocity nu c: In the quasi-elastic region (nu(i)<=nu(c)), the restitution coefficient had a constant value of epsilon qe regardless of the impact velocity and could be explained by using Dilley's viscous dissipation model. In the inelastic region (nu(i )>= nu(c)), the restitution coefficient decreased with the impact velocity and could be explained by using the improved Andrews' plastic deformation model. We then determined the porosity dependence of the epsilon qe and nu c empirically for collisions between the porous ice ball and the porous ice plate from our results. Then we extrapolated the porosity dependence of the restitution coefficient by substituting the calculated epsilon(qe )and nu(c) for the porosity of 10 to 70%. The restitution coefficient was found to decrease with increasing porosity of the porous ice, and to be strongly dependent on the porosity of the porous ice. Considering the energy budget in the steady-state dense ring system which is controlled by the restitution coefficient of the ring particles, the velocity dispersion of the ring particles was estimated to be similar to 10(-2) mm s(-1) to cm s(-1) for the ring particles with the porosity from 45% to 70% and < 10-90 cm s(-1) for those with the porosity <45%.