Using local N-body simulation, we examine viscosity in self-gravitating planetary rings. We investigate the dependence of viscosity on various parameters in detail, including the effects of particle surface friction. In the case of self-gravitating rings with low optical depth, viscosity is determined by particle random velocity. Inclusion of surface friction slightly reduces both random velocity and viscosity when particle random velocity is determined by inelastic collisions, while surface friction slightly increases viscosity when gravitational encounters play a major role in particle velocity evolution, so that viscous heating balances with increased energy dissipation at collisions due to surface friction. We find that including surface friction changes viscosity in dilute rings up to a factor of about two. In the case of self-gravitating dense rings, viscosity is significantly increased due to the effects of gravitational wakes, and we find that varying restitution coefficients also change viscosity in such dense rings by a factor of about two. We confirm that our numerical results for viscosity in dense rings with gravitational wakes can be well approximated by a semianalytic expression that is consistent with a previously obtained formula. However, we find that this formula seems to overestimate viscosity in dense rings far from the central planet, where temporary gravitational aggregates form. We derive semianalytic expressions that reproduce our numerical results well for the entire range of examined parameters.
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