  We suggest that the irregular structure in Saturn's B ring arises from the
formation of shear-free ring-particle assemblies of up to ~100 km in radial
extent. The characteristic scale of the irregular structure is set by the
competition between tidal forces and the yield stress of these assemblies; the
required tensile strength of ~10^5 dyn/cm^2 is consistent with the sticking
forces observed in laboratory simulations of frosted ice particles. These
assemblies could be the nonlinear outcome of a linear instability that occurs
in a rotating fluid disk in which the shear stress is a decreasing function of
the shear. We show that a simple model of an incompressible, non-Newtonian
fluid in shear flow leads to the Cahn-Hilliard equation, which is widely used
to model the formation of structure in binary alloys and other systems.
