The drift of plasma ions relative to charged grains in a dusty plasma can give rise to a dust/ion acoustic instability. We investigate the linear properties of the instability by numerically solving an appropriate linear dispersion equation and examine the nonlinear behavior through one-dimensional electrostatic particle simulations, in which the plasma and dust ions are treated as discrete particles and the electrons are modeled as a Boltzmann fluid. The instability saturates by trapping some of the plasma ions. The instability is slightly weaker when the dust particles have a range of sizes, and corresponding range of charges and masses. It is argued that due to dust particles that comprise planetary rings, this process can contribute to ion heating and diffusion observed in the inner magnetosphere of Saturn. ¿ American Geophysical Union 1995