Collisions have traditionally been neglected in calculating the shielding around a small spherical collector in a plasma, and the plasma flow to the collector. We show analytically that, in dusty plasmas under typical discharge conditions, ion charge-exchange collisions lead to the buildup of negative-energy trapped ions which dominate the shielding cloud in the nonlinear region near a dust grain and substantially increase the ion current to the grain, even when the mean-free path is much greater than the Debye length.