The motion of heavy particles in potential vortex flows on the unit disk is investigated theoretically and numerically. Configurations with one vortex and with two vortices are considered. In both cases, each vortex follows a regular path on the disk. In the one-vortex case, it is shown that small, heavy particles may accumulate in elliptic regions of the flow, counter-rotating with respect to the vortex. When the particle Stokes number exceeds a threshold depending on the vortex configuration, all particles are expelled from the circular domain. A stability criterion for particle accumulation is derived analytically and verified by numerical results. In the two-vortex case, heavy particles are shown to accumulate in elliptic islands of regular motion. Again, this result is explained by a stability analysis. The results may be useful in the design of gas-particle separators containing a helical vortex filament.