Point particles with inertia are centrifuged out of vortex cores. This is a classical result: the Maxey-Riley equation shows that particles denser than the surrounding fluid spiral outward in rotation, accumulating at the edges of vortices. Trapping a heavy particle at a vortex center is impossible.
Assen, Calzavarini, and Toschi show that extended particles can be trapped. A dumbbell — two spheres connected by a rigid rod — samples the velocity field at two separated points simultaneously. This nonlocal sampling breaks the point-particle centrifugal mechanism because the flow experienced by the dumbbell depends on the velocity gradient across its length, not just the local value at its center of mass.
The trapping is non-monotonic in Stokes number. At very low Stokes number (small inertia), the dumbbell follows the flow and isn't trapped. At very high Stokes number (large inertia), the dumbbell is too heavy to respond and isn't trapped. At an intermediate Stokes number, the combination of inertial response and nonlocal sampling produces a net inward force that traps the dumbbell at the vortex center.
The mechanism requires the dumbbell to rotate. As it rotates in the vortex, the two ends sample alternating high-velocity and low-velocity regions. The asymmetry between outward centrifugal force (strong when aligned with the flow) and inward pressure gradient force (strong when perpendicular) averages to a net inward drift over one rotation period.
A point particle flies out. A dumbbell falls in. The difference is that the dumbbell can feel the velocity field in two places at once.