Radial oscillations and enhanced collision rates of heavy inertial particles in the vicinity of a vortex

Trajectories of heavy inertial particles near a vortex are expected to converge to an outgoing spiral with a short transient wherein the radius increases monotonically. These transients are considered the cause of caustics. We present results on the dynamics and collision rates of inertial particles finitely denser than the surrounding fluid in the vicinity of a vortex, using the Maxey-Riley equation, with and without the Basset-history force. Contrary to conventional wisdom, we find that in the regime of vortex-associated particle Stokes number > 1, heavy particles starting even outside the vortex core can move inward, and proceed to perform several radial oscillations before converging to an outgoing spiral. This gives rise to a rich particle caustics profile, as well as a significantly higher particle collision rate around the vortex than if these transients were ignored. We particularly highlight how the history force makes non-trivial changes to the transients, by significantly altering the duration of transients, collision rates and distribution of locations of caustic events, hence making a case for why Basset history force shouldn't be ignored.