  The motion of tiny heavy particles transported in a co-rotating vortex pair,
with or without particle inertia and sedimentation, is investigated. The
dynamics of non-inertial sedimenting particles is shown to be chaotic, under
the combined effect of gravity and of the circular displacement of the
vortices. This phenomenon is very sensitive to particle inertia, if any. By
using nearly hamiltonian dynamical system theory for the particle motion
equation written in the rotating reference frame, one can show that small
inertia terms of the particle motion equation strongly modify the Melnikov
function of the homoclinic trajectories and heteroclinic cycles of the
unperturbed system, as soon as the particle response time is of the order of
the settling time (Froude number of order unity). The critical Froude number
above which chaotic motion vanishes and a regular centrifugation takes place is
obtained from this Melnikov analysis and compared to numerical simulations.
Particles with a finite inertia, and in the absence of gravity, are not
necessarily centrifugated away from the vortex system. Indeed, these particles
can have various equilibrium positions in the rotating reference frame, like
the Lagrange points of celestial mechanics, according to whether their Stokes
number is smaller or larger than some critical value. An analytical stability
analysis reveals that two of these points are stable attracting points, so that
permanent trapping can occur for inertial particles injected in an isolated
co-rotating vortex pair. Particle trapping is observed to persist when
viscosity, and therefore vortex coalescence, is taken into account. Numerical
experiments at large but finite Reynolds number show that particles can indeed
be trapped temporarily during vortex roll-up, and are eventually centrifugated
away once vortex coalescence occurs.
