  Collisional growth of droplets, such as occurring in warm clouds, is known to
be significantly enhanced by turbulence. Whether particles collide depends on
their flow history, in particular on their encounters with highly intermittent
small-scale turbulent structures, which despite their rarity can dominate the
overall collision rate. Intuitively, strong vortices may act as slings for
inertial particles, leading to intersections where several streams of particles
collide at large velocities. Here, we develop a quantitative criterion for
sling events based on the velocity gradient history along particle paths. We
demonstrate by combination of theory and simulations that the problem reduces
to a one-dimensional localization problem as encountered in condensed matter
physics. The reduction demonstrates that the creation of slings is completely
controlled by the smallest negative eigenvalue of the velocity gradient tensor.
We use fully resolved turbulence simulations to confirm our predictions and
study their Stokes and Reynolds number dependence. We also discuss
extrapolations to the parameter range relevant in clouds, showing that sling
events at high Reynolds numbers are significantly enhanced for small Stokes
numbers.
