Caustics of finitely dense inertial particles in 2D flows, and the “lucky” drops

Caustics occur where inertial particles suspended in flows collide. They can be identified in a continuum as regions where the divergence of the particle velocity field diverges to negative infinity. We show that less dense particles need to go through stronger strain to form caustics. However, not all particles going through such high strain undergo caustics, and we propose a mechanism for this.
In a sea of tiny droplets, a larger drop, owing to its larger inertia, has more potential to col-lide with smaller drops, coalesce with them, and grow. We derive an equation of motion of these big lucky droplets. In turbulence, we show that their growth scales with the smaller drops’ inertia, and point to the advantage enjoyed by luckier drops starting out in vortical regions.