Enhanced droplet collision rates and impact velocities in turbulent flows: The effect of poly-dispersity and transient phases

We compare the collision rates and the typical collisional velocities amongst droplets of different sizes in a poly-disperse suspension advected by two- and three-dimensional turbulent flows. We show that the collision rate is enhanced in the transient phase for droplets for which the size-ratios between the colliding pairs is large as well as obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. Our results suggest that an explanation of the rapid growth of droplets, e.g., in warm clouds, may well lie in the dynamics of particles in transient phases where increased collision rates between large and small particles could result in runaway process. Our results are also important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining precise coalescence kernels in such systems.