How Violent are the Collisions of Different Sized Droplets in a Turbulent Flow?

TL;DR

This paper provides a theoretical and numerical analysis of collision velocities among droplets of different sizes in turbulent flows, crucial for understanding processes like rain formation.

Contribution

It offers the first precise theoretical estimates of impact velocities based on particle size ratios in turbulent flows, validated by direct numerical simulations.

Findings

Impact velocity saturates exponentially with inverse size ratio

Theoretical estimates match simulation data

Results inform models of droplet coalescence and fragmentation

Abstract

We study the typical collisional velocities in a polydisperse suspension of droplets in two and three-dimensional turbulent flow and 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. We show that the impact velocity saturates exponentially with the inverse of the particle-size ratios. Our results are important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining precise coalescence kernels to describe the growth of water droplets which trigger rain in warm clouds.