Critical charges for droplet collisions

TL;DR

This paper investigates the transition point where electrostatic forces dominate droplet collision efficiency, considering hydrodynamic breakdown and charge effects for micron-sized water droplets in air.

Contribution

It provides a quantitative analysis of the critical charge levels at which electrostatic forces override hydrodynamic effects in droplet collisions.

Findings

Oppositely charged droplets transition at ~10^3 elementary charges.

Same polarity charged droplets transition at ~10^4 elementary charges.

Collision efficiency depends on Kn number for small charges, independent for large charges.

Abstract

The collision efficiency of uncharged micron-sized water droplets in air is determined by the breakdown of hydrodynamics at droplet separations of the order of the mean-free path, by van-der-Waals forces, or a combination of the two. In contrast, electrostatic forces determine the collision efficiency of charged droplets if the charge is large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically-interacting droplets settling in quiescent air, including the breakdown of hydrodynamics at small interfacial distances. For oppositely charged droplets, the transition occurs when a saddle point of the relative droplet-dynamics exits the region where the hydrodynamics breaks down. For droplets with radii $16\,\mu$m and $20\,\mu$m, this occurs at $\sim 10^3$ elementary charges $e$. For smaller charges, the collision efficiency depends upon the Kn number (defined as the ratio of the mean-free-path of air to the mean droplet radius), whereas for larger charges it does not. For droplets charged with the same polarity, the critical charge is $\sim 10^4\,e$ for the above radii.