  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.
