Cloud droplets tend to carry charges. The resulting electrostatic forces affect droplet-collision rates and thus the droplet-size distribution. The collision dynamics of charged cloud droplets has been studied by numerical integration of model equations. But it is not known when these models work, how they fail, how Coulomb forces compete with hydrodynamic effects to determine the rate at which charged droplets settling through a cloud grow by collision. There is no theory explaining the parametric dependence upon charge, droplet size, and velocity.
We investigate the effect of electrical charge on collisions of hydrodynamically interacting, micron-sized water droplets settling through quiescent air. We used Lagrangian tracking to analyse experimental data on collisions of microscopic, charged droplets. Our theory explains the observed collision dynamics (Figure 1) by characterising its fixed points and their invariant manifolds. Our analysis describes how the collision dynamics depends on droplet charges and radii, amongst other parameters. The theory is accurate for the charges we consider. We discuss how it breaks down for smaller charges.
Figure 1. (a) Spatial separation of neutral droplets in the rest frame of the smaller droplet (green disk). Experiments (solid lines) and fitted model imulations (dashed lines). Blue lines indicate that the experiment resulted in a collision, red lines a miss. (b) Same but for oppositely charged droplets. The red encircled cross indicates the location of a saddle point together with its stable and unstable manifolds (solid black lines). From Ref. .
Figure 2. Collision and coalescence of oppositely charged micron-sized droplets settling in still air. From Ref. .
 Collisions of micron-sized, charged water droplets in still air
G Magnusson, A Dubey, R Kearney, GP Bewley & B Mehlig, preprint arXiv:2106.11543