Critical charges for droplet collisions

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.

arXiv comment14 pages, 2 figures

References in corpus (5)

• Statistical models for spatial patterns of heavy particles in turbulence
• Time-dependent lift and drag on a rigid body in a viscous steady linear flow
• Settling of an asymmetric dumbbell in a quiescent fluid
• Collisions of micron-sized, charged water droplets in still air
• Bifurcations in droplet collisions