Bouncing of charged droplets: An explanation using mean curvature flow

TL;DR

This paper explains the bouncing behavior of oppositely charged droplets using mean curvature flow, providing a unified energy-based explanation and predicting the critical charge differential for bouncing versus coalescence.

Contribution

It introduces a novel explanation for droplet bouncing phenomena using mean curvature flow, advancing beyond surface energy minimization models.

Findings

Accurately predicts the threshold charge differential for bouncing.

Demonstrates that energy considerations fully explain the bouncing behavior.

Provides a mathematical framework linking mean curvature flow to droplet interactions.

Abstract

Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens when the charge difference is sufficiently small. However, Ristenpart et al discovered a remarkable physical phenomenon whereby for large enough charge differentials, the droplets bounce off each other as they make contact. Explanations based on minimisation of area under a volume constraint have been proposed based on the premise that consideration of surface energy cannot be sufficient. However, in this note we explain that on the contrary, the bouncing phenomenon can be completely explained in terms of energy, including an accurate prediction of the threshold charge differential between coalescence and bouncing.