Bouncing of charged droplets: An explanation using mean curvature flow

¹ Sintzenichstr. 11, 81479 München, Germany
² Mathematics Institute, University of Warwick - Coventry, CV4 7AL UK

^(a) shelmensdorfer@googlemail.com
^(b) p.m.topping@warwick.ac.uk

Received: 27 August 2013
Accepted: 29 October 2013

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 letter 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.