A model for the behaviour of fluid droplets based on mean curvature flow

TL;DR

This paper introduces a theoretical model based on mean curvature flow to explain the complex behavior of charged fluid droplets, including attraction, repulsion, and coalescence, supported by new mathematical proofs.

Contribution

The paper develops a novel mean curvature flow model that predicts droplet behavior and provides a new proof for multiple flow evolutions of double cones, extending previous results.

Findings

Model accurately predicts droplet attraction, repulsion, and coalescence.

Provides a new proof for existence of multiple mean curvature flow solutions.

Shows decreasing surface energy can explain complex droplet phenomena.

Abstract

During his experiments W. D. Ristenpart made a very remarkable discovery. If two oppositely charged droplets of fluid are close enough, at first they attract each other and touch eventually. Surprisingly after that the droplets are repelled from each other, if the initial strength of the charges is high enough. Otherwise they coalesce and form a big drop, as one might expect. We present a theoretical model for this observation, using mean curvature flow. With the help of appropriate barriers for the flow we can predict the observed droplet behaviour. This shows that, contrary to general belief, decreasing surface energy can explain the phenomenon. The barrier construction includes a new proof for the existence of multiple mean curvature flow evolutions of certain double cones, first discovered by Angenent, Chopp and Ilmanen. Our proof yields a slightly stronger result.