A Note on Electrified Droplets

TL;DR

This paper analyzes a family of electrified droplets, introduces a technique for finding new solutions, and discusses potential extensions to more complex droplet configurations.

Contribution

It provides a detailed analysis of existing droplet solutions and proposes a new method for discovering additional solutions, including multi-component droplets.

Findings

Re-derivation of a family of physical droplets

Development of a technique for solving droplet equations

Discussion on extending solutions to multiple components

Abstract

We give an in-depth analysis of a 1-parameter family of electrified droplets first described in D. Khavinson et. al. (2005). We also investigate a technique for searching for new solutions to the droplet equation, and rederive via this technique a 1-parameter family of physical droplets, which were first discovered by D. Crowdy (1999). We speculate on extensions of these solutions, in particular to the case of a droplet with multiple connected components.