Simulations of Coulombic Fission of Charged Inviscid Drops

TL;DR

This paper uses boundary-integral simulations to study how charged inviscid droplets evolve, showing the formation of sharp tips and progeny drops, with results matching experimental observations of charged drop behavior.

Contribution

It introduces detailed boundary-integral simulations of charged droplet evolution, revealing the formation of cone-shaped tips and progeny drops depending on conductivity.

Findings

Sharp tip formation with self-similar cone shape

Progeny drops form at tips with nearly critical charge

Conductivity influences progeny drop size and emission behavior

Abstract

We present boundary-integral simulations of the evolution of critically charged droplets. For such droplets, small ellipsoidal perturbations are unstable and eventually lead to the formation of a "lemon"-shaped drop with very sharp tips. For perfectly conducting drops, the tip forms a self-similar cone shape with a subtended angle identical to that of a Taylor cone. At the tip, quantities such and pressure and fluid velocity diverge in time with power-law scaling. In contrast, when charge transport is described by a finite conductivity, we find that small progeny drops are formed at the tips whose size decreases as the conductivity is increased. These small progeny drops are of nearly critical charge, and are precursors to the emission of a sustained flow of liquid from the tips as observed in experiments of isolated charged drops.