Development of strongly nonlinear structures at the charged boundary of a non-conducting liquid in an electric field

TL;DR

This paper uses direct numerical simulation to study the nonlinear development of surface instabilities in a charged non-conducting liquid under an electric field, revealing two distinct stages and the evolution of bubble formation.

Contribution

It presents a detailed numerical analysis of the nonlinear stages of surface instability, highlighting the transition from dimples to bubbles and their size dependence on the electric field.

Findings

Identification of two main instability stages: dimples and bubbles.

Bubble size increases with stronger electric fields.

Scale of dominant instability mode decreases as the field increases.

Abstract

Direct numerical simulation of the strongly nonlinear stages of instability development for a non-conducting liquid with a charged free surface in a normal electric field is performed. It is demonstrated that two main stages of the instability can be distinguished: an initial stage, during which dimples appear on the surface, and a developed stage, during which these dimples transform into expanding bubbles. The bubble size increases with increasing applied field, despite the fact that the scale corresponding to the dominant mode of the instability decreases.