The role of charge relaxation in electrified tip streaming

TL;DR

This paper investigates how charge relaxation influences tip streaming in electrified droplets, revealing oscillatory behavior and the importance of charge transfer limitations in jet formation.

Contribution

It combines experimental and numerical analysis to show the role of charge transfer and oscillations in the onset of tip streaming, advancing understanding of electrohydrodynamic instabilities.

Findings

Oscillations occur before jet ejection at low conductivity.

Charge transfer limitations reduce electrostatic pressure at the droplet tip.

Global stability analysis matches experimental onset but predicts non-oscillatory instability.

Abstract

We study experimentally and numerically the onset of tip streaming in an electrified droplet. The experiments show that, for a sufficiently small dimensionless conductivity, the droplet apex oscillates before ejecting a liquid jet. This effect is caused by the limited charge transfer from the bulk to the interface. This reduces the electrostatic pressure at the droplet's stretching tip, preventing liquid ejection. This reduction of electrostatic pressure is compensated for by the electric shear stress arising during the apex oscillations, which eventually leads to the jet formation. The stability limit calculated from the global stability analysis perfectly agrees with the experimental results. However, this analysis predicts non-oscillatory, non-localized instability in all the cases, suggesting that both the oscillatory behavior and the small local scale characterizing tip streaming arise during the nonlinear droplet deformation.