The role of charge relaxation in electrified tip streaming

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 the electrostatic pressure is compensated for by the electric shear stress arising during apex oscillations, which eventually leads to the jet formation. The stability limit calculated from the global stability analysis perfectly agrees with 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.