Shape deformations of surface-charged microdroplets

Abstract

We present the deformation pathway of critically charged glycol and water droplets from the onset of the Rayleigh instability and compare it to numerical results, obtained for perfectly conducting inviscid droplets. In this simple model presented here, the time evolution of the droplet shape is given by the velocity potential equation. The Laplace equation for the velocity potential is solved by expanding the potential onto harmonic functions. For the part of the pathway dominated by electrostatic pressure, the calculations reproduce the experimental data nicely, obtained for both, glycol and water microdroplets. We find that the droplet shape and in particular the tips, just before charge emission, are well fitted by a lemon shape. We stress that the tip is tangent to a cone of 39 degrees and thus significantly narrower than a Taylor cone.