Droplet shape oscillations in the presence of alternating electric fields

The succession of prolate-oblate shape oscillations of liquid droplets and gas bubbles is a fundamental problem in fluid dynamics that has led to multiple studies that date back to Rayleigh in 1879. It is recognized in the literature that viscous droplets have a natural frequency of oscillation f_n which is dependent on the physical properties of the liquid and droplet size. Deformation and breakup of freely falling droplets finds applications in ink-jet printing, spraying systems, microfluidic systems, among others. Further, large degrees of droplet deformation and breakup lead to an increased surface-to-volume ratio which modulates transport phenomena through the droplet. In the presence of an electric field, a droplet of leaky dielectric fluid undergoes higher degrees of deformation due to electrostatic stresses at its surface.

In this study, computational and experimental work was carried out to characterize the shape deformation of viscous droplets under the effects of external AC electric fields. The degree of deformation and oscillation frequency was investigated with respect to applied voltage amplitude and AC frequency (f_AC). In particular, we studied the droplet response at excitation frequencies f_AC/f_n ≈ 1 and f_AC/f_n >> 1. Further, the effect of gravitational acceleration on droplet deformation which leads to vortex shedding was investigated in the computational simulations along with the distribution of charges. Our results indicate an increase in deformation amplitude to the point of breakup as well as a modification in oscillations with increasing applied voltage. Resonance effects are described for an f_AC/f_n ≈ 1, while at higher frequencies the natural frequency of oscillation is dominant, at the observed time scales.