Pulsating Electrohydrodynamic Cone-Jets: from Choked Jet to Oscillating Cone

Pulsating cone-jets occur in a variety of electrostatic spraying and printing systems. We report an experimental study of the pulsation frequency to reconcile two models based on a choked jet and an oscillating cone, respectively. The two regimes are demarcated by the ratio of the supplied flow rate ($Q_s$) to the minimum flow rate ($Q_m$) required for a steady Taylor cone-jet. When $Q_s < Q_m$, the electrohydrodynamic flow is choked at the nozzle because the intermittent jet, when on, emits mass at the minimum flow rate; the pulsation frequency in the choked jet regime is proportional to $Q_s/Q_m$. When $Q_s > Q_m$, the Taylor cone anchored at the nozzle experiences a capillary oscillation analogous to the Rayleigh mode of a free drop; the pulsation frequency in the oscillating cone regime plateaus to the capillary oscillation frequency which is independent of $Q_s/Q_m$.