Pulsating emission of droplets from an electrified meniscus

A numerical description is given for the pulsating emission of droplets from an electrified meniscus of an inviscid liquid of infinite electrical conductivity which is injected at a constant flow rate into a region of uniform, continuous or time periodic, electric field. Under a continuous field, the meniscus attains a periodic regime in which bursts of tiny droplets are emitted from its tip. At low electric fields this regime consists of sequences of emission bursts interspersed with sequences of meniscus oscillations without droplet emission, while at higher fields the bursts occur periodically. These results are in qualitative agreement with experimental results in the literature. Under a time periodic electric field with square waveform, the electric stress that acts on the surface of the liquid while the field is on may generate a tip that emits tiny droplets or may accelerate part of the meniscus and lead to a second emission mode in which a few large droplets are emitted after the electric field is turned off. Conditions under which each emission mode or a combination of the two are realized are discussed for low frequency oscillatory fields. A simplified model is proposed for high electric field frequencies, of the order of the capillary frequency of the meniscus. This model allows computing the average emission rate as a function of the amplitude, duration and bias of the electric field square wave, and shows that droplet emission fails to follow the applied field above a certain frequency.