This article develops a leaky-dielectric model to study the axisymmetric breakup of an electrified jet, using the phase field method to treat interfacial phenomena. The model is used to analyze the breakup in a wide range of the Taylor number ($\mathrm{\Gamma }$), the Ohnesorge number (Oh), and the wave number relevant to electrosprays operating in the cone-jet mode. The phase field technique accurately captures the behavior of the jet after pinch-off and predicts the formation of primary and satellite droplets. The numerical results are compared with existing experimental and numerical studies, extending them to account for the formation of sub-satellite droplets. It is found that for highly viscous jets, $\text{Oh}\gg 1$, the number of subsatellite droplets generated increases with the Taylor number when compared to low viscous jets, hence widening the size distribution of droplets. At fixed $\mathrm{\Gamma }$ and Oh the primary droplets are charged to an approximately constant ratio of the Rayleigh charge limit, regardless of the wave number. Furthermore, the primary droplets are charged below the Rayleigh limit for $\mathrm{\Gamma }\lesssim 1.5$ and charged above the Rayleigh limit when $\mathrm{\Gamma }\gtrsim 1.5$. Thus, most primary droplets are expected to be unstable at Taylor numbers exceeding 1.5.

• Received 6 February 2022
• Accepted 24 May 2022

DOI:https://doi.org/10.1103/PhysRevFluids.7.064004