Tip streaming of jets emanating from Rayleigh breakup of a charged viscous droplet

An isolated liquid drop charged beyond its Rayleigh limit becomes unstable and emits a fraction of charge and mass in the form of a jet which further disintegrates into progeny droplets. The formation of conical tips and the associated jet emission are the complex fluid dynamical phenomena and are still unclear. When a drop is modelled as a perfect conductor and solved using axisymmetric boundary element method (BEM) it is observed to form sharp conical ends where the numerical approach fails to predict the jet emission due to the occurrence of shape singularity. This indicates the dominance of normal electrical stresses over capillary stresses. To predict the jet formation in conducting drops, a modified electrostatic model is used in this work by including the surface charge dynamics. This accounts for the finite charge relaxation timescales over which the drop surface is charged as well as the convection of charges by the interfacial flow. The simulations show that it gives rise to the tangential electrical stresses which are expected to exert an axial momentum on the fluid and accelerate the proto-jet out of the tip of the drop. The jet grows progressively and forms progenies at the tip whose sizes are observed to vary inversely with the conductivity of the liquid drop.