Jet and progeny formation in the Rayleigh breakup of a charged viscous drop

Past experimental studies have indicated that the Rayleigh fission of a charged drop occurs via the formation of a jet followed by emission of progeny droplets. In order to understand this process, we model the evolution of a drop using an axisymmetric boundary element method in the viscous limit. In this work, the electrostatic model of a charged viscous liquid drop is modified by including surface charge dynamics. This model accounts for the finite charge relaxation time scales over which the drop surface is charged as well as the convection of charges by the interfacial flow. It is observed that, as the drop deforms with time, the generally applied assumption of an equipotential surface becomes invalid near the conical ends that experience singularly fast dynamics and the associated surface charge dynamics gives rise to tangential electric stresses. These tangential electric stresses exert an axial momentum on the fluid and are responsible for the formation of a jet and progeny droplets. Further, the progeny droplets are found to follow an inverse power-law scaling with the conductivity of the liquid and the smaller sized progenies carry a charge close to its Rayleigh limit.