Direct evidence of jets emanating from droplets at the Rayleigh charge-induced instability point

Abstract: Highly charged liquid droplets are unstable above the critical charge squared-to-volume ratio given by the Rayleigh limit. The instability leads to ion ejection from jets formed on the droplet's surface. Despite the many experiments that have been performed to capture the jet formation the precise fission mechanism has not yet been observed because of its brief transient nature. Here, we present the first atomistic simulations that reveal the mechanism of Rayleigh fission. We demonstrate that ion ejection takes place through a drop's deformation from a spherical into a distinct shape that contains a conical protrusion. We assert that the latter state is a free energy minimum along an order parameter that measures the degree of droplet asphericity. The charged droplet's long-time evolution proceeds by alternating between the two minima above and below the critical value that are reached through solvent evaporation and ion ejection, respectively. For the first time, this mechanism allows one to explain the nature of the progeny droplets and the percentage of charge lost during fission. We determine that the cone half-angle is close to the value predicted from the solution of the electrostatic equation for the dielectric liquid. It is found that the conical deformation is independent of the effect of electrohydrodynamic forces reported in experiments. Contrary to the experimental observations of two diametrically opposite jets for droplets suspended in the electric field, we found that a single jet is formed at the Rayleigh limit. This indicates that super-charged droplet states may have been detected in the experiments.