Electric field induced ion evaporation from charged nano-droplets undergoing Rayleigh fission

It is well understood that droplets charged beyond a certain charge (referred to as the Rayleigh limit) are unstable and undergo fission, where the parent droplet sheds a significant fraction of its charge in the form of smaller progeny droplets. Alternatively, charged droplets in the nano-metric size regime can support electric field large enough to directly extract ions from the surface of the droplet (referred to as the ion emission process). The two competing mechanisms are of fundamental practical importance in the electrospray community such as electrospray ionization mass spectrometry (ESI-MS) and electrospray propulsion. However, studying the fate of ion emitting charged droplets has been challenging due to the nano-metric length scale along with the fast transient nature of these processes. We developed a continuum phase field numerical model to study the effects of ion emission and Rayleigh fission processes on charged droplets. The minimum electric field required to trigger the emission of ions along with the amount of charge the parent droplets shed in the form of ions and smaller progeny droplets is numerically quantified. We show that for droplets with size <50nm, ion emission completely suppresses the Rayleigh fission process, thereby having a stabilizing effect. However, ion emission is not sufficient to suppress Rayleigh fission for relatively larger droplets (50-100nm). For these larger droplets, both ion emission and the Rayleigh fission processes are at play with the droplet overall shedding 23% of its original charge as ions and 15% as smaller progeny droplets.