Behavioral mode transition of nanoscale ionic liquid droplets in the ion emission regime

Conductive droplets in strong electric fields are prone to Coulombic explosions. At the nanoscale, the electric field strength on the droplet surface can become sufficiently intense to directly extract ions from the liquid, a phenomenon termed ion field evaporation. Previous studies have demonstrated that ion field evaporation profoundly alters the dynamics of Coulombic explosions by depleting the charge carried by droplets. This study incorporates the mass loss due to ion field evaporation, a crucial factor for nanoscale droplets that was previously overlooked. Utilizing a sharp immersed electrohydrodynamic model, the behavior of neutral droplets composed of the ionic liquid [C2C1Im][BF4] is analyzed for radii ranging from 5 to 500 nm under electric fields exceeding the Coulombic limit. A new mode emerges as the droplet radius falls below a critical threshold, which, for the selected ionic liquid, typically lies between 10 and 50 nm. In this mode, intense ion field evaporation at the droplet's surface induces weak Stokes flows within the droplet, leading to a gradual reduction in volume. A scaling law for the critical radius is derived, which shows good agreement with the numerical results.