The influence of the curvature dependence of the surface tension on the geometry of electrically charged menisci

We evaluate how the curvature dependence of surface tension affects the shape of electrically charged interfaces between a perfectly conducting fluid and its vapour. We consider two cases: i) spherical droplets in equilibrium with their vapour; ii) menisci pending in a capillary tube in presence of a conducting plate at given electric potential drop. Tolman-like dependence of surface tension on curvature becomes important when the "nucleation radius" is comparable with the interface curvature radius. In case i) we prove existence of the equilibrium minimal radius and estimate its dependence on the electric fields and Tolman-like curvature effects. In case ii) the menisci are subject to the gravitational force, surface tension and electrostatic fields. We determine the unknown surface of the menisci to which the potential is assigned using an iterative numerical method and show that Tolman-like corrections imply: 1) a variation of the height (up to 10% in some cases) of the tip of the menisci; 2) a decrease of the maximum electrical potential applicable to the menisci before their breakdown amounting to 40V over 800V in the considered cases. We conjecture that these effects could be used in new experiments based on electric measurements to determine the dependence of the equilibrium surface tension on curvature.