Universal scaling law for electrified sessile droplets on a lyophilic surface

Electrified sessile droplets on solid surfaces are ubiquitous in nature as well as in several practical applications. Although the influence of electric field on pinned sessile droplets and soap bubbles has been investigated experimentally, the theoretical understanding of the stability limit of generic droplets remains largely elusive. By conducting a theoretical analysis in the framework of lubrication approximation, we show that the stability limit of a sessile droplet on a lyophilic substrate in the presence of an electric field exhibits a universal power-law scaling behavior. The power-law exponent between the critical electric field and the droplet volume is found to be -1. The existence of this scaling law is further explained by virtue of minimization of the total free energy of the electrified droplet.