Electrocoalescence Criterion of Conducting Droplets Suspended in a Viscous Fluid

Abstract

Coalescence of conducting droplets dispersed in an immiscible medium can be facilitated by an electric field. However, droplets recoil promptly after contact in sufficiently high electric fields if the cone angle between droplets exceeds a critical value. To elucidate the critical condition for droplet coalescence, the behavior of two suspended droplets after contact with a direct current electric field is studied. It is shown that the critical angle is determined not only by the droplet geometry but also conductivity, surfactant concentration, and size. As the droplet conductivity increases, more identical ions accumulate on the adjacent interfaces of two droplets due to the faster ionic migration, which results in Coulombic repulsion between droplets and a reduced critical angle. For surfactant-laden droplets, film drainage induces a surfactant concentration gradient on the leading edges of droplets, and then Marangoni stress is formed to reduce the critical angle. In the case of large droplets, the bridge transiently expands under the action of directional flow caused by further droplet deformation, but eventually breaks due to opposite electrostatic forces. Based on this finding, the electrocoalescence criterion can be determined and employed to facilitate droplet coalescence in various applications.