Role of surface charge convection on oblate droplets in different conductivity regimes

Abstract

This paper presents a robust numerical model to simulate the electro-hydrodynamic flows of a neutrally buoyant liquid droplet suspending in another liquid for varying electrical conductivities ranging from near-dielectric to highly conductive fluids. The effect of such conductivity on the interfacial charge transport in the droplets has been investigated. The model is first validated with the theory of electro-rotation corresponding to the strong electric field. The results are compared with the theoretical predictions from the Quincke theory. The angular velocities at different electric field ratios agree well with theoretical predictions. Furthermore, droplet investigations are performed in distinct conductivity regimes with the electric Reynolds number ranging from 10−2 to 104. The findings reveal that conductivity influences the evolution of diverse droplet shapes in the corresponding regimes through surface charge convection. We observe prolate shapes at very low electric conductivities, while larger conductivities of droplets and suspending media lead to oblate drop shapes. With increasing electrical conductivity of the droplet and the medium, we observe the onset of distinct droplet shapes similar to the existing literature. The mechanism for the onset of different regimes is adequately explained by quantifying surface properties like tangential stress and velocity.