A phase field model for multiphase electro-hydrodynamic flow

The principles of electro-hydrodynamics have been known for more than a century and extensive experimental studies have been carried out. Insight about such types of flows have been widely adopted for industrial applications, e.g. fluid mixing and de-mixing, but analytical solutions only exist in a limited number of cases, e.g. small deformation of a single droplet in a uniform and steady electric field. Numerical modeling of such phenomena can provide significant insights into electro-hydrodynamic multi-phase flows. In the present paper we propose a phase field model for studying two-phase electro-hydrodynamic flow generated by an electric field. The proposed model is validated and found to be in good agreement with existing analytical solutions and numerical studies in the literature. We also investigate the influence of viscosity ratio and surface tension in binary coalescence of drops in an immiscible fluid.