Numerical simulation of deformation / motion of a drop suspended in viscous liquids under influence of steady electric fields

Abstract

The deformation / motion of a droplet suspended in a viscous liquid under the influence of an applied external electrical field are investigated through numerical simulations. The two-phase flow field of the drop suspension system is simulated using a front tracking / finite volume method for solving the full Navier-Stokes equations. Three different electric field models are applied in order to take into account the effects of the electric field, electric charge, and electrical properties of liquids. Drops with no net charge but finite electrical conductivity are simulated using a leaky dielectric model. Perfect dielectric model is used for the drops of electrically isolating fluid. To take into account the presence of a net charge on drop surface, we proposed a simplified constant surface charge model. In addition, the simulation code using the leaky dielectric model and perfect dielectric model is validated systematically against the results of theoretical analysis, the available experimental data, and the simulations by other researchers. It shows that the proposed numerical method (front tracking / finite volume method coupled with various electric field models) can make reasonable prediction on droplet deformation / motion under externally applied electrical field. Under different combinations of liquid properties, the droplets may deform into either prolate or oblate shape, and induce different inner and outer circulating flow patterns. When a net charge presents on the droplet surface and an electrical field is applied, both droplet deformation and motion can be reasonably predicted by the constant charge model. The simulation results demonstrate that the current numerical method may provide an effective approach to quantitatively analyze the complex electrohydrodynamic problems.