Numerical study of droplet dynamics in a steady electric field using a hybrid lattice Boltzmann and finite volume method

Abstract

A hybrid method is developed for simulation of electrohydrodynamics interfacial flows. This method uses a lattice Boltzmann color model to describe the immiscible two-phase flow and a finite volume method to solve the Poisson equation for electric potential. The lattice Boltzmann and finite volume simulations are coupled by the leaky dielectric model. The method is applied to simulate a single droplet subject to a steady electric field, in which the influence of electric capillary number (CaE), dielectric constant ratio (Q) inside and outside of the droplet, and electric conductivity ratio (R) is studied for both oblate and prolate droplets. For a droplet undergoing small deformation, our numerical results are found to agree well with theoretical predictions, justifying the numerical method. Results of oblate droplets show that at low R, the droplet undergoes the transition from steady deformation to breakup with CaE, and the critical electric capillary number for droplet breakup, CaEB, decreases with increasing Q, whereas at high R, the droplet does not break up but finally reaches a steady shape regardless of the value of CaE. For prolate droplets, the droplet state may undergo the transition from steady shape to periodic oscillation and finally to breakup as CaE increases. Increasing Q increases both CaEB and the critical electric capillary number CaEO, which characterizes the transition from steady shape to periodic oscillation, but the increase in CaEO is less significant. In the CaE-R diagram, the periodic oscillation is limited to a small range, and increasing R decreases CaEB.