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

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 (Ca_E), 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 Ca_E, and the critical electric capillary number for droplet breakup, Ca_EB, 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 Ca_E. For prolate droplets, the droplet state may undergo the transition from steady shape to periodic oscillation and finally to breakup as Ca_E increases. Increasing Q increases both Ca_EB and the critical electric capillary number Ca_EO, which characterizes the transition from steady shape to periodic oscillation, but the increase in Ca_EO is less significant. In the Ca_E-R diagram, the periodic oscillation is limited to a small range, and increasing R decreases Ca_EB.