Numerical analysis of two-phase electrohydrodynamic flows in the presence of surface charge convection

The mechanism of surface charge convection (SCC) reveals inherently nonlinear coupling between the electrostatic problem and the hydrodynamic flow in the Melcher-Taylor electrohydrodynamic (EHD) model. Considering that most previous numerical models are based on decoupled leaky dielectric equations, the quantitative effect of SCC on two-phase EHD under different parameters remains unclear. In the present study, we propose a new numerical scheme to solve the two-phase EHD problems in the framework of the lattice Boltzmann method. The fully coupled equations including the Navier-Stokes equations, the Nernst-Planck equations, and the Poisson equation are solved using three well-designed lattice Boltzmann equations. The problem of droplet deformation under a uniform electric field is studied. By neglecting SCC at a small electric Reynolds number Re-E << 1, our model successfully reproduces previous theoretical and numerical results. When considering the SCC mechanism at finite values of Re-E, the intensity of the EHD flow is reduced. Consequently, oblate droplets are predicted to be less deformed, while prolate droplets are enhanced. In addition, the SCC effect increases as the values of both Re-E and the electric capillary number, Ca, increase. In addition, a sharp variation in surface charge density is observed near the equator of the droplet due to SCC.