A phase-field-based lattice Boltzmann modeling of two-phase electro-hydrodynamic flows

In this paper, a simple and accurate lattice Boltzmann (LB) model based on phase-field theory is developed to study the two-phase electro-hydrodynamics flows. In this model, three LB equations are utilized to solve the Allen-Cahn equation for the phase field, the Poisson equation for the electric potential, and the Navier-Stokes equation for the flow field. To test the proposed model, the deformation of a single droplet under a uniform electric field is considered. It is found that under a small deformation, the results are in good agreement with the previous work. For a large deformation, however, the theoretical results would give a large deviation, while the present results are close to the available numerical work.