A fully explicit incompressible smoothed particle hydrodynamics method for simulating 2-D electrohydrodynamic multi-phase flows based on leaky dielectric model

This paper presents a fully explicit two-dimensional electrohydrodynamics (EHD) numerical model, which scrutinizes multiphase flows' dynamics and interactions when exposed to an external electric field. The electrostatic phenomena are interconnected with hydrodynamics through the resolution of the Maxwell's equations, which are simplified along with its boundary conditions based on the leaky dielectric model. An explicit smoothed particle hydrodynamics formulation is developed to discretize the Poisson equation in order to calculate the electric potential and the consequent forces that are derived through the divergence of the Maxwell's equations. This approach offers the advantage of having low computational costs while simultaneously simplifying its implementation. Furthermore, to interpolate the physical properties on the discretized domain, i.e. particles, our recently proposed quartic-spiky kernel function is used. Comparisons with both analytical and numerical data from literature are performed. Then, various test cases are presented and new benchmarks are incorporated. This includes the EHD of a drop deformation within a fluid, interactions between two and three drops, as well as the Rayleigh-Taylor instability under an external electric field. The results herein presented clearly illustrate the strong capability of the proposed method and its robustness in simulating multiphase flows with intricate interfaces under a constant external electric field.