Phase separation of crude oil is a vital and common problem in the petroleum industry, and electric field assisted water droplets coalescence is regarded as one of the most efficient demulsification approaches. The correlative principles about electrohydrodynamics have been developed accompanied by experiments. In this study, we adopt the phase field method to develop a multi-field coupling multiphase model with the impact of an electric field. The Poisson equation is used to characterise the electric potential distribution, the Navier-Stokes equations modified with additional electrokinetic effect source terms are used to characterise the laminar flow in a channel, and the moving interface is tracked by solving the Cahn-Hillard equations. Subsequently, the model is employed to simulate the flow of emulsions in a channel and the coalescence of water droplets stimulated by an applied electric field. The journey of oil-water interphase shows that the whole process of electrocoalescence is explicitly separated into the approaching stage and aggregating stage. Among those various electrokinetic mechanisms, the dipole-dipole interaction plays a dominant role in facilitating the coalescence of droplets. The dielectrophoresis caused by the non-uniformity of electric fields has both positive and negative effects on the enhancement of electrocoalescence. The simulation about the Poiseuille flow driven by pressure gradient shows that the flow velocity decreases with the increase of electric intensity and zeta potential. It is acquired that the resistance effect of the electric double layer gives rise to a flow rate loss, which indicates the necessity to research the material properties of fluids and wall surface in the future.