A phase field numerical study of 3D bubble rising in viscous fluids under an electric field

In this paper, a 3D phase field model is presented for a numerical study of the hydrodynamic behavior of a bubble rising in fluid subject to an external electric field. The computational model entails a numerical solution to the Laplace equation for electric field, the Navier–Stokes equation for fluid flow and Cahn–Hilliard equation for interface deformation and morphology. These equations are discretized by time marching finite difference scheme and an in-house FORTRAN code program is developed to enable the simulation. The coupled electric-fluid-flow model is capable of predicting the evolution of electric field and the deformation of rising bubble in medium fluid. Special interests are focused on the influence of electrical force on the motion of a bubble as it ascends through the viscous medium liquid. It is found that a vertical electric field accelerates the ascending of a bubble while a horizontal one decelerates it. Also, the electric field, either horizontal or vertical, affects the morphology of the bubble as it rises by buoyancy.