Multi-bubble motion behavior of electric field based on phase field model* *Project supported by the National Natural Science Foundation of China (Grant Nos. 51661020, 11504149, and 11364024), the Postdoctoral Science Foundation of China (Grant No. 2014M560371) and the Funds for Distinguished Young Scientists of Lanzhou University of Technology, China (Grant No. J201304).

Abstract

By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation, electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble. The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong (E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method (LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.