Deformation and mechanical behavior of electrohydrodynamic droplet under external electric field

Droplet deformation and mechanical behavior under external electric field are fundamental in electrohydrodynamic research. Based on the volume-of-fluid (VOF) method and adding electric force to Navier-Stokes equations as an additional source term, a simulation method considering fluid flow and electric field in two-way coupling is proposed. Using this method, the deformation/motion of leaky dielectric droplet and charged droplet under external uniform and non-uniform electric field is investigated respectively. The shape deformation coefficient calculated by the proposed method is close to the theory value of leaky dielectric droplet under uniform electric field in small deformation condition; thus the validity of the numerical method proposed in this study is verified. The results show that the charge redistribution modes of leaky dielectric droplet depend on the property difference between droplet and the around fluid, and the droplet may deform into either prolate or oblate shapes. The electric field strength only affects the droplet shape deformation coefficient. The external uniform electric field induces strong circulation motion inside the leaky dielectric droplet without moving the droplet. Because of the effect of Coulomb force, the charged droplet may deform into prolate and move along the electric field direction. However both leaky dielectric droplet and charged droplet may move along the electric field direction, resulting in different shapes simultaneously under the non-uniform electric field. The numerical method coupling fluid flow with electric field proposed in this paper could provide an effective approach to electrostatic spray, electrophoresis and other complex engineering electrohydrodynamic researches.