Deformation and breakup of an electrohydrodynamic falling droplet in viscous fluids under vertical/horizontal electric fields

Droplet dynamics is a class of phenomena ubiquitous in both natural and industrial processes. In this paper, we developed a phase-field lattice Boltzmann method to investigate the electrohydrodynamic falling droplet under vertically and horizontally applied electric fields. The electric field model is based on the leaky dielectric theory, and numerical results are validated by Taylor's theory, showing good agreement under small deformation conditions. It was found that the vertical electric field suppresses the depression at the droplet tail. When the intensity of the electric field is high, the droplet stretches along the electric field direction, which ultimately results in the droplet breakup. In contrast, a horizontal electric field drives lateral expansion, which facilitates the formation of a crescent-shaped structure, followed by the bubble breakup. An increase in the conductivity ratio enhances the lateral deformation of the droplet, while an increase in the dielectric constant ratio suppresses the occurrence of lateral deformation. This study reveals the regulatory mechanism of electric fields on droplet morphology and motion, providing a theoretical basis and numerical foundation for droplet manipulation in complex multi-physical field environments.