Numerical Study of Microdroplet Deformation and Breakup Under a Steady Electric Field

Manipulation of microdroplets in a precise manner by an external electric field has received much attention due to its importance in the fields of chemical engineering, biomedicine, energy and environment. In order to accurately manipulate the droplet behavior in microfluidic devices, it is necessary to study and gain an in-depth understanding of the deformation and breakup of a viscous droplet under an external electric field. In this paper, a hybrid method, in which the color lattice Boltzmann and the finite difference methods are coupled by the leaky dielectric model, is used to study the deformation and breakup of a droplet under a steady electric field. The hybrid method is first validated by simulating the droplet subject to a small deformation. We then investigate the influence of the intensity of the electric field, the ratio of the dielectric permittivity inside and outside of the droplet, as well as the ratio of the electric conductivity on the droplet behavior. It is found that the oblate droplet can exhibit four different shapes or states, i.e. ellipse, quasi-ellipse, dumbbell, and droplet breakup, which are strongly dependent on the electrical capillary number. Distinct from the oblate droplet, the prolate droplet does not exhibit the dumbbell shape but the periodic oscillation. For either prolate or oblate droplet, increasing electrical capillary number leads to an increased droplet deformation when the deformation occurs, and to a shorter time for the droplet to break up when the breakup occurs. This study provides the theoretical foundation for a deep understanding of droplet deformation and breakup in the presence of electric field.