Transient oscillation response characteristics of an electrohydrodynamic settling drop subjected to a uniform electric field

The transient oscillation response of an electrohydrodynamic settling drop under a uniform electric field is numerically investigated. The governing equations are solved in the lattice Boltzmann framework through the application of the leaky dielectric model and the pseudopotential model for the multi-phase electrohydrodynamic problem. A viscous drop with inertia is considered for non-density matched settling systems. Numerical simulations are performed over a range of electric capillary numbers CaE, Eotvos numbers Eo, and Ohnesorge numbers Oh. The results indicate that three typical development stages, namely, the electric stress-dominated stage, the force competition stage, and the inertia-dominated stage, are identified in terms of the deformation evolution characteristics. Our study also demonstrates the role of the three dimensionless numbers in the deformation response at each stage. It is found that, at the earlier stage of settling, the maximum achievable deformation is sensitive to CaE and Oh, while the influence of Eo on the first oscillatory peak at the deformation-time curve is approximately neglectable. Moreover, the deformation response time is determined by the interaction of the electric field, the gravitational field, and viscosity. Specifically, the corresponding oscillatory peak time correlates positively with Eo and Oh numbers and exponentially grows with CaE.