Electrohydrodynamics of confined two-dimensional liquid droplets in uniform electric field

In this study, the electrohydrodynamics of viscous droplets in a confined domain under the action of a uniform electric field is investigated numerically. Considering both the phases to be perfect dielectric or leaky dielectric, two-dimensional numerical simulations are performed to obtain the shape deformation of droplets placed between two parallel plate electrodes. The aim of this study is to show the effect of domain confinement on the droplet morphology and temporal droplet deformation. Perfect dielectric systems always deform into a prolate shape, and the magnitude of deformation is augmented or reduced in a confined domain depending on the electrical permittivity ratio. For leaky dielectric systems, the electrical conductivity ratio comes into play and the droplet can attain an oblate or prolate shape depending on the size of the droplet relative to the channel height. A regime diagram is constructed to show the impact of domain confinement on the droplet shape. Additionally, the steady-state deformation parameter undergoes some non-monotonic variation with domain confinement for the leaky dielectric systems. The domain confinement can significantly decrease the droplet deformation and thereby suppress the droplet breakup phenomenon for few leaky dielectric systems. The domain confinement markedly affects the temporal evolution of the droplet deformation. The temporal evolution of the droplet shape shows that the droplet deforms more sluggishly toward its final steady configuration in a confined domain when the inertial effects are negligible. The oscillations in droplet deformation at the finite inertial regime are also suppressed in a confined domain. Finally, the interaction of two droplets is also studied, which shows that coalescence and detachment of the droplet pairs take place at a slower rate in a confined domain with respect to an unbounded domain. Thus, the present study shows the possibility of modulating the droplet morphology by tuning the domain confinement, which can be of potential use in designing droplet-based microfluidic devices