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.

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Understanding and modulating the cross-stream motion of a surfactant-coated droplet in pressure driven flow has great implications in many practical applications. A combination of interfacial viscosity and Marangoni stress acting over a surfactant-coated droplet in pressure driven flow offers greater flexibility to modulate the cross-stream motion of it. Despite the intense theoretical and numerical research towards manipulating the surfactant-laden Newtonian droplets in Poiseuille flow, the experimental investigations are seldom explored. Herein, we report our study on understanding the influence of interfacial viscosity on the cross-stream motion of a surfactantcoated Newtonian droplet in both isothermal and non-isothermal Poiseuille flow from a theoretical as well as an experimental perspective. A theoretical model has been developed to understand the effect of interfacial viscosity on the lateral migration of a droplet under the assumptions of no shape deformation and negligible fluid inertia or thermal convection. Theoretical analysis is performed under two limiting conditions: (i) when the transport of surfactants is dominated by surface-diffusion and (ii) when the transportation of surfactants is dominated by surface-convection. Our theoretical analysis shows that both the dilatational as well as the shear surface viscosities suppress the lateral migration velocity of the droplet. Experiments have been performed to validate the theoretically predicted droplet trajectories and to understand the influence of channel confinement on the lateral migration of the droplet. It has been observed from the experiments that the droplet travels faster towards the centerline of the flow in a highly confined domain. The results presented in this study could provide new vistas in designing and analyzing various droplet-based microfluidic, biomedical and bio-microfluidic devices.

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