  The present study deals with the numerical as well as asymptotic analysis of
the electrohydrodynamic interaction between two deformable droplets in a
confined shear flow. Considering both the phases as leaky dielectric, we have
performed numerical simulations to study the effect of channel confinement on
the drop trajectories in the presence of a uniform electric field. Two
important varieties of motion are identified in the present analysis, namely
(i) the reversing motion and (ii) the passing over motion. The study suggests
that conversion of the passing over motion to the reversing motion or vice
versa is possible via modulating the strength of the imposed electric field.
Such a conversion of the pattern of droplet migration is also possible in a
confined domain due to change in different electrical properties of the system.
The present numerical model is also able to predict the pattern of the
trajectory of individual droplets depending on the initial distance separating
the two. For example, a smaller initial distance results in a reversing motion
whereas a passing over motion is predicted when the distance between the
droplets is significantly large. However, the final positions of the droplets
are found to be independent of their initial positions. Interestingly, presence
of electric field is found to prevent droplet coalescence to a certain extent
depending on its strength, thus rendering the emulsion stable. A small
deformation asymptotic model is also developed under the assumption of
negligible fluid inertia to support the numerical results for the limiting case
of an unbounded flow. The current investigation successfully presents a novel
technique to predict the precise positions of a system of droplets in a
micro-channel and how electric field can be used as a tool to modulate droplet
trajectories in an emulsion.
