  The present study deals with the dynamics of a double emulsion confined in a
microchannel under the presence of a uniform electric field. Towards
investigating the non-trivial electrohydrodynamics of a compound droplet,
confined in between two parallel plate electrodes, a phase field approach has
been adopted. Under the assumption of negligible fluid inertia and small shape
deformation, an asymptotic model is also developed to predict the transient as
well as the steady state droplet dynamics in the limiting case of an unbounded
suspending medium. The phases involved are either assumed to be perfect
dielectric or leaky dielectric. Subsequent investigation shows that shape
deformation of either of the interfaces of the droplet increase with rise in
the channel confinement for a perfect dielectric system. However, for a leaky
dielectric system, the deformation of inner droplet and outer droplet can
increase or decrease with the rise in channel confinement depending on the
electric properties (conductivity and permittivity) of the system. The present
study further takes into account the effect of eccentricity of the inner
droplet. Depending on the relative magnitude of the permittivity and
conductivity of the system, the inner droplet, if eccentrically located, may
exhibit a to and fro or a simple translational motion. It is seen that increase
in the channel confinement results in a translational motion of the inner
droplet thus rendering its motion independent of any electrical properties.
Since the compound droplet model approximately mimics the structure of a cell,
the current investigation is expected to provide a significant impact towards
predicting the effect of an externally imposed electrical field on the dynamics
of a cell in any fluidic confinement and hence has the potential towards
widespread applications in the field of medical diagnostics.
