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The present study deals with the dynamics of a double emulsion confined in amicrochannel under the presence of a uniform electric field. Towardsinvestigating the non-trivial electrohydrodynamics of a compound droplet,confined in between two parallel plate electrodes, a phase field approach hasbeen adopted. Under the assumption of negligible fluid inertia and small shapedeformation, an asymptotic model is also developed to predict the transient aswell as the steady state droplet dynamics in the limiting case of an unboundedsuspending medium. The phases involved are either assumed to be perfectdielectric or leaky dielectric. Subsequent investigation shows that shapedeformation of either of the interfaces of the droplet increase with rise inthe channel confinement for a perfect dielectric system. However, for a leakydielectric system, the deformation of inner droplet and outer droplet canincrease or decrease with the rise in channel confinement depending on theelectric properties (conductivity and permittivity) of the system. The presentstudy further takes into account the effect of eccentricity of the innerdroplet. Depending on the relative magnitude of the permittivity andconductivity of the system, the inner droplet, if eccentrically located, mayexhibit a to and fro or a simple translational motion. It is seen that increasein the channel confinement results in a translational motion of the innerdroplet 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 towardspredicting the effect of an externally imposed electrical field on the dynamicsof a cell in any fluidic confinement and hence has the potential towardswidespread applications in the field of medical diagnostics.

Electrohydrodynamics of compound droplet in a microfluidic confinement