Electrohydrodynamics of a liquid drop in confined domains

The steady-state electrohydrodynamics of a leaky dielectric drop in confined domains is investigated analytically. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky dielectric theory and for the creeping flow regime. The domain confinement strengthens or weakens the electric field, depending on R>1 or R<1, respectively, where R=σi/σo is the ratio of electric conductivity of the drop to that of the surrounding fluid. Similarly, the flow intensity decreases for R<1, but it remains unchanged or increases for R>1, depending on the interplay of electric and hydrodynamic effects. An expression for the drop deformation for small distortion from the spherical shape is found using the domain perturbation technique. It is shown that below a threshold domain size the confinement effect will lead to the reversal of the tendency of the net normal hydrodynamic stress in deforming the drop to an oblate or a prolate shape, and that below a critical domain size the necessary condition for having an oblate drop will be opposite to the classical one for an unbounded domain.