Electrohydrodynamics of a liquid column under a transverse electric field in confined domains

The steady state electrohydrodynamics of a leaky dielectric fluid column in confined domains is investigated. The governing electrohydrodynamic equations are solved, in a plane normal to the column axis, for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and for creeping flow regime. The domain confinement strengthens or weakens the electric field, depending on R > 1 or R < 1, respectively, R = σi/σo being the ratio of electric conductivity of the column 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 interface deformation for small distortion from the circular 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 interface to an oblate or a prolate shape, and that below a critical domain size the necessary condition for having an oblate column will transfer from R < S to R > S, where S = ϵi/ϵo is the permittivity ratio.