  Electrocapillary-driven two-phase flows in a confined configuration of a
classical experiment of Melcher and Taylor are studied. The computed
streamlines of the flow of the heavier dielectric liquid (corn oil)
qualitatively represents the corresponding experimental image. With the
increase of electrocapillary forcing, the flow pattern changes, so that the
main circulation localizes near boundary with a larger electric potential. When
a dielectric liquid is replaced by a poorly conducting one, the system becomes
non-isothermal owing to the Joule heating. Then the flow is driven also by
buoyancy and thermocapillary convection, whose effect becomes noticeably
stronger than the electrocapillary one. With the increase of electric
conductivity, the electrocapillary effect is further weakened compared to the
two others, while the electrocapillary and thermocapillary forces remain
comparable at the central part of the interface, where the thermocapillary
force changes its sign. The results show that consideration of the two-phase
model is mandatory for obtaining correct flow patterns in the lower heavier
fluid. The Lippmann equation, connecting electrically induced surface tension
with non-uniform surface electric potential, is numerically verified for both
isothermal and non-isothermal formulations and was found to hold in both of
them.
