Electrocapillary, thermocapillary, and buoyancy convection driven flows in the Melcher-Taylor experimental setup

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 represent the corresponding experimental image. With the increase of electrocapillary forcing, the flow pattern changes, so that the main circulation localizes near a boundary with a larger electric potential. When a dielectric liquid is replaced by a poorly conducting one, the system becomes nonisothermal 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. 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 nonuniform surface electric potential, is numerically verified for both isothermal and nonisothermal formulations and is found to hold in both of them.