The role of surface conductivity in electromechanics and electrohydrodynamics of a dielectric drop

A new technology of the electric-field manipulation by dielectric particles in dielectric liquids and drops has been developed in the last decades. To simulate electromechanics of microparticles in a weaklyconducting dielectric drop the Taylor's leaky-dielectric model is extended. To achieve this electric-potential distribution inside and outside a weakly-conducting dielectric sphere embedded in a weakly-conducting dielectric in an electric field is determined taking into account the interfacial current. The conventional definition of the total, bulk plus surface, conductance of the sphere is detailed allowing for its dependence on the angular distribution of the external electric field. Technology of microparticles moving over the interface of the drop is based on the application of electrohydrodynamic (EHD) drag and dielectrophoretic (DEP) forces. The surface conductivities of the drop and individual microparticles can have a significant influence on the surface charge and thereby on the DEP and EHD drag forces. Thus, we show that recent explanation of manipulation by microparticles trapped at the interface of a silicone-oil drop immersed in castor oil is misleading. Taking into account the surface conductivity of the microparticles, we find that EHD drag and DEP forces are of the same direction but not opposite at zero or low frequencies as stated previously. Due to the reversal of the DEP force with the field frequency the motion of microparticles turns back. Surface conductivity of the drop can also explain experiments in which the prolate deformation persists after liquids of the drop and ambient medium are interchanged.