The Role of Surface Conductivity in Electro-Mechanics of Microparticles in a Meakly-Conducting Dielectric Drop

In order to simulate motion of microparticles in a weakly-conducting dielectric drop the Taylor's leaky-dielectric model is extended taking into account the interfacial current. Electric-potential distribution inside and outside a weakly-conducting dielectric sphere embedded in a weakly-conducting dielectric in a uniform alternating-current (AC) electric field is determined. 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. Migration of microparticles over the interface of the drop due to the electrohydrodynamic (EHD) drag and dielectrophoretic (DEP) forces is concluded to depend strongly on the surface conductivities of the drop and individual microparticles. Thus, we show that recent explanation of manipulation by microparticles across the surface of a silicone-oil drop immersed in castor oil is misleading. Allowing for 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. The motion of microparticles turns back because of the reversal of the DEP force with the field frequency. Surface conductivity of the drop can also explain experiments in which the prolate deformation persists after liquids of the drop and ambient media are interchanged.