The Role of Surface-Charge Transport in Electrohydrodynamics and Electromechanics of a Dielectric Sphere

Abstract

To simulate the electrokinetic processes in weakly-conducting dielectric media, the Taylor–Melcher leaky-dielectric model is widely used, though its applicability conditions are unknown. To define them, the electric-potential distributions inside and outside a dielectric sphere placed in an electric field are determined, by assuming the sphere and the environment are weakly conducting and by considering the electric and diffusion interfacial currents and the surface-charge decay. Earlier, an electric-field characteristic of a dielectric sphere, for example, the real part of the Clausius–Mossotti factor found for a direct current (DC) field was commonly thought to be a single-valued function of two parameters, the conductivities of the sphere and the environment. Now, it depends on a larger number of parameters and, in the dc case, can range from the perfect-dielectric to perfect-conductor values even for a particle of a good insulator. Using the proposed theory, a variety of the experimental results on the electrohydrodynamic (EHD) fluid circulation and dielectrophoretic (DEP) motion of microparticles in the dielectric drops are explained for the first time or in a new way. The dielectrophoretic inflection and cross-over frequencies are defined allowing for the decay of the surface charge. A dependence of the effective conductivity of a sphere on the angular field distribution is predicted for the first time.