Effect of the of Surface-Charge Diffusion on the Polarization of a Dielectric Sphere and Its Role in Electrohydrodynamics and Electromechanics

To simulate 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 distribution inside and outside a dielectric sphere placed in a uniform electric field is determined assuming the sphere and ambient medium are weakly conducting and taking into account electric and diffusion interfacial currents and surface-charge decay. Earlier, an electric-field characteristic of a dielectric sphere, for example, the real part of the Clausius-Mossotti factor found for the direct current (DC) field, was commonly thought to be a single-valued function of two parameters, the conductivities of the sphere and ambient medium. Now, it depends on a larger number of parameters and, in the DC case, ranges from the perfect dielectric to perfect-conductor values even for a particle of a good insulator. The dielectrophoretic (DEP) inflection and crossover 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. The proposed model is confirmed by a review of phenomena observed mainly in a silicone-oil drop suspended in castor oil with microparticles at the interface.