Induced-charge electroosmosis, polarization, electrorotation, and traveling-wave electrophoresis of horn toroidal particles

A theoretical framework is presented for calculating the polarization and induced-charge electrophoretic mobility of a polarizable closed (horn) toroidal micro-particle exposed to a non-uniform axial AC electric forcing. The analysis is based on employing the standard (linearized) ‘weak-field’ electroosmotic model for a symmetric electrolyte. In particular, we discuss the case of traveling-wave excitation and provide analytic expressions for the tori induced-phoretic velocity in the Stokes regime in terms of the frequency and wavelength of the ambient electric field. In addition, we consider the non-linear electroosmotic flow problem about a stationary torus, which is subject to a uniform field, and provide explicit expressions for the resulting Stokes’ stream function driven by the surface Helmholtz–Smoluchowski velocity slip. Finally, we analyze the case of asymmetric (transverse) two-component electrorotation and by calculating the Maxwell electric torque, provide analytic solution for the induced-charge angular velocity of a freely suspended conducting horn torus.