Electro-phoretic rotation and orientation of polarizable spheroidal particles in AC fields

A theoretical study is provided for determining the angular rotation rate of an ideally polarized (metallic) spheroidal particle freely suspended in a symmetric electrolyte under general alternating current ambient electric excitations. In particular, we discuss cases of electro-rotation (ROT) and electro-orientation (EOR) of such nano/micro particles incited by two orthogonal electric field components which may be out of phase. The analysis is carried under the Poisson-Nernst-Planck approximation and the "weak" field model. The analytic expressions thus obtained are valid for a conducting prolate spheroid with arbitrary eccentricity including the limiting cases of isotropic spheres and infinitely long cylindrical rods. The total dipolophoretic (DIP) angular velocity is decomposed from contributions due to dielectrophoresis (DEP) induced by the dipole-moment within the particle and by the induced-charge electrophoresis (ICEP) mechanism near the conducting surface. It is demonstrated that the explicit expressions for the DIP angular velocities reduce to the well-known ROT solution for the sphere as well as to the recently found expressions (based on slender-body approximation) for both ROT and EOR of metal nanowires [Arcenegui et al., "Electro-orientation and electrorotation of metal nanowires," Phys. Rev. E 88(6), 063018 (2013)]. Some comparisons with available experimental data are also provided for slender spheroidal geometries including a detailed discussion of DEP and ICEP effects and their relative contributions to the overall DIP rotational velocity.