Generalized multipolar dielectrophoretic force and electrorotational torque calculation

Generalized expression for the dielectrophoretic (DEP) force and electrorotational (ROT) torque are obtained for a spherical particle under the influence of an arbitrary elliptically polarized quasistatic electric field. The method of analysis employs equivalent multipole-moments mathematically represented by derivatives of the spatial impulse function. The force and torque are expressed in terms of scalar and vector electromechanical potentials that are functions of the imposed electric field. The DEP force consists of two components: one proportional to the product of the gradient of a scalar electromechanical potential and the real part of the particle polarizability and the other proportional to the product of the curl of a newly introduced electromechanical vector potential and the imaginary part of the polarizability. In any linearly polarized field, the curl term vanishes. The ROT torque is directly proportional to the product of the new electromechnical vector potential and the imaginary part of the polarization.