Multipolar dielectrophoretic and electrorotation theory

A new dyadic tensor representation for multipolar moments is used to formulate expressions for the dielectrophoretic force and electrorotational torque exerted on lossy spherical particles by an arbitrary electric field. The new tensor expressions for the moments satisfy the requirement of symmetry. When combined with previously derived expressions for the induced moments in terms of the electric field and its derivatives, the theory accommodates electrically linear spherical particles with any type of ohmic or dielectric loss in any sinusoidally-varying electric field. The special case of a plant protoplast suspended in an aqueous medium and subjected to a traveling electric field wave is chosen to demonstrate the theory's easy adaptation to the practical planar or multi-planar microelectrode geometries now used to move, rotate, or position small particles such as biological cells.