EQUILIBRIA AND DYNAMICS OF DEP-LEVITATED PARTICLES - MULTIPOLAR THEORY

Recent designs for dielectrophoretic (DEP) levitators with practical applications in the suspension and manipulation of biological cells feature salient pole electrodes and a zero of the electric field along the central axis. The levitation force on a dielectric particle centered in such a structure cannot be accounted for by the conventional theory of dielectrophoresis because the net induced dipole moment is zero. Instead, higher-order multipoles are induced which provide the force. In this paper, a new multipolar theory for dielectrophoresis is combined with a general analytical form for the electrostatic potential due to salient pole electrodes in order to formulate the equilibria and dynamics of levitated particles. Results obtained for the special case of axisymmetric electrodes are found to be consistent with earlier work. The method makes it easy to predict the particle size above which higher-order multipolar force terms become important in any given levitator. The formulation, which accepts field coefficients obtained analytically or numerically, can be used as a tool for the design of DEP levitators, micromotors, and other miniature electromechanical devices.