Multipole Corrections to Dielectrophoretic Force

Calculation of the dielectrophoretic (DEP) force on a neutral dielectric partide in a nonuniform electric field is simplified by using the effective dipole method. Once the instantaneous effective dipole moment peff(t) has been correctly identified using Gauss´s law, then the expression (peff(t)¿)E0(t) is used to determine the force on the particle. Recent work has demonstrated that the effective dipole method produces a result consistent with integration of the Maxwell stress tensor. In the present paper, the issues concerning identification of peff(t) are aired, and an alternate derivation of the DEP force on a conducting dielectric sphere immersed in a conducting dielectric fluid is offered. Then the effective dipole theory is generalized to account for higher order (multipole) contributions. This new effective multipole theory is restricted to spherical particles in a cylindrically symmetric cusped electric field, but the analysis leads to straightforward computation of the quadrupolar correction factor for the DEP force. A quantitative example is provided.