Precise calculation of dielectrophoretic force in arbitrary field

Abstract

The conventional expression for the Dielectrophoretic (DEP) force is based on the equivalent dipole method, in which the force is calculated as the interaction of the induced dipole moment and the non-uniform external field. The DEP force calculation presented in this paper is the generalization of the equivalent dipole moment method, and the DEP interaction between higher harmonic components of external field and the induced multi-pole moment is treated. The mathematical basis of this method is the re-expansion of the field in Legendre harmonics around an arbitrary position in space. An important result obtained is that the field with single harmonic component will not yield DEP effects. This is because the n-th external potential yields the n-th induced dipole and ( n−1)-th field, which are mathematically orthogonal to each other and cannot interact. The method is applied for the DEP force calculation in a multi-pole field, and the result is compared with that obtained by the dipole approximation. It is shown that the effect of higher harmonics becomes dominant near the center of the multipole field.