Calculation of electric field and dielectrophoretic force on spherical particles in chain

Abstract

This article presents an analytical method for calculating electric field and dielectrophoretic force in three-dimensional arrangements of spherical particles. The analytical method is based on the method of images that utilizes the multipole re-expansion and the fundamental solutions for several arrangements of a multipole. It is capable of calculating electric field for various conditions of particles and energization. The method needs much less memory than the already proposed one. The calculation results show that force on a dielectric particle chain in a dielectric fluid depends on the number of particles and the chain direction. However, the maximal attractive and repulsive forces reach their saturation values at about 32 and 12 particles, respectively. When the lower particle of a two-particle chain is in contact with a plate electrode, the dielectrophoretic force on the chain becomes higher on the whole, and it always attracts the chain to the electrode. As a result, the particle chain is stabilized for a wider range of the angle between the chain and the applied field. Neglecting the interaction between the electrodes and particles usually gives adequate accuracy in the force calculation, unless the electrodes are not very close to particles.