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.

Analysis of the electric field and force in an arrangement of a conducting sphere and a plane electrode with a dielectric barrier

“…The method of multipole images [5,6] is used to calculate the electric field in the arrangement of Figure 1. The method is principally the classical method of images [22] using multipoles of higher orders than point or dipole charges, e.g.…”

“…Details of the multipole re-expansion and the image for a conducting sphere are described in [5,6]. Note that, starting from the second iteration, multipoles of higher degrees ( , , 3 …”

“…The behavior of the field and the force on a particle decisively depends on whether the particle is dielectric or conducting. For the dielectric particle, the electric field and force have been analyzed under various conditions for high-voltage insulation equipment or electrorheological fluid [2][3][4][5][6]. For the conducting particle, most of the works reported deal with configurations of two particles [7][8][9][10] or those of a particle and a plane electrode [11,12].…”

Calculation of the electric field in arrangements of intersecting spheres

“…10,11 It is more general than that using the inversion or transformation, 1-3 as it can treat spheres of unequal radii that intersect each other at an arbitrary angle. The method is extended from the one proposed for configurations of separated spheres.…”

Can a Century Old Experiment Reveal Hidden Properties of Water?

“…In 1996 Hughes et al calculated both trapping and a translational dielectrophoretic forces on particles travelling in electric fields [107], and in 2006, Techaumnat et al calculated the electric field and the dielectrophoretic force on spherical particles in a chain in a dielectric fluid [108] and found stable regimes, which could be an important basis for similar considerations concerning the floating water bridge.…”