Dielectrophoretic interaction of two spherical particles calculated by equivalent multipole-moment method

A generalized equivalent multipole-moment theory is developed for the dielectrophoretic interactions between two arbitrarily oriented spherical dielectric particles in an external field. The method is based on the re-expansion technique: first, the electrostatic potential disturbance created by one of the dielectric spheres is expressed as a series of spherical harmonic terms with r^-(n+1)-dependence. This potential, having no singularities except at the center of the sphere, is then re-expanded about the center of the second sphere as a new series of spherical harmonics with rⁿ-dependence. Once this re-expansion is done, the effect of one sphere on its neighbor can be represented by an externally applied potential, and the interaction force thus calculated. The analytical results make it possible to investigate the strong angular dependence of the interaction force as particle spacing and permittivity are varied