On the effective dielectric constant of columns or layers of dielectric spheres

Publisher Website
Google Scholar
Abstract
The equivalent dielectric constant of an inhomogeneous medium consisting of columns or layers of regularly spaced dielectric spheres is calculated using the method of Rayleigh as modified by Lam. A regular spacing of columns or layers is assumed, with only interactions from spheres within individual columns or layers taken into account. Interactions between columns (or layers) are ignored. The unit cell structure chosen for each geometry allows independent variation of volume fraction and inter-sphere spacing. For fixed sphere-to-sphere spacing, the plot of dielectric constant versus volume fraction is linear, and the slope is an infinite series of multipolar terms from neighbouring spheres. This series converges quickly except for the case of closely spaced spheres with high relative dielectric constant. The results for columns and layers may be used to bracket the effective dielectric constant of particle beds.