Electrical conductivity and dielectric permittivity of sphere packings: Measurements and modelling of cubic lattices, randomly packed monosize spheres and multi-size mixtures

New and literature measurements are compared for the electrical transport properties of densely packed spherical particles. Measurements of electrical conductivity in cubic lattices are presented and were found to agree closely with numerical solutions for the conductivity presented in the literature. Electrical conductivity and dielectric permittivity of dense random packings are presented. Deviation from the Maxwell/Maxwell-Garnett models is clearly observed. The deviation is considered to be due to the interacting electrical fields of neighbouring particles in a densely packed system. Both electrical conductivity and dielectric permittivity were described using a model containing a heuristic parameter that can be adjusted to account for this interaction (Sihvola and Kong, IEEE Trans. Geosci. Remote Sens. 26 (1988) 420). The heuristic parameter can range between 0 and 1, and a value of about 0.2 was found to describe both the electrical conductivity and permittivity data. A more physically rigorous model developed by Torquato (J. Appl. Phys. 58(10) (1985) 3790) also described the data for cubic lattices and random packings exceptionally well. The model was rigorously derived containing a 3-point correlation function ζ2 to describe the interaction due to the micro-geometry.