Particle shape effects on the effective permittivity of anisotropic or isotropic media consisting of aligned or randomly oriented ellipsoidal particles

The effective permittivity (dielectric constant) of anisotropic or isotropic porous media is affected by the shape of particles composing the mixture. Directional permittivities are influenced by extreme aspect ratio particles, often found aligned with the bedding plane of rock or soil. Our objectives were to determine the effects of particle shape and preferential orientation on the effective permittivity of porous media. Confocal spheroids (ellipsoids of revolution) were used to mathematically describe a range of particle shapes from disks to spheres to needles. Dielectric mixing models which account for the polarization due to inclusion shape and axial alignment were used to estimate the shape effect. Permittivity measurements in an anisotropic packing of disk-shaped mica particles using time domain reflectometry showed an alteration of the permittivity due to the shape effect. Two- and three-phase predictions based on Maxwell-Garnett [1904] showed trends similar to measurements in anisotropic packings of mica. Particle shape effects can be a significant factor in dielectric permittivity measurements and should be a consideration especially where particle aspect ratio deviates by more than an order of magnitude from that of a sphere (unity). As the particle shape is less spherical, the resulting effective permittivity of the mixture is more similar to the inclusion permittivity and differs more from the permittivity of the background. Ellipsoid size and surface area provide an estimate of the combined effects of bound water and particle shape on the effective mixture permittivity. For high aspect ratio particles, shape effects on the effective permittivity appear to be comparable in magnitude to those of bound water prevalent in clay-sized media.