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

Abstract

Abstract. 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.

Effect of particle size distribution on the effective dielectric permittivity of saturated granular media

“…It is probably the less regular and spherical shape of the sand grains that reduces the effective permittivity of both the monosize packing and the mixtures. Knowing the Maxwell-Garnett predictions for glass spheres appear accurate, an effective aspect ratio can be determined for an isotropic packing of oblate ellipsoids of revolution [Sihvola and Kong, 1988;Jones and Friedman, 2000]. An aspect ratio of 4 (4:4:1, disk-shaped particles) was determined to give an upper bound; this is not to say that the particles are ellipsoids of this shape but that the effect that they have on the shape of the water bodies is equivalent to oblate ellipsoids with this aspect ratio.…”

New concept in assessing compactness of woven structure in terms of its resistivity

“…Other inclusions properties, such as size and shape, can also have an effect on electroconductive properties of composite [24]. The potential range of considered inclusion shapes extends from flat disks to spheres to long needles [25].…”

“…The more general case for oriented ellipsoids, with a depolarization factor (demagnetization coefficient) in the direction of current flow was discussed by Sen et al [28]. The polarizability is a function of inclusion geometry, independent of volume, and orientation with respect to the applied electrical field [25]. Depolarization factor indicates the influence of the geometrical shape on the polarization of the dielectric ellipsoid in an electric field and the magnetization of the magnetic ellipsoid in a magnetic field [29].…”

The Influence of Water Coating on the Optical Scattering Properties of Fractal Soot Aggregates

“…Modeling the radiative impact of soot clusters in a manageable way in climate models is therefore an important matter. In humid atmospheric environments, soot aggregates frequently acquire a water coating, which introduces further complexity to the problem of determining the optical properties of the aggregates (Hanel 1976;Jones and Friedman 2000;Kocifaj et al 2008;Yin and Liu 2010). As described below, this study conceptually separates the geometric effects of aggregate structure from the effects of water coating and focuses on the latter.…”