Useful Relationships between Dielectric Properties and Bulk Densities of Granular and Powdered Materials

When knowledge of the dielectric properties, or permittivity, of granular or powdered materials is important, as in dielectric heating applications or in the sensing of moisture content by radio-frequency or microwave instruments, some reliable relationship between the dielectric properties and the bulk density of the material is required. Linear relationships between functions of the permittivity and bulk density have been observed, and dielectric mixture equations have been explored to obtain useful relationships for determining the dielectric properties of granular and powdered materials. These findings are reviewed, useful permittivity-density relationships are identified, and an equation is provided that permits reliable calculation of the permittivity of a particulate material at any given bulk density, if the permittivity is known or measured at another known bulk density. The relationships are illustrated for pulverized coal, wheat, ground wheat, limestone, and a coal-limestone mixture. The useful mixture equation is valid for granular and powdered materials with permittivities in the same range as those for grain, coal and limestone. Introduction When the permittivity, or dielectric properties, of granular or powdered solid materials are important, some reliable relationship between the permittivity and the bulk density of the air-particle mixture is required. Examples of such applications include radio-frequency or microwave dielectric heating of these materials and the use of correlations between permittivity and water content of hygroscopic materials for sensing moisture content. Also, relationships between the permittivities of pulverized or granular samples of materials and those of the solid materials have long been of interest for use in determining the permittivities of the solids from measured permittivities of the particulate samples. Dielectric mixture equations have been developed and investigated for this purpose [1-3]. An extrapolation procedure, based on the linearity with density of functions of the real and imaginary parts of the permittivity of pulverized and granular materials, has also been used to obtain estimates of the permittivity of the solid material [4, 5]. Both of these methods, calculation by dielectric mixture equations and the extrapolation procedure, will be described in the following sections for estimating the permittivity of solids from measured permittivity data on granular or powdered samples of those materials. Dielectric Mixture Equations Many different dielectric mixture equations have been proposed to represent the effective permittivity of mixtures of dielectric materials, and the characteristics and performance of these equations for various applications have been discussed in the literature [6-11]. The complex permittivity relative to free space is represented here as ε ε ε ′ ′ − ′ = j , where ε ′ is the dielectric constant and ε ′ ′ is the dielectric loss factor. Dielectric mixture equations for a two-phase mixture can be used to calculate the dielectric properties of a solid material from the dielectric properties of an air-particle mixture of air and pulverized or granular particles of the solid. To use the mixture equations, one needs to know the permittivity of the pulverized sample at its bulk density (air-particle mixture density), ρ , and the specific gravity or density of the solid material, 2 ρ . The fractional part of the total volume of the mixture occupied by the particles (volume fraction), , is then given by 2 v 2 ρ ρ / .