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

When the permittivities, 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 for estimating the permittivity of solids from measured permittivity data on granular or powdered samples of those materials. 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 . Several well-known dielectric mixture equations have been studied to relate the permittivities of the solid material to the permittivities of granular or pulverized samples of the same material [5, 12-15]. Two of these equations are the Complex Refractive Index mixture equation [16-22],