A geometrical model of bound water permittivity based on weighted averages: the allophane analogue

The soil permittivity is affected by the volume fractions of bound and free water, but also by the geometries of the soil components and the shape of water inclusions. Allophanic clays have a hollow spherical geometry with high water holding capacity, and thus representing an ideal system to investigate geometrical effects on the permittivity of water in porous media. A new weighted averaging procedure is developed which provides estimates of the permittivity of rotationally hindered water bonded to allophane spherules, and takes into account both the spherical shape of allophane and the number of water layers stored. This averaging procedure renders two distinct estimates for the inner and outer allophane water permittivity in agreement with previous experimental results. These distinctive dielectric constants for allophane water are shown to be relevant to most water content reading applications near and below the Gigahertz range. Is shown that presented averaging procedure may, more generally, serve as a simple mechanism to include geometrical effects on water absorbed to other non-planar structures such as micropores and soil particles of cylindrical or ellipsoidal geometry.