A saturation degree-dependent composite spheres model for describing the effective dielectric constant of unsaturated porous media

Understanding the relation between the effective dielectric constant (relative permittivity) of soils and their volumetric water content is important because measurements of the dielectric constant of soils by capacitance sensors, time domain reflectometry (TDR) probes, and remote-sensing radar devices are used to determine their moisture content. In the present study a physical model is proposed which relates the effective dielectric constant of unsaturated mineral soils at TDR frequencies to their volumetric water content, porosity, and specific surface area. It is assumed that the solid, water, and air components form a mixture of composite spheres and that the radial order of the single-phase concentric shells depends on the saturation degree of the medium. The dielectric constant of the aqueous phase is smaller than that of free water, because of interfacial solid-liquid forces, and the dependence of this reduction on the moisture content and on the specific surface area is represented here via a general approximated relationship. The model prediction is based on readily available soil properties (porosity, specific surface area, or texture), and it does not require any calibration. Tests of the model predictions against measurements made here on 3 porous media and against published data for an additional 19 media resulted in a promising agreement, with the proposed model's predictions being better than those given by the commonly used empirical relations for mineral soils. It is believed that the model performance could be further improved by better representation of the saturation degree-dependent, three-phase configuration by considering nonspherical soil particles and by a more realistic incorporation of interfacial relaxation processes.