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DIVISION S-1-SOIL PHYSICS

New Dielectric Mixture Equation for Porous Materials Based on Depolarization Factors

^a IMAG-DLO, P.O. Box 43, NL-6700 AA, Wageningen, The Netherlands
^b Dep. of Water Resources, Wageningen Agricultural Univ., Wageningen, The Netherlands
^c DLO, P.O. Box 59, NL-6700 AB, Wageningen, The Netherlands

m.a.hilhorst{at}imag.wag-ur.nl

A change in the relative proportions of the constituents of a porous material like soil will cause a change in its electrical permittivity. The measured permittivity reflects the impact of the permittivities of the individual material constituents. Numerous dielectric mixture equations are published, but none of these equations are generally applicable. A new theoretical mixture equation is derived, using the principle of superposition of electric (E) fields. This mixture equation relates the measured permittivity to a weighted sum of the permittivities of the individual material constituents and includes depolarization factors to account for electric field refractions at the interfaces of the constituents. The depolarization factors are related to physical properties of the material. Most other mixture equations contain one or more empirical factors. The concept of the depolarization factor is comparable with that of the "shape factor" of particles as described by other authors. A special case of the new mixture equation, for which the depolarization factors equals one (no depolarizations), appeared equal to a mixture equation for fluids derived from using thermodynamics. The new mixture equation is compared with other mixture equations. Comparison of the new mixture equation with measured data for glass beads and fine sand was promising. Concluding, depolarization factors in the new mixture equation relate the microstructural and compositional material properties to the measured bulk permittivity of a material. Although not shown, depolarization factors can be calculated from physical material properties.

Abbreviations: E, electric [field] • FD, frequency domain • TDR, time domain reflectometry

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