THEORETICAL EVIDENCE FOR LICHTENECKERS MIXTURE FORMULAS BASED ON THE EFFECTIVE-MEDIUM THEORY

In order to calculate the electrical permittivity property of a multip hase mixture, a beta function distribution of the geometrical shapes o f inclusions is considered. By using the effective medium theory toget her with the assumption of self-consistency, it is shown that the beta function distribution leads to Lichtenecker's formulae. This gives a theoretical model for this mixing formula, which had hitherto been con sidered empirical. This result is important because the first Lichtene cker's is already used for time domain reflectometry (TDR) calibration purposes, namely conversion from permittivity measurement to water co ntent of heterogeneous materials.