Analysis of the complex effective permittivity of a heterogeneous sample by the finite-difference time-domain method

Numerical results of the complex effective permittivity and DC conductivity of heterogeneous samples with random constituents' distribution are analyzed to search for a suitable mixture law. The calculation method consists of the simulation of a time-domain reflectometry experiment by means of the finite-difference time-domain (FDTD) algorithm. The permittivity and conductivity of several series of samples with their constituents distributed at random are calculated. Numerical results, as a function of the volume fractions of the mixture's constituents, are compared with analytical mixture laws. For lossless binary media, it is found that both the Bruggeman law and a weighted geometric mean provide a good agreement. The last one can be generalized to composites with more than two constituents, with good results. On the other hand, for lossy binary mixtures it is shown that the weighted geometric mean of the constituents' complex permittivities matches the numerical results obtained for the effective complex permittivity of the mixture. PACS Nos: 72.20.-i, 77.84.Lf, 77.22.Gm, 72.80.Tm Dans la recherche d'une loi de melange adequate, nous avons analyse des resultats numeriques sur la permittivite complexe effective et la conductivite DC d'echantillons heterogenes dont les constituants sont distribues au hasard. La methode de calcul consiste a simuler une experience de reflectometrie dans un domaine de temps, en utilisant l'algorithme FDTD. Nous avons calcule la permittivite et la conductivite de plusieurs series d'echantillons dont les constituants etaient distributes au hasard. Nous comparons nos resultats numeriques, en tant que fonctions des fractions volumiques, avec les lois analytiques de melange. Pour les milieux binaires sans perte, nous trouvons que la loi de Brugeman et de la moyenne par poids geometriques sont en bon accord. Cette derniere peut etre generalisee, avec de bons resultats, a des echantillons de plus de deux constituants. De plus, pour des milieux binaires avec perte, nous trouvons que la moyenne a poids geometriques des permittivites complexes des constituants reproduit le resultat numerique obtenu pour la permittivite complexe du melange. [Traduit par la Redaction]
1. Introduction Finding the effective permittivity, DC conductivity, or thermal conductivity of a heterogeneous mixture of two substances constitute three analogue problems that have been thoroughly studied for more than [...]