Dielectric mixing formula for multiphase mixtures

We assume that the mixtures consist of an isotropic background medium in which several component inclusions are embedded. Let all inclusions of each mixture component be spherical. The microstructure of multiphase mixtures is random dislocation from a periodic distribution. Following Tateiba´s method, under the random condition that the perodicity in the particle distribution can be neglected (Tateiba 1987, 1989; Tateiba et al. 1993; Nanbu and Tateiba 1995), we approximately transfer the effective permittivity of the original mixture with random dislocation from a periodic distribution as those of the other mixture, the background medium of which is a continuous medium, the scatterer number density of which is the same as that of the original mixture. But inclusions of each component of the transformed mixture are greatly changed. Actually, the static polarization of a transformed scatterer can be approximately described as the polarization difference of two homogeneous spheres