Equivalent permittivity tensor in anisotropic random media

An explicit result for the equivalent (or effective) permittivity tensor is derived for dispersions of anisotropic (biaxial) particles embedded in an isotropic matrix. The overall medium has a positional disorder but an orientational order and it exhibits a uniaxial behaviour. Each crystal is partially oriented along a given director (preferential direction) and the degree of orientation is taken into account by a suitable order parameter. The equivalent permittivity tensor of the whole heterogeneous material is described in terms of the order parameter, the volume fraction of the dispersed phase, the principal values of the permittivity tensor of the crystals and the components of the director along which the crystals are preferentially aligned.