The reader may have grown exhausted by this time by the endless emphasis on the Maxwell Garnett-type mixtures. Indeed, the discussion has heretofore concentrated heavily on a single approach to the homogenisation. One of the components is treated as environment, and the inclusion phase is considered as a perturbation against this background. And in particular, the local field that excites a single scatterer in the mixture was calculated by replacing all neighbours by a uniform polarisation density in which a hole was carved. This treatment is clearly approximate, as was pointed out in Chapter 8 where the limitations of Maxwell Garnett philosophy were discussed. But on the other hand, no exact solution exists for the electrostatic problem in a random heterogeneous geometry. Multiple opinions can flourish when nobody knows for certain. It is evident that the Maxwell Garnett model cannot remain at the scene as the only ruling formula. Many rival mixing rules are being used in the modelling of heterogeneous materials. In the present chapter, some of the most common competitor models are presented.

Inspec keywords: electromagnetic wave polarisation; Maxwell equations; electrostatics; electromagnetic wave scattering

Other keywords: uniform polarisation density; heterogeneous material modelling; Bruggeman formula; Maxwell Garnett-type mixtures; electrostatic problem; generalised mixing rules; random heterogeneous geometry; coherent potential formula; single scatterer

Subjects: Electromagnetic waves: theory