Effective permittivity of a random mixture with spherical inclusions

The paper reports the results of a numerical analysis of electric field in random dielectric materials. The effective permittivity of a three-dimensional mixture is calculated by the finite difference method. The studied mixture is a two-component mixture with a homogeneous background in which spheres of another material are embedded in random positions. A new technique to derive difference equations in the neighborhood of material interfaces is considered. Hundreds of mixture samples with different random inclusion distributions are analysed to get a good insight into average characteristics of the mixture material. The calculated permittivity distributions are also compared with well-known theoretical models such as Maxwell Garnett and Bruggeman models.