Static permittivity of a multiphase system of spheres

The objective of this work is the computation of the static effective permittivity for a multiphase system of spheres located in an arbitrary lattice. It is assumed for now that there is more than one type of particle (i.e., phase), as shown, but overall there is sufficient symmetry to ensure isotropy. This paper begins with the computation of the scalar potential scattered by a lattice containing an arbitrary number of spherical phases. The T-matrix method is used to compute this scattering. Next, a derivation of the effective permittivity expression is given followed by representative results from a three-phase system. The method shown in this paper is numerically "exact" in the sense that the effective permittivity is computed using methods capable of accurately computing the potential scattering and accounts for all mutual coupling between inclusions.