Effective permittivity of random inhomogeneous media

We present a computational study for precise calculations of the effective (bulk) permittivity of two-phase lossless disordered composite media. The method is based on: (i) a finite-element description of composites in which both the host and the randomly distributed inclusions are isotropic phases, and (ii) an ordinary Monte Carlo sampling. We describe an algorithm which permits to generate distributions of hard circular disks made of a lossless dielectric (permittivity ε₂) randomly placed in a plane made of a lossless homogeneous dielectric (permittivity ε₁) at different surface fractions. Numerical examples are presented to connect the macroscopic property such as the effective permittivity to microstructural characteristics such as the radial distribution function. In addition, several approximate effective medium theories, exact bounds and exact dilute limit are used to test and validate the finite element algorithm.