A generalized dipole-enhanced approximation for a dielectric mixture

This paper presents a generalized dipole-enhanced approximation, considering the interactions among particles in a dielectric mixture, to calculate the electric field distributions at the surface of an arbitrarily selected spherical particle in a uniform external field. An approximate formula whose calculated results agree well with the exact numerical solutions obtained by the finite-element method is derived. This formula provides analytic solutions for the dielectric mixtures with high-volume fraction particles because it truly reveals the perturbations due to all the other particles. As the difference between the exact solutions and the ideal dipole approximations reflects the perturbations due to all the other particles, the difference calculated based on the dipole-enhanced approximation is applied to the prediction of effective permittivity for dielectric mixtures, and a modified mixing formula is presented.