Derivation of an explicit formula for determining the effective permittivity of a three-component composite

The author extends the Bergman-Milton formula of the effective permittivity of a two-component heterogeneous dielectric mixture to the case of a three-component mixture. He validates the introduction of a unique two-variable density function which describes the microgeometry. He also supplements the theoretical approach by discussing the significance and the forms of the percolation terms. The geometrical density functions, which correspond to the well-known Lichtnecker, C.R.I.M. and Looyenga formulae are explicitly given as cases for illustrating the general approach.