Generalization of Bruggeman’s unsymmetrical effective-medium theory to a three-component composite

A unified treatment of effective-medium theory for the dielectric constant and conductivity of a macroscopically inhomogeneous medium based on renormalization is presented. Our expression recovers in appropriate limits Bruggeman's unsymmetrical as well as symmetrical results. In addition, the same expression also describes a ternary system such as brine-and-oil-saturated porous media.