Effective medium theories for artificial materials composed of multiple sizes of spherical inclusions in a host continuum

This paper presents the application of nonempirical effective medium theories to describe composite mixtures of spherical inclusions within a host continuum. It is shown that the most common effective medium theories collapse into Bruggeman's (1935) asymmetric formula when they are implemented in an iterative scheme to extend their validity to higher volume fractions. Comparisons of DC and 4-GHz data show that of all the formulas Bruggeman's asymmetric formula corresponds best with experiment for large differences between the complex permittivities of the host and inclusion materials. Permeability values are also formulated and compared with experiment and a simple scheme is considered to extend the effective medium theories herein to a description of the diamagnetic effect of induced current in metal spherical inclusions.