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