Self-consistency aspects of dielectric mixing theories

Dielectric mixing formulas that relate the effective permittivity of a heterogeneous medium with the properties of the constituent materials are considered. The restriction for this approach is that the sizes of the inclusions in the mixture have to be considerably smaller than the wavelength to avoid scattering effects. The mixing rules are presented for cases where the scatterers can be homogeneous or multilayer spheres. The formula contains a free parameter v, and for different choices of this parameter, many mixing formulae result as special cases of the given mixing rule. Mixing formulas presented in the literature are also reviewed and the results from different formulae are compared, using dry and wet snow as paradigmatic examples