Inclusion of scattering losses in the models of the effective permittivity of dielectric mixtures and applications to wet snow

Several dielectric models have been previously proposed to explain the permittivity of mixtures from the known dielectric constant and volume fractions of the constituents. The materials may be lossy and this leads to a complex effective permittivity for the mixture where the imaginary part stands for the absorption losses of the mixture. However, the scattering losses are not incorporated in the effective permittivity. The result is therefore confined to a low-frequency limit. In this paper an attempt is made to incorporate the scattering losses in the effective permittivity of the medium consisting of the discrete scatterers immersed in a host material. The inclusions are assumed to be spherical. The results are applicable to general multiphase mixtures, and the scattering spheres of the different phases may have size distribution. The results are applied to calculating the complex effective permittivity of wet snow. The prediction of the model seems to agree with the experimental data if the scattering losses and the distribution of liquid water in the pore space have been taken into account.