Effective Permittivity of Multiphase Mixtures: The Scatterer as a Two-Layer Sphere

摘要

A theory is presented for calculating the macroscopic effective permittivity of mixtures that are composed of a background medium and inhomogeneous scatterers. The inhomogeneity is limited: the scatterers are two-component spheres where both the spherical core and the spherical shell that forms the surface of the scatterer are homogeneous with a constant permittivity. The results are applied to calculating the microwave attenuation of melting hail where the hydrometeors are assumed to be of the form of a spherical ice core with a spherical water coating shell. At the frequency of 1 GHz where the results are calculated, the hydrometeors surely are much smaller than the wavelength. There is a very strange peak in the attenuation of hail as it falls through a warm layer: the attenuation is greater with a thin water coating than it is when the hail particle has completely melted.