Theory of dielectric relaxations due to the interfacial polarization for two-component suspensions of spheres

A theoretical formula of dielectric relaxation in a form of complex relative permittivity is derived for dilute suspensions of spherical particles of two kinds on the basis of the Maxwell-Wagner theory of interfacial polarization. Another theoretical formula is derived further for concentrated suspensions of spheres of two kinds on condition that the formula derived above holds for the infinitesimally increasing process in concentration of the dispersed spheres. Furthermore a theoretical formula is derived for concentrated suspensions of shelled spheres of two kinds as the extension of the formula for concentrated suspensions. By use of the theoretical formulas proposed, values of the permittivities and the conductivities of the two-component suspensions were calculated for some examples with different sets of phase parameters. Results of the numerical calculation demonstrates dielectric relaxation profiles full of variety and characteristic of the suspensions containing two kinds of spheres covered with or without shells.