The Electric Permittivity of a Dilute Suspension of Membrane-Covered Ellipsoids

Abstract

This theoretical paper deals with the low frequency permittivity (ε) of a dilute suspension (conductivity σ, volume concentration ρ), in a conducting medium (conductivity σ_s, permittivity ε_s), of ellipsoidal particles (major axis 2a) each composed of a conducting core covered with a nonconducting surface membrane (thickness t, permittivity ε_m). The quantity ${\mathrm{[\epsilon -(\sigma /\sigma }}_s{\mathrm{)\epsilon }}_s{\mathrm{]/(\rho a\epsilon }}_m\mathrm{/t)}$ is expressed in terms of Weierstrass' elliptic functions of the axial ratios, for parallel and random arrangement of the ellipsoidal axis. A table of its numerical values is given.