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

This theoretical paper deals with the low frequency permittivity (ε) of a dilute suspension (conductivity σ, volume concentration ρ), in a conducting medium (conductivity σs, permittivity εs), of ellipsoidal particles (major axis 2a) each composed of a conducting core covered with a nonconducting surface membrane (thickness t, permittivity εm). The quantity [ε−(σ/σs)εs]/(ρaεm/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.