Dynamic dipole polarizability of a dielectric sphere in an electrolyte

The response of a suspension of spherical particles to a periodic electric field is given by the real and imaginary part of the effective dielectric number εeff(ω). In order to describe its dispersion within an enhanced dipole residual interaction model, the polarizability α(ω) of a single sphere has to be found first. This calculation is facilitated by the smallness of the ratio of the Debye length δ to the radius a of the sphere. In a thin double layer approximation, an improved expansion in δ/a is found for α(ω) in the long wavelength limit k→0. In contrast to Schwarz (Ref. 1) who assumed tangential diffusion effects around the spheres, the volume diffusion is the dominant feature here. A comparison with a simple relaxation time ansatz is given in order to show the significance of diffusion.