the linear response operator specific to the given shape. We consider a suspension of identical, randomly oriented particles of arbitrary shape and dielectric permittivity, ε$_{1}$ , immersed in a dielectric medium of dielectric permittivity, ε$_{0}$ . The dielectric permittivities are in general complex quantities and the theory described here applies also for time-dependent fields, providing that the size of a particle is much smaller than the wavelength. When an applied uniform electric field interacts with the suspension, the response of the system is linear with the applied field and an effective permittivity for the whole sample can be measured and is defined by [25–27]: This result is obtained in the limit of low concentration, weak intensity of the stimulus field, and using an effective medium theory within the dipole approximation. Here f = NV$_{1}$/V is the volume fraction of all N particles, each of volume V$_{1}$ , with respect to the total volume of the suspension V . The averaged normalized polarizability α of a particle is defined as [25, 27, 28] where E ( N ) is the electric field perturbation created inside the particle under a normalized applied electric excitation with direction N and d Ω$_{N}$ is the solid angle element generated by that direction. The above normalized polarizability is dimensionless and is obtained by multiplying the standard polarizability of a particle with the factor 4 π/V$_{1}$ . In the following we will refer only to normalized polarizability, thus, without any confusion, the normalized polarizability α will be simply called polarizability. The directional average in (2) is equiv- alent to the averaged sum over three orthogonal axes due to the fact that the problem is linear with respect to the applied field. The latter is more convenient from computational point of view. The electric field inside a particle is obtained by solving the following Laplace equation 4 II. THEORY A. Effective permittivity of a suspension ε sus = ε$_{0}$ + f αε$_{0}$ 1 − f α 3 . (1) α = 1 4 π V$_{1}$ ∫ V 1 ∫ Ω$_{N}$ ( ε$_{1}$ − ε$_{0}$ ε$_{0}$ ) E ( N ) · N d Ω$_{N}$ dV (2)