Effective ac response of graded colloidal suspensions

The alternating current (ac) response has been investigated theoretically in colloidal suspensions consisting of suspended radially inhomogeneous graded particles having complex permittivity profiles under an external ac electric field. The gradation in the colloidal particles is modeled by physically motivated graded profiles as the dielectric function may only vary slightly along the radius, while the conductivity profile may vary rapidly along the radius. More precisely, the dielectric function is assumed to be a constant, while the conductivity has a power-law dependence on the radius variable r, namely, epsilon(i)(r)=A+cr(k)/(i omega). In previous attempts, this model was solved numerically via the differential effective dipole approximation. In this work, we will demonstrate the existence of exact analytical solutions of the local potentials in the graded particles in terms of the hypergeometric functions, and hence the effective ac response is calculated in the dilute limit. Our exact results will be applied to graded biological cell suspensions. Extensions to nonlinear ac response will be discussed.