Brownian motion in a viscoelastic medium modelled by a Jeffreys fluid

The theory of Brownian motion of a particle in a viscoelastic Jeffreys fluid is extended for the case of rotational motion. The employed rheological model combines two viscous mechanisms (instantaneous and retarded) and, in contrast to the Maxwell model, does not produce artifacts and works robustly when applied to the diffusion of tracer particles in real complex fluids. With the aid of this model, specific features of the dynamic susceptibility of a magnetic Jeffreys suspension and the viscous power losses induced by an ac field are analyzed and conclusions are derived that are valid for active microrheology and magnetic hyperthermia. In general, it is shown that the developed phenomenology provides an archetypal frame for a number of mesoscopic models used to describe confined random walk transport processes in a variety of systems of both biological and inorganic origin.