Rotating spherical particle in a continuous viscoelastic medium -- a microrheological example situation

Using analytical calculations, we characterize the rotational behavior of a rigid spherical particle when subject to a net external torque in a continuous viscoelastic environment. On long time scales, the embedding medium can either feature a net terminal flow, like a fluid, or damped reversible dynamics, like an elastic solid. The coupling of the sphere to its environment together with the therein induced deformations and flows are taken into account explicitly. In reality, using magnetically anisotropic particles, the torque can, for instance, be applied via magnetic fields. We calculate corresponding response functions. This connects our study to evaluations of microrheological investigations.