Tracer motion in an active dumbbell fluid

The diffusion properties of spherical tracers coupled through a repulsive potential to a system of active dumbbells are analyzed. We model the dumbbells' dynamics with Langevin equations and the activity with a self-propulsive force of constant magnitude directed along the main axis of the molecules. Two types of tracers are considered. Thermal tracers are coupled to the same bath as the dumbbells while athermal tracers are not; both interact repulsively with the dumbbells. We focus our attention on the intruders' mean square displacement and how it compares to the one of the dumbbells. We show that the dynamics of thermal intruders, with mass similar to the one of the dumbbells, display the typical four time-lag regimes of the dumbbells' mean square displacement. The thermal tracers' late-time diffusion coefficient depends on their mass very weakly and it is close to the one of the dumbbells at low Péclet only. Athermal tracers only have ballistic and late-time diffusive regimes. The late time diffusion coefficients of athermal tracers and dumbbells have similar values at high Péclet number when their masses are of the same order, while at low Péclet number this coefficient gets close to the one of the dumbbells only when the tracers are several order of magnitude heavier than the dumbbells. We propose a generalization of the Enskog law for dilute hard disks, that describes the athermal tracers' mean square displacement in the form of a scaling law in terms of their mass.