Collective migration and diffusion of inertial swimmers under gravity

Transport phenomena in swimmer suspensions are ubiquitous in biological environments. In this study, we numerically investigate the transport of swimmers modelled as squirmers in semi-dilute suspensions, with a particular focus on the effects of fluid inertia and sedimentation. In the case of neutrally buoyant swimmers, we demonstrate that the swimmer diffusion can be either suppressed or enhanced with increasing Reynolds number, depending on whether the swimmer behaves as a puller or a pusher. Scaling analysis shows that the diffusion coefficient is inversely proportional to the volume fraction of swimmers in the weakly inertial regime; however, this scaling breaks down as inertia becomes strong. For settling swimmers, we show that sedimentation has only a weak influence on diffusion behaviour at low Reynolds numbers. In contrast, in the moderate-Reynolds-number regime, settling swimmers preferentially reorient opposing gravity, due to fluid-inertial torques. This alignment suppresses the spreading of pushers, while significantly enhancing the settling velocity and vertical diffusion of pullers by promoting the formation of strong vertical structures when the settling effect is strong. Overall, our results highlight the significance of fluid inertia and gravitational sedimentation in regulating transport and collective motion in active suspensions.