Collective behaviour in suspensions of microswimmers is often dominated by the impact of longranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to N = 3 × 10 6 ) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length-and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.Here, λ is the tumbling frequency by which individual swimmers randomise their swimming direction and κ is the stresslet magnitude, defined below. In order to probe the properties of J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-10 | 1 arXiv:1904.03069v2 [cond-mat.soft] 26 Aug 2019 J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-10 | 9

Suspensions of rear-and front-actuated microswimmers immersed in a fluid, known respectively as "pushers" and "pullers," display qualitatively different collective behaviors: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher-puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction χ of pullers is increased and disappears for χ ≥ 0.5. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1∶1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer-swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1∶1 pusher-puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium longrange interacting systems.