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Suspensions of rear- and front-actuated microswimmers immersed in a fluid,known respectively as ``pushers'' and ``pullers'', display qualitativelydifferent collective behaviours: beyond a characteristic density, pushersuspensions exhibit a hydrodynamic instability leading to collective motionknown as active turbulence, a phenomenon which is absent for pullers. In thisLetter, we describe the collective dynamics of a binary pusher--puller mixtureusing kinetic theory and large-scale particle-resolved simulations. We deriveand verify an instability criterion, showing that the critical density foractive turbulence moves to higher values as the fraction $\chi$ of pullers isincreased and disappears for $\chi \geq 0.5$. We then show analytically andnumerically that the two-point hydrodynamic correlations of the 1:1 mixture areequal to those of a suspension of noninteracting swimmers. Strikingly, ournumerical analysis furthermore shows that the full probability distribution ofthe fluid velocity fluctuations collapses onto the one of a noninteractingsystem at the same density, where swimmer--swimmer correlations are strictlyabsent. Our results thus indicate that the fluid velocity fluctuations in 1:1pusher--puller mixtures are exactly equal to those of the correspondingnoninteracting suspension at any density, a surprising cancellation with nocounterpart in equilibrium long-range interacting systems.

Symmetric mixtures of pusher and puller microswimmers behave as noninteracting suspensions