Symmetric Mixtures of Pusher and Puller Microswimmers Behave as Noninteracting Suspensions

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 fractions of pullers is increased and disappears for chi >= 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 arc 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 long-range interacting systems.