Collective motion in bacterial suspensions is scale-free

Abstract

In suspensions of swimming bacteria, individual cells interact via long-range hydrodynamic forces and self-organize into collective states that drive large-scale chaotic flows, commonly referred to as “bacterial turbulence.” Despite extensive experimental and theoretical work, it remains unclear whether an intrinsic length scale underlies the observed patterns. To directly address this question and shed light on the mechanisms driving active turbulence, we investigate the emergence of large-scale flows in E. coli suspensions confined within flat cylindrical chambers, systematically varying the confinement height over more than two orders of magnitude. We first demonstrate that the critical density for the onset of collective motion scales inversely with the confinement height without saturation. Near the onset, both the observed length and time scales increase sharply, with the length scale limited only by the vertical confinement. Importantly, both scales exhibit clear power-law dependence on the confinement height, demonstrating the absence of an intrinsic length scale in bacterial collective motion. Close to the instability onset, we observed transient coherent vortices, reaching up to 4,000 times the size of a single bacterium and spanning the full chamber width, further reinforcing the conclusion that bacterial turbulence is scale-free. Our experimental results, which characterize the onset of collective motion and demonstrate that bacterial turbulence is scale-free, discriminate between competing theoretical models and provide essential input for theories seeking to capture the dynamics and constitutive relations of wet active matter.