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Collective motion in bacterial suspensions is scale-free.

Benjamín Pérez-Estay1, Vincent Martinez2, Carine Douarche3

  • 1Physique et Mécanique des Milieux Hétérogènes, École supérieure de physique et de chimie industrielles Paris, Université Paris Sciences et Lettres, Université Paris Cité, Sorbonne Université, CNRS, Paris 75005, France.

Proceedings of the National Academy of Sciences of the United States of America
|May 22, 2026
PubMed
Summary

Bacterial turbulence, chaotic flows from swimming bacteria, lacks an intrinsic length scale. Confinement height directly influences collective motion scales, demonstrating scale-free dynamics in E. coli suspensions.

Keywords:
E. coli suspensionsactive matteractive turbulencecollective motioninstability

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Area of Science:

  • Microbiology
  • Fluid Dynamics
  • Soft Matter Physics

Background:

  • Swimming microorganisms like E. coli exhibit collective behaviors driven by hydrodynamic interactions.
  • Bacterial suspensions can self-organize into complex patterns, leading to large-scale chaotic flows known as bacterial turbulence.
  • The existence of an intrinsic length scale governing these patterns remains an open question in active matter research.

Purpose of the Study:

  • To investigate the emergence of large-scale flows in E. coli suspensions.
  • To determine if bacterial collective motion possesses an intrinsic length scale.
  • To elucidate the mechanisms driving active turbulence under confinement.

Main Methods:

  • Experiments were conducted using E. coli suspensions confined in flat cylindrical chambers.
  • The confinement height was systematically varied over more than two orders of magnitude.
  • Critical density for collective motion and emergent length/time scales were measured.

Main Results:

  • The critical density for collective motion onset scales inversely with confinement height.
  • Observed length and time scales increase sharply near onset, limited by confinement.
  • Both scales show power-law dependence on confinement height, indicating scale-free behavior.
  • Transient coherent vortices, thousands of times larger than individual bacteria, were observed.

Conclusions:

  • Bacterial collective motion, or bacterial turbulence, is scale-free, lacking an intrinsic length scale.
  • Confinement height is a critical factor determining the scales of active turbulence.
  • Results provide crucial data for theoretical models of active matter dynamics.