Lagrangian structure, stretching and transport in bacterial turbulence

In active matter systems, dense suspensions of self-propelled agents spontaneously exhibit large-scale, chaotic flow structures.

Descriptions of the dynamics of these systems have predominately focused on characterization of spatiotemporal correlation of the velocity field, but their transport properties and mixing kinematics remain largely unknown. In this work, we use Lagrangian analysis techniques to study the chaotic flow fields generated by "bacterial turbulence'' in dense suspensions of a model bacterium (Bacillus subtilis). High-resolution velocity fields are measured using particle image velocimetry across a range of bacterial swimming speeds, where the computed Lagrangian stretching visualizes the induced stretching and folding, characteristic of mixing. Close inspection of the finite-time Lyapunov exponent (FTLE) field reveals time and swimming speed dependent FTLE statistics reminiscent of intermittent dynamics in classical chaotic dynamical systems. At moderate Péclet numbers, experiments and Langevin simulations reveal that manifolds of the FTLE field guide scalar mixing and regulate transport in these active suspensions, which is ecologically relevant to the dispersal of chemical resources and particulates in dense bacterial colonies.