The Aquatic Dance of Bacteria

Abstract

Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over 2 orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between kinetic energy and enstrophy. The best-fit model allows for quantitative agreement with experimental data. [3][4][5][6][7][8] and microscale selforganization in motility assays [9,10]. Although very different in size and composition, these systems are often jointly termed ''active'' fluids, for which there is now a range of continuum theories [12,[14][15][16][17][18][19][20][21][22][23][24]. From these have come important qualitative insights into instability mechanisms [13][14][15][16]21,25] driving dynamical pattern formation, but a quantitative picture remains inchoate; even for the simplest active (e.g., bacterial or algal) suspensions uncertainty remains about which hydrodynamic equations and transport coefficients [26,27] provide an adequate minimal description, due in large part to the inability of existing data to constrain the manifold parameters in these models. One approach to remedy this problem is to characterize collective turbulent dynamics of bacteria [17,18] and other low Reynolds number swimmers, just as in high Reynolds number fluid turbulence, in terms of kinetic energy, mean squared vorticity (enstrophy) and spatiotemporal correlation functions, and to compare with an appropriate longwavelength theory (i.e., Navier-Stokes-type equations). We present such an analysis here, measuring collective behavior in dense suspensions of the bacterium Bacillus subtilis in comparison to predictions of a (fourth-order) continuum model for bacterial flow [7,28]. [3,4,29,30], freestanding films [5,8,27,31], on surfaces [6,32,33], or quasi-2D microfluidic chambers [7] focused separately on the bacterial and fluid components, leaving uncertain how accurately passive tracers [34,35] reflect collective bacterial dynamics. The experiments reported here, performed in closed 3D microfluidic chambers, allowed near-simultaneous measurements of cell and tracer motion, and exploit a natural reduction in bacterial swimming activity due to oxygen depletion [8,29,36] to obtain data spanning 2 orders of magnitude in fluid kinetic energy. Combined with extensive 3D numerical simulations of the model, this data allows robust parameter estimates. Quantitative agreement between experiment and theory suggests that this model presents a viable generalization of the Navier-Stokes equations to incompressible active fluids. Previous experimental studies of bacterial s...

Rectification of chaotic fluid motion in two-dimensional turbulence

“…Hydrodynamic turbulence, on the other hand, is a chaotic state of a macroscopic system generated and dominated by inertia. The physical properties of hydrodynamic turbulence are obviously different from the recently discovered active bacterial turbulence [34,36]. The vehicles reported here are coupled to turbulent fluctuations on a fluid surface at typical Reynolds number of the order of 100; those hydrodynamical fluctuations have a complex spatiotemporal structure whose origin and features close to a wall are quite different from those of fluctuations observed in either bacterial turbulence or granular gases.…”

Theory of Active Suspensions

“…Numerous experiments have focused on the dynamics in suspensions of swimming bacteria. Some of the observations that have been made on this system include: the emergence of [1]; (b) dynamic clusters in swarms of bacteria, where arrows show the direction of motion of the particles [2]; (c) spontaneous motion in a suspension of microtubules and kinesin motors confined at a two-dimensional interface [3]; (d) large-scale swirling motion in a suspension of actin filaments transported by wall-tethered myosin molecular motors [4]; (e) swarming of self-propelling liquid droplets in a Hele-Shaw cell [5]; (f) long-range order of vibrated polar disks on a two-dimensional substrate [6]. (Reproduced with permission) complex chaotic flows on length scales much greater than the particle dimensions and characterized by unsteady whirls and jets [10-12, 26, 27], enhanced particle velocities [10], a transition to collective motion when the bacterial density exceeds a certain threshold [11], local polar ordering [11], complex patterns and density fluctuations [28], enhanced swimmer and passive tracer diffusion [29][30][31][32], efficient fluid mixing [28,33,34], and bizarre rheologies created by particle activity [35][36][37][38].…”

Rapid expulsion of microswimmers by a vortical flow

“…Interactions of bacteria with fluid and solid surfaces are exceptionally complex and are the topic of active research 1 2 3 4 5 6 7 8 9 . In addition to a variety of chemical and physical factors, swimming trajectories are also affected by macroscopic shear flow.…”