We experimentally study the emergence of collective bacterial swimming, a phenomenon often referred to as bacterial turbulence. A phase diagram of the flow of 3D E. coli suspensions spanned by bacterial concentration, the swimming speed of bacteria and the number fraction of active swimmers is systematically mapped, which shows quantitative agreement with kinetic theories and demonstrates the dominant role of hydrodynamic interactions in bacterial collective swimming. More importantly, we trigger bacterial turbulence by suddenly increasing the swimming speed of light-powered bacteria and image the transition to the turbulence in real time. Our experiments identify two unusual kinetic pathways, i.e., the one-step transition with long incubation periods near the phase boundary and the two-step transition driven by long-wavelength instabilities deep inside the turbulent phase. Our study provides not only a quantitative verification of existing theories, but also new insights into interparticle interactions and transition kinetics of bacterial turbulence.
We use the mean-bacterial-velocity model to investigate the \textit{irreversibility} of two-dimensional (2D) \textit{bacterial turbulence} and to compare it with its 2D fluid-turbulence counterpart. We carry out extensive direct numerical simulations of Lagrangian tracer particles that are advected by the velocity field in this model. Our work uncovers an important, qualitative way in which irreversibility in bacterial turbulence is different from its fluid-turbulence counterpart: For large positive (or large but negative) values of the \textit{friction} (or \textit{activity}) parameter, the p…
We demonstrate that collective turbulent-like motion in a bacterial bath can power and steer directed transport of mesoscopic carriers through the suspension. In our experiments and simulations, a microwedge-like "bulldozer" draws energy from a bacterial bath of varied density. We obtain that a maximal transport speed is achieved in the turbulent state of the bacterial suspension. This apparent rectification of random motion of bacteria is caused by polar ordered bacteria inside the cusp region of the carrier, which is shielded from the outside turbulent fluctuations.
We propose a simple model of self-propelled particles to show that coherent structures, such as jets and swirls, can arise from a plausible microscopic mechanisms: (i) the elongated shape of the self-propelled particles with (ii) the hardcore interactions among them. We demonstrate via computer simulation that these coherent structures, which emerge at sufficiently high densities of particles, have characteristics that are similar to those observed in recent experiments in bacteria baths.
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 two orders of magnitude in kinetic energy, revealing a decrease…
Bacterial turbulence drives interfacial waves and shape dynamics in phase-separated droplets
School of Physics and Astronomy, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University（上海交通大学物理与天文学院、自然科学研究院和MOE-LSC）；Fujian Provincial Key Laboratory for Soft Functional Materials Research, Research Institute for Biomimetics and Soft Matter, Department of Physics, Xiamen University（厦门大学物理系仿生与软物质研究院福建省软功能材料研究重点实验室）；Universal Biology Institute, Graduate School of Science, The University of Tokyo（东京大学理学研究科全球生物学研究所）
We experimentally study density fluctuations and energy spectra of bulk \textit{E. coli} suspensions of different concentrations. Our results verify the predicted scaling law of giant number fluctuations in three-dimensional (3D) wet active fluids. We find that such a scaling behavior persists at small scales even in low concentration suspensions well below the transition concentration to active turbulence. Our experiments also support the prediction on the energy spectra of dilute pusher swimmers and illustrate the spectral properties of the active turbulence of dense bacterial suspensions in…
We experimentally investigate the effects of polymer additives on the collective dynamics of swarming Serratia marcescens in quasi two-dimensional (2D) liquid films. We find that even minute amounts of polymers (< 20 ppm) can significantly enhance swimming speed and promote largescale coherent structures. Velocity statistics show that polymers suppress large velocity fluctuation, transforming the velocity distributions from super-Gaussian to Gaussian. Spatial and temporal correlation functions suggest that polymers increase both the size and lifetime of flow structures. The energy spectra show…
Understanding the role of frictional drag in diffusive transport is an important problem in the field of active turbulence. Using a continuum model that applies well to bacterial suspensions, we investigate the role of Ekmann friction on the transport of passive (Lagrangian) tracers that go with the local flow. We find that the crossover from ballistic to diffusive regime happens at a time scale $τ_c$ that attains a minimum at zero friction, meaning that both injection and dissipation of energy delay the relaxation of tracers. We explain this by proposing that $τ_c \sim 2 \ell^*/u_{\text{rms}}…
In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. Two-regime power-law behavior for short and long time evolutions were identified experimentally, which were separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be $0.94$ and $0.97$ for short and long times evolutions, respectively. F…
Growing tissue and bacterial colonies are active matter systems where cell divisions and cellular motion generate active stress. Although they operate in the non-equilibrium regime, these biological systems can form large-scale ordered structures such as nematically aligned cells, topological defects, and fingerings. Mechanical instabilities also play an essential role during growth by generating large structural folding. How active matter dynamics and mechanical instabilities together develop large-scale order in growing tissue is not well understood. Here, we use chain forming Bacillus subti…
We report the selective stabilization of chiral rotational direction of bacterial vortices, from turbulent bacterial suspension, in achiral circular microwells sealed by an oil-water interface. This broken-symmetry, originating from the intrinsic chirality of bacterial swimming near hydrodynamically different top and bottom surfaces, generates a chiral edge current of bacteria at lateral boundary and grows stronger as bacterial density increases. We demonstrate that chiral edge current favors co-rotational configurations of interacting vortices, enhancing their ordering. The interplay between …
Despite their inherent non-equilibrium nature, living systems can self-organize in highly ordered collective states that share striking similarities with the thermodynamic equilibrium phases of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies, microbial suspensions and tissues to the coherent macro-scale dynamics in schools of fish and flocks of birds. Yet, the generic mathematical principles that govern the emergence of structure in such artificial and biological systems are elusive. It is not clear when, or even w…
Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior amongst the simplest forms of life, and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active non-equilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific, or which ge…
Inspired by the Turing mechanism for pattern formation, we propose a simple self-propelled particle model with short-ranged alignment and anti-alignment at larger distances. It is able to produce orientationally ordered states, periodic vortex patterns as well as meso-scale turbulence. The latter phase resembles observations in dense bacterial suspensions. The model allows a systematic derivation and analysis of a kinetic theory as well as hydrodynamic equations for density and momentum fields. A phase diagram with regions of such pattern formation as well as spatially homogeneous orientationa…
The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense supensions of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade…
We investigate the emergence of global alignment in colonies of dividing rod-shaped cells under confinement. Using molecular dynamics simulations and continuous modeling, we demonstrate that geometrical anisotropies in the confining environment give rise to imbalance in the normal stresses, which, in turn, drives a collective rearrangement of the cells. This behavior crucially relies on the colony's solid-like mechanical response at short time scales and can be recovered within the framework of active hydrodynamics upon modeling bacterial colonies as growing viscoelastic gels characterized by …
Bacterial swarms display intriguing dynamical states like active turbulence. Using a hydrodynamic model we now show that such dense active suspensions manifest super-diffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared-displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behaviour of microorganisms, our study underlines the essential differences between active and inertial tu…
Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterised by mesoscale turbulence, the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organises into a spin-state where neighbouring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elast…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent wit…
Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large-scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed experimental studies revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested b…
In a viscoelastic flow over a microfluidic canopy of polymeric pillars, we report the spontaneous emergence of waves in the form of propagating regions of low flow velocity compared to the surrounding flow. The occurrence of the wave is chaotic and shows characteristics of elastic turbulence. We systematically study the coupling between the low velocity wave and the microfluidic canopy by combining flow velocimetry experiments and high speed tracking of the pillars. The waves form an angle $β$ with the primary flow direction that depends on the geometry of the pillar array. If the canopy is co…
In this Letter, we study the collective behaviour of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedently large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is non-perturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers …
The sedimentation process in a suspension of bacteria is the result of the competition between gravity and the intrinsic motion of the microorganisms. We perform simulations of run-and-tumble "squirmers" that move in a fluid medium, focusing on the dependence of the non-equilibrium steady state on the bacterial swimming properties. We find that for high enough activity, the density profiles are no longer simple exponentials; we recover the numerical results via the introduction of a local effective temperature, suggesting that the breakdown of the Perrin-like exponential form is a collective e…
From the formation of animal flocks to the emergence of coordinate motion in bacterial swarms, at all scales populations of motile organisms display coherent collective motion. This consistent behavior strongly contrasts with the difference in communication abilities between the individuals. Guided by this universal feature, physicists have proposed that solely alignment rules at the individual level could account for the emergence of unidirectional motion at the group level. This hypothesis has been supported by agent-based simulations. However, more complex collective behaviors have been sys…
We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates towards the confinement core over multiple rotation cycles, while…
Fully developed active turbulence defined through a non-equilibrium phase transition
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Universitat de Barcelona（巴塞罗那大学）；Institute of Nanoscience and Nanotechnology, IN2UB, Universitat de Barcelona（巴塞罗那大学纳米科学与技术研究所）；Northwest University（西北大学）
