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 the bulk limit. By comparing density fluctuations and kinetic energy in active turbulence, we identified a universal density-independent and scale-invariant correlation between the two quantities across a wide range of length scales.
As a paradigmatic model of active fluids, bacterial suspensions show intriguing rheological responses drastically different from their counterpart colloidal suspensions. Although the flow of bulk bacterial suspensions has been extensively studied, the rheology of bacterial suspensions under confinement has not been experimentally explored. Here, using a microfluidic viscometer, we systematically measure the rheology of dilute E. coli suspensions under different degrees of confinement. Our study reveals a strong confinement effect: the viscosity of bacterial suspensions decreases substantially …
We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering perturbations in the shear-rate and bacterial concentration. Non-linear simulations show that the instability eventually leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the bands. Our results show that long-ranged hydrodynamic interactions are sufficient to explain recent observations of shear-bands in bact…
Chiral symmetry breaking is ubiquitous in biological systems, from DNA to bacterial suspensions. A key unresolved problem is how chiral structures may spontaneously emerge from achiral interactions. We study a simple model of bacterial suspensions in three dimensions that effectively incorporates active motion and hydrodynamic interactions. We perform large-scale molecular dynamics simulations (up to $10^6$ particles) and describe stable (or long-lived metastable) collective states that exhibit chiral organization although the interactions are achiral. We elucidate under which conditions these…
Drying of bacterial suspensions is frequently encountered in a plethora of natural and engineering processes. However, the evaporation-driven mechanical instabilities of dense consolidating bacterial suspensions have not been explored heretofore. Here, we report the formation of two different crack patterns of drying suspensions of \textit{Escherichia coli} (\textit{E. coli}) with distinct motile behaviors. Circular cracks are observed for wild-type \textit{E. coli} with active swimming, whereas spiral-like cracks form for immotile bacteria. Using the elastic fracture mechanics and the poroela…
Swimming bacteria create long-range velocity fields that stir a large volume of fluid and move around passive particles dispersed in the fluid. Recent experiments and simulations have shown that long-time mean-squared displacement of passive particles in a bath of swimming bacteria exhibits diffusive behaviour with the effective diffusion coefficient significantly larger than its thermal counterpart. Comprehensive theoretical prediction of this effective diffusion coefficient and understanding of the enhancement mechanism remain a challenge. Here, we adapt the kinetic theory by Lin et al., J. …
We analyse the time dependent non-linear rheology of a dilute bacterial suspension (e.g. E. coli) for a pair of impulsively started linear flows - simple shear and uniaxial extension. The rheology is governed by the bacterium orientation distribution which satisfies a kinetic equation that includes rotation by the imposed flow, and relaxation to isotropy via rotary diffusion and tumbling. The relevant dimensionless parameters are the Peclet number $Pe\equiv \dotγτ$, which dictates the importance of flow-induced orientation anisotropy, and $τD_r$, which quantifies the relative importance of the…
To survive in harsh conditions, motile bacteria swim in complex environment and respond to the surrounding flow. Here we develop a PDE model describing how the flagella bending affects macroscopic properties of bacterial suspensions. First, we show how the flagella bending contributes to the decrease of the effective viscosity observed in dilute suspension. Our results do not impose tumbling (random re-orientation) as it was done previously to explain the viscosity reduction. Second, we demonstrate a possibility of bacterium escape from the wall entrapment due to the self-induced buckling of f…
We probe non-equilibrium properties of an active bacterial bath through measurements of correlations of passive tracer particles and the response function of a driven, optically trapped tracer. These measurements demonstrate violation of the fluctuation-dissipation theorem and enable us to extract the power spectrum of the active stress fluctuations. In some cases, we observe $1/\sqrtω$ scaling in the noise spectrum which we show can be derived from a theoretical model incorporating coupled stress, orientation, and concentration fluctuations of the bacteria.
The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer-tracer hydrodynamic interactions at low-Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient $β$, as observed experimentally. The coefficient $β$ scales as the tracer-swimmer cross section times the mean square displacement produced by single scatterings. The displacements depend on the swimmer propulsio…
Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration c. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling towar…
Active matter such as swarming bacteria and motile colloids exhibits exotic properties different from conventional equilibrium materials. Among these properties, the enhanced diffusion of tracer particles is generally deemed as a hallmark of active matter. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in quasi-two-dimensional bacterial bath. Our study reveals a nonlinear enhancement of both translational and rotational diffusions. More importantly, we uncover an anomalous coupling between translation and rotation that is strictly prohibited in the cla…
We describe a new kind of self-propelling motion of bacteria based on the cooperative action of rotating flagella on the surface of bacteria. Describing the ensemble of rotating flagella in the framework of the hydrodynamics with spin the reciprocal theorem of Stokesian hydrodynamics is generalized accordingly. The velocity of the self-propulsion is expressed in terms of the characteristics of the vector field of flagella orientation and it is shown that unusually high velocities of \textit{Thiovulum majus} bacteria may be explained by the cooperative action of the rotating flagella. The expre…
Bacterial suspensions--a premier example of active fluids--show an unusual response to shear stresses. Instead of increasing the viscosity of the suspending fluid, the emergent collective motions of swimming bacteria can turn a suspension into a "superfluid" with zero apparent viscosity. Although the existence of active "superfluids" has been demonstrated in bulk rheological measurements, the microscopic origin and dynamics of such an exotic phase have not been experimentally probed. Here, using high-speed confocal rheometry, we study the dynamics of concentrated bacterial suspensions under si…
Confining surfaces play crucial roles in dynamics, transport and order in many physical systems, but their effects on active matter, a broad class of dynamically self-organizing systems, are poorly understood. We investigate here the influence of global confinement and surface curvature on collective motion by studying the flow and orientational order within small droplets of a dense bacterial suspension. The competition between radial confinement, self-propulsion, steric interactions and hydrodynamics robustly induces an intriguing steady single-vortex state, in which cells align in inwardly-…
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.
By developing a molecular dynamics model of bacterial chemotaxis, we present the first investigation of tracer statistics in bacterial suspensions where chemotactic effects are considered. We demonstrate that the non-Gaussian statistics of full-coated tracer arises from the athermal bacterial noise. Moreover, Janus (half-coated) tracer performs a composite random walk combining power-law-tail distributed Lévy flights with Brownian jiggling at low coating concentration, but turns to an enhanced directional transport (EDT) when coating concentration is high. Unlike conventional self-propelled pa…
The rheology of semidilute bacterial suspensions is studied with the tools of kinetic theory, considering binary interactions, going beyond the ideal gas approximation. Two models for the interactions are considered, which encompass both the steric and short range interactions. In these, swimmers can either align polarly regardless of the state previous to the collision or they can align axially, being possible the end up antiparallel if the relative angle between directors is large. In both cases, it is found that an ordered phase develops when increasing the density, where the shear stress o…
The rheological response under simple shear of an active suspension of Escherichia coli is determined in a large range of shear rates and concentrations. The effective viscosity and the time scales characterizing the bacterial organization under shear are obtained. In the dilute regime, we bring evidences for a low shear Newtonian plateau characterized by a shear viscosity decreasing with concentration. In the semi-dilute regime, for particularly active bacteria, the suspension display a "super-fluid" like transition where the viscous resistance to shear vanishes, thus showing that macroscopic…
We present a joint experimental and computational study of the effect of bacterial motion on micron-scale colloids contained in a two-dimensional suspension of Bacillus subtilis. With respect to previous work using E. coli, here we introduce a novel experimental set-up that allows us to realise a two-dimensional bacterial suspension insensitive to either evaporation or fluid flow. By analysing the mean square displacements of both bacteria and colloids, we confirm the existence of a crossover from super-diffusive behaviour at short time scales to normal diffusion at longer times. We also study…
Active matter consists of units that generate mechanical work by consuming energy. Examples include living systems, such as assemblies of bacteria and biological tissues, biopolymers driven by molecular motors, and suspensions of synthetic self-propelled particles. A central question in the field is to understand and control the self-organization of active assemblies in space and time. Most active systems exhibit either spatial order mediated by interactions that coordinate the spatial structure and the motion of active agents or the temporal synchronization of individual oscillatory dynamics.…
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}}…
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…
A simple model for simulating flows of active suspensions is investigated. The approach is based on dissipative particle dynamics. While the model is potentially applicable to a wide range of self-propelled particle systems, the specific class of self-motile bacterial suspensions is considered as a modeling scenario. To mimic the rod-like geometry of a bacterium, two dissipative particle dynamics particles are connected by a stiff harmonic spring to form an aggregate dissipative particle dynamics molecule. Bacterial motility is modeled through a constant self-propulsion force applied along the…
Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such `active nematics' systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here we introduce a new active n…
We study the interplay of activity, order and flow through a set of coarse-grained equations governing the hydrodynamic velocity, concentration and stress fields in a suspension of active, energy-dissipating particles. We make several predictions for the rheology of such systems, which can be tested on bacterial suspensions, cell extracts with motors and filaments, or artificial machines in a fluid. The phenomena of cytoplasmic streaming, elastotaxis and active mechanosensing find natural explanations within our model.
Bacterial biofilms cost an enormous amount of resources in the health, medical, and industrial sectors. To understand early biofilm formation, beginning from planktonic states of active bacterial suspensions (such as Escherichia coli) to microcolonization, it is vital to study the mechanics of accumulation near surfaces and subsequent deposition. In this study, analytical expressions for the mean orientation, density and angular distributions, and deposition rates in such bacterial suspensions are derived, with and without the effects of external guiding or taxis fields. Simulations of confine…
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…
We experimentally investigate the rheology and stress fluctuations of granules densely suspended in silicone oil. We find that both thickening strength and stress fluctuations significantly weaken with oil viscosity $η_0$. Comparison of our rheological results to the Wyart-Cates model for describing different dynamic jamming states suggests a transition from frictional contacts to lubrication interactions as $η_0$ increases. To clarify the contribution from viscous interactions to the rheology, we systematically measure stress fluctuations in various flow states. Reduction of stress fluctuatio…
We point out unconventional mechanical properties of confined active fluids, such as bacterial suspensions, under shear. Using a minimal model of an active liquid crystal with no free parameters, we predict the existence of a window of bacteria concentration for which a suspension of \textit{E.~Coli} effectively behaves, at steady-state, as a negative viscosity fluid and reach quantitative agreement with experimental measurements. Our theoretical analysis further shows that a negative apparent viscosity is due to a non-monotonic local velocity profile, and is associated with a non-monotonic st…
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…
Spontaneous oscillations and geometric cutoff in confined bacterial swarms
Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences (UCAS)（中国科学院大学材料科学与光电技术学院物质科学与光电工程中心）；Department of Physics, Hong Kong Baptist University（香港浸会大学物理系）；Center for Interdisciplinary Studies, Westlake University（西湖大学交叉研究中心）
A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale-invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue and active colloides, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent cl…
We introduce a novel approach to reveal ordering fluctuations in sheared dense suspensions, using line scanning in a combined rheometer and laser scanning confocal microscope. We validate the technique with a moderately dense suspension, observing modest shear-induced ordering and a nearly linear flow profile. At high concentration ($ϕ= 0.55$) and applied stress just below shear thickening, we report ordering fluctuations with high temporal resolution, and directly measure a decrease in order with distance from the suspension's bottom boundary as well as a direct correlation between order and …
Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and artificial environments. Here, we experimentally investigate sedimentation of passive particles in water containing various concentrations of the bacterium E. coli. Results show that the presence of living bacteria reduces the velocity of the sedimentation front even in the dilute regime, where the sedimentation velocity is expected to be independent of particle concentration. Bacteria increase the effective diffusion coefficient of the passive particles, which determines the width…
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…
We confine a dense suspension of motile \textit{Escherichia coli} inside a spherical droplet in a water-in-oil emulsion, creating a "bacterially" propelled droplet. We show that droplets move in a persistent random walk, with a persistence time $τ\sim 0.3\, {\rm s}$, a long-time diffusion coefficient $D\sim 0.5\, μ{\rm m}^2/{\rm s}$, and an average instantaneous speed $V\sim 1.5\, μ{\rm m/s}$ when the bacterial suspension is at the maximum studied concentration. Several droplets are analyzed, varying the drop radius and bacterial concentration. We show that the persistence time, diffusion coef…
A dilute non-interacting suspension of micro-swimmers exhibits a finite velocity variance and short-ranged correlations that decay over a swimmer length. For a suspension of interacting straight swimmers, however, pair-interactions leads to a non-decaying velocity covariance, and a variance that diverges logarithmically with system size. The divergence is arrested on inclusion of orientation decorrelation mechanisms. Results for suspensions of run-and-tumble particles (RTPs) are presented, where the underlying straight-swimmer divergence leads to a broad cross-over between the ballistic and di…
Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.
In dilute suspensions of swimming microorganisms the local fluid velocity is a random superposition of the flow fields set up by the individual organisms, which in turn have multipole contributions decaying as inverse powers of distance from the organism. Here we show that the conditions under which the central limit theorem guarantees a Gaussian probability distribution function of velocities are satisfied when the leading force singularity is a Stokeslet, but are not when it is any higher multipole. These results are confirmed by numerical studies and by experiments on suspensions of the alg…
We discuss a recent effort in the modelling of binary component thin films, which yielded the same conclusions and stability limits as earlier work, despite a different method of incorporating constraints into the gradient dynamics description of the system.
We present measurements of the thermal fluctuations of the free surface of an aging colloidal suspension, Laponite. The technique consists in measuring the fluctuations of the position of a laser beam that reflects from the free surface. Analysing the data statistics, we show that, as the fluid ages, the dynamics becomes intermittent. The intermittent events correspond to large changes in the local slope of the free surface over a few milliseconds. We show that those quakes are uncorrelated, although they are kept in memory by the surface over short time scales.
We analyze fluctuations of particle displacements and stresses in a sheared athermal suspension of elastic capsules (red blood cells). Upon variation of the volume fraction from the dilute up to the highly concentrated regime, our numerical simulations reveal different characteristic power-law regimes of the fluctuation variances and relaxation times. In the jammed phase and at high shear rates, anomalous scaling exponents are found that deviate from pure dimensional predictions. The observed behavior is rationalized via kinetic arguments and a dissipation balance model that takes into account…
