Turning Bacteria Suspensions into Superfluids

Effective viscosity of a two-dimensional passive suspension in a liquid crystal solvent

Suspension of particles in a fluid solvent are ubiquitous in nature, for example water mixed with sugar or bacteria self-propelling through mucus. Particles create local flow perturbations that can modify drastically the effective (homogenized) bulk properties of the fluid. Understanding the link between the properties of particles and the fluid solvent, and the effective properties of the medium is a classical problem in fluid mechanics. Here we study a special case of a two-dimensional model of a suspension of undeformable particles in a liquid crystal solvent. In the dilute regime, we calculate asymptotic solutions of the perturbations of the velocity and director fields and derive an explicit formula for an effective shear viscosity of the liquid crystal medium. Such effective shear viscosity increases linearly with the area fraction of particles, similar to Einstein formula but with a different prefactor. We provide explicit asymptotic formulas for the dependence of this prefactor on the material parameters of the solvent. Finally, we identify a case of decreasing the effective viscosity by increasing the magnitude of the shear-flow alignment coefficient of the liquid crystal solvent.

Dynamics of an active chiral polymer in shear flow

We explore the complex formation of an active flexible polymer chain in linear shear flow by using monomer-resolved Brownian dynamics simulations in two spatial dimensions. The chiral head monomer is active and circling, while all other monomers are passive, following both the motion of the head polymer and the shear flow. By the combination of activity, chirality, and shear rate, a wealth of different states are found, including the formation of a linear/complex folding and a spiraling state with both head-in and head-out morphologies. As the vorticity of the applied shear competes with the circling sense of the head, the chirality of the whole complex can be tuned by activity. Our results are relevant to characterize the response of living and artificial chiral active polymer chains to complex flow fields.

Ergodicity breaking in well-behaved generalized Langevin equations

By means of the concepts of dissipative stability and stochastic realizability, the phenomenon of ergodicity breaking observed in Generalized Langevin Equations (GLEs) in the presence of nonvanishing friction factors [Phys. Rev. E 83, 062102 (2011)1539-375510.1103/PhysRevE.83.062102] can be properly explained: it occurs at the boundary of the region of dissipative stability; in those cases, this region coincides with that of stochastic realizability. This is the case of the Plyukhin model that considers a generalized Debye kernel. In the presence of dissipative kernels characterized by real-valued relaxation rates corresponding to the rheological behavior of viscoelastic fluids, since the domain of stochastic realizability is strictly contained within the region of dissipative stability, this phenomenon cannot be observed if Kubo's theory of fluctuation-dissipation holds. The hydromechanic theory of GLEs also provides a physical interpretation of the ergodicity breaking reported by [Chin. Phys. Lett. 22, 1845 (2005)0256-307X10.1088/0256-307X/22/8/006] that stems from a dissipationless ''fluid-inertial" effect, leading to superdiffusion.

The 2025 motile active matter roadmap

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

Long-lived unidirectional flow of active particles within long narrow channels

Revealing the mechanism of directed transport of active matter is critical for advancing our fundamental understanding of non-equilibrium physics. Asymmetric microstructures are commonly used to rectify random movement of active particles. However, it remains unclear as to how to achieve unidirectional movement of active particles in long narrow channels. Here, we study the dynamics of active particles in a device which is divided into two chambers by V-shaped barriers and connected by a narrow channel. We find three distinct movement modes of active particles within this symmetric channel, including stochastic movement, self-sustained oscillation, and long-lived unidirectional flows. We demonstrate that the three movement modes are determined by the competition between the ratchet effect induced by the V-shaped barriers and the particle transport mediated by the long-narrow channel. Finally, we show that the unidirectional particle flow can serve as an "energy battery" to continuously supply energy for the directed transport of other objects. Our findings offer valuable insights into a unique approach for realizing unidirectional movement of active matter and open new avenues for application in microfluidics and material transport.

Where physics and biology meet

As part of this special issue on physics and biology, we invited several leading experts that bridge these disciplines to provide their views on the reciprocal contributions of each field and the benefits and challenges of working across physics and biology: introduction provided by Wallace Marshall.

Phases and correlations in active nematic granular systems

We investigate the statistical behavior of a system comprising fore-aft symmetric rods confined between two vertically vibrating plates using numerical simulations closely resembling the experimental setup studied by V. Narayan et al., Science, 2007, 317, 105-108. Our focus lies in studying the phase transition of the system from an isotropic phase to a nematic phase as we increase either the rod length or the rod concentration. Our simulations confirm the presence of long-range ordering in the ordered phase. Furthermore, we identify a phase characterized by a periodic ordering profile that disrupts translation symmetry. We also provide a detailed analysis of the translational and rotational diffusive dynamics of the rods. Interestingly, the translational diffusivity of the rods is found to increase with the rod concentration.

Microrheology of active suspensions

We study the microrheology of active suspensions through direct hydrodynamic simulations using model pusher-like microswimmers. We demonstrate that the friction coefficient of a probe particle is notably reduced by hydrodynamic interactions (HIs) among a moving probe and the swimmers. When a swimmer approaches a probe from the rear (front) side, the repulsive HIs between them are weakened (intensified), which results in a slight front-rear asymmetry in swimmer orientation distribution around the probe, creating a significant additional net driving force acting on the probe from the rear side. The present drag-reduction mechanism qualitatively differs from that of the viscosity-reduction observed in sheared bulk systems and depends on probing details. This study provides insights into our fundamental knowledge of hydrodynamic effects in active suspensions and serves as a practical example illuminating distinctions between micro- and macrorheology measurements.

Microfluidic Platform with Precisely Controlled Hydrodynamic Parameters and Integrated Features for Generation of Microvortices to Accurately Form and Monitor Biofilms in Flow

Microorganisms often live in habitats characterized by fluid flow, and their adhesion to surfaces in industrial systems or clinical settings may lead to pipe clogging, microbially influenced corrosion, material deterioration, food spoilage, infections, and human illness. Here, a novel microfluidic platform was developed to investigate biofilm formation under precisely controlled (i) cell concentration, (ii) temperature, and (iii) flow conditions. The developed platform central unit is a single-channel microfluidic flow cell designed to ensure ultrahomogeneous flow and condition in its central area, where features, e.g., with trapping properties, can be incorporated. In comparison to static and macroflow chamber assays for biofilm studies, microfluidic chips allow in situ monitoring of biofilm formation under various flow regimes and have better environment control and smaller sample requirements. Flow simulations and experiments with fluorescent particles were used to simulate bacteria flow in the platform cell for calculating flow velocity and direction at the microscale level. The combination of flow analysis and fluorescent strain injection in the cell showed that microtraps placed at the center of the channel were efficient in capturing bacteria at determined positions and to study how flow conditions, especially microvortices, can affect biofilm formation. The microfluidic platform exhibited improved performances in terms of homogeneity and robustness for in vitro biofilm formation. We anticipate the presented platform to be suitable for broad, versatile, and high-throughput biofilm studies at the microscale level.

Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells

Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Thinning by cluster breaking: Active matter and shear flows share thinning mechanisms

Among many unexpected phenomena of active matter is the recently observed superfluid-like thinning (viscosity drop) behavior of bacteria suspensions. Understanding this peculiar self-propelled thinning by active matter is of theoretical and practical importance. Here, we find that, although distinct in driving mechanisms, active matter and shear flows exhibit similar thinning behaviors upon the increase of self-propulsion and shear forces, respectively. Our structural characterizations reveal that they actually share the same cluster-breaking mechanism of thinning. How fast and how shattered the cluster is broken determines the (dis)continuity of the thinning. This explains why adding active particles to Newtonian fluids can cause thinning, in which rotation of active particles play a key role in breaking clusters. Our work proposes a mechanism of self-propelled thinning and further establishes the underlying connections between active matter and shear flows.

Programming tunable active dynamics in a self-propelled robot

We present a scheme for producing tunable active dynamics in a self-propelled robotic device. The robot moves using the differential drive mechanism where two wheels can vary their instantaneous velocities independently. These velocities are calculated by equating robot's equations of motion in two dimensions with well-established active particle models and encoded into the robot's microcontroller. We demonstrate that the robot can depict active Brownian, run and tumble, and Brownian dynamics with a wide range of parameters. The resulting motion analyzed using particle tracking shows excellent agreement with the theoretically predicted trajectories. Later, we show that its motion can be switched between different dynamics using light intensity as an external parameter. Intriguingly, we demonstrate that the robot can efficiently navigate through many obstacles by performing stochastic reorientations driven by the gradient in light intensity towards a desired location, namely the target. This work opens an avenue for designing tunable active systems with the potential of revealing the physics of active matter and its application for bio- and nature-inspired robotics.

Order, chaos, and dimensionality transition in a system of swarmalators

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, the system exhibits hyperchaos, maintaining spatial correlation under certain conditions and breaking it under others on what we interpret as a dimensionality transition.

Self-enhanced mobility enables vortex pattern formation in living matter

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

Colloidal Self-Assembly: From Passive to Active Systems

Self-assembly fundamentally implies the organization of small sub-units into large structures or patterns without the intervention of specific local interactions. This process is commonly observed in nature, occurring at various scales ranging from atomic/molecular assembly to the formation of complex biological structures. Colloidal particles may serve as micrometer-scale surrogates for studying assembly, particularly for the poorly understood kinetic and dynamic processes at the atomic scale. Recent advances in colloidal self-assembly have enabled the programmable creation of novel materials with tailored properties. We here provide an overview and comparison of both passive and active colloidal self-assembly, with a discussion on the energy landscape and interactions governing both types. In the realm of passive colloidal assembly, many impressive and important structures have been realized, including colloidal molecules, one-dimensional chains, two-dimensional lattices, and three-dimensional crystals. In contrast, active colloidal self-assembly, driven by optical, electric, chemical, or other fields, involves more intricate dynamic processes, offering more flexibility and potential new applications. A comparative analysis underscores the critical distinctions between passive and active colloidal assemblies, highlighting the unique collective behaviors emerging in active systems. These behaviors encompass collective motion, motility-induced phase segregation, and exotic properties arising from out-of-equilibrium thermodynamics. Through this comparison, we aim to identify the future opportunities in active assembly research, which may suggest new application domains.

Time-dependent properties of run-and-tumble particles: Density relaxation

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equation with anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross section and D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.

Flow states of two dimensional active gels driven by external shear

Using a minimal hydrodynamic model, we theoretically and computationally study the Couette flow of active gels in straight and annular two-dimensional channels subject to an externally imposed shear. The gels are isotropic in the absence of externally- or activity-driven shear, but have nematic order that increases with shear rate. Using the finite element method, we determine the possible flow states for a range of activities and shear rates. Linear stability analysis of an unconfined gel in a straight channel shows that an externally imposed shear flow can stabilize an extensile fluid that would be unstable to spontaneous flow in the absence of the shear flow, and destabilize a contractile fluid that would be stable against spontaneous flow in the absence of shear flow. These results are in rough agreement with the stability boundaries between the base shear flow state and the nonlinear flow states that we find numerically for a confined active gel. For extensile fluids, we find three kinds of nonlinear flow states in the range of parameters we study: unidirectional flows, oscillatory flows, and dancing flows. To highlight the activity-driven spontaneous component of the nonlinear flows, we characterize these states by the average volumetric flow rate and the wall stress. For contractile fluids, we only find the linear shear flow and a nonlinear unidirectional flow in the range of parameters that we studied. For large magnitudes of the activity, the unidirectional contractile flow develops a boundary layer. Our analysis of annular channels shows how curvature of the streamlines in the base flow affects the transitions among flow states.

Characteristic features of self-avoiding active Brownian polymers under linear shear flow

We present Brownian dynamics simulation results of a flexible linear polymer with excluded-volume interactions under shear flow in the presence of active noise. The active noise strongly affects the polymer's conformational and dynamical properties, such as the stretching in the flow direction and compression in the gradient direction, shear-induced alignment, and shear viscosity. In the asymptotic limit of large activities and shear rates, the power-law scaling exponents of these quantities differ significantly from those of passive polymers. The chain's shear-induced stretching at a given shear rate is reduced by active noise, and it displays a non-monotonic behavior, where an initial polymer compression is followed by its stretching with increasing active force. The compression of the polymer in the gradient direction follows the relation ∼WiPe-3/4 as a function of the activity-dependent Weissenberg number WiPe, which differs from the scaling observed in passive systems ∼WiPe-1/2. The flow-induced alignment at large Péclet numbers Pe ≫ 1, where Pe is the Péclet number, and large shear rates WiPe ≫ 1 displays the scaling behavior WiPe-1/2, with an exponent differing from the passive value -1/3. Furthermore, the polymer's zero-shear viscosity displays a non-monotonic behavior, decreasing in an intermediate activity regime due to excluded-volume interactions and increasing again for large Pe. Shear thinning appears with increasing Weissenberg number with the power-laws WiPe-1/2 and WiPe-3/4 for passive and active polymers, respectively. In addition, our simulation results are compared with the results of an analytical approach, which predicts quantitatively similar behaviors for the various aforementioned physical quantities.

50-year history and perspective on biomechanics of swimming microorganisms: Part II. Collective behaviours

The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years. Parts I and II are divided not by the period covered, but by the content of the research: Part I explains the behaviours of individual microorganisms, and Part II explains collective behaviour. In the 1990s, the description of microbial suspensions as a continuum progressed, and macroscopic flow structures such as bioconvection were analysed. The continuum model was later extended to analyse various phenomena such as flow induced trapping of microorganisms and accumulation of cells at interfaces. In the 2000s, the collective behaviour of swimming microorganisms came into the limelight, and physicists as well as biomechanics researchers carried out many studies probing microorganism collectivity. In particular, research on the turbulence-like flow structure of dense bacterial suspensions has led to dramatic developments in the field of microbial biomechanics. Efforts to bridge the cellular scale to the macroscopic scale by extracting macroscopic physical quantities from the microstructure of cell suspensions are also underway. This Part II reviews these collective behaviours of swimming microorganisms and discusses future prospects of the field.

Fluid-Glass-Jamming Rheology of Soft Active Brownian Particles

We numerically study the shear rheology of a binary mixture of soft active Brownian particles, from the fluid to the disordered solid regime. At low shear rates, we find a Newtonian regime, where a Green-Kubo relation with an effective temperature provides the linear viscosity. It is followed by a shear-thinning regime at high shear rates. At high densities, solidification is signaled by the emergence of a finite yield stress. We construct a "fluid-glass-jamming" phase diagram with activity replacing temperature. While both parameters gauge fluctuations, activity also changes the exponent characterizing the decay of the diffusivity close to the glass transition and the shape of the yield stress surface. The dense disordered active solid appears to be mostly dominated by athermal jamming rather than glass rheology.

Bacterial bioconvection confers context-dependent growth benefits and is robust under varying metabolic and genetic conditions

Microbes often respond to environmental cues by adopting collective behaviors-like biofilms or swarming-that benefit the population. During "bioconvection," microbes gather in dense groups and plume downward through fluid environments, driving flow and mixing on the scale of millions of cells. Though bioconvection was observed a century ago, the effects of differing physical and chemical inputs and its potential selective advantages for different species of microbes remain largely unexplored. In Bacillus subtilis, vertical oxygen gradients that originate from air-liquid interfaces create cell-density inversions that drive bioconvection. Here, we develop Escherichia coli as a complementary model for the study of bioconvection. In the context of a still fluid, we found that motile and chemotactic genotypes of both E. coli and B. subtilis bioconvect and show increased growth compared to immotile or non-chemotactic genotypes, whereas in a well-mixed fluid, there is no growth advantage to motility or chemotaxis. We found that fluid depth, cell concentration, and carbon availability affect the emergence and timing of bioconvective patterns. Also, whereas B. subtilis requires oxygen gradients to bioconvect, E. coli deficient in aerotaxis (Δaer) or energy-taxis (Δtsr) still bioconvects, as do cultures that lack an air-liquid interface. Thus, in two distantly related microbes, bioconvection may confer context-dependent growth benefits, and E. coli bioconvection is robustly elicited by multiple types of chemotaxis. These results greatly expand the set of physical and metabolic conditions in which this striking collective behavior can be expected and demonstrate its potential to be a generic force for behavioral selection across ecological contexts. IMPORTANCE Individual microorganisms frequently move in response to gradients in their fluid environment, with corresponding metabolic benefits. At a population level, such movements can create density variations in a fluid that couple to gravity and drive large-scale convection and mixing called bioconvection. In this work, we provide evidence that this collective behavior confers a selective benefit on two distantly related species of bacteria. We develop new methods for quantifying this behavior and show that bioconvection in Escherichia coli is surprisingly robust to changes in cell concentration, fluid depth, interface conditions, metabolic sensing, and carbon availability. These results greatly expand the set of conditions known to elicit this collective behavior and indicate its potential to be a selective pressure across ecological contexts.

Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns

We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.

Active XY model on a substrate: Density fluctuations and phase ordering

We explore the generic long-wavelength properties of an active XY model on a substrate, consisting of a collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation, and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it displays generalized quasi-long-range order (QLRO): It shows phase ordering which is generically either logarithmically stronger than the conventional QLRO found in its equilibrium limit, together with "miniscule number fluctuations," or logarithmically weaker than QLRO along with "giant number fluctuations," showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short-range phase order are found, characterized by the presence or absence of stable clusters of finite sizes. In a surprising connection, the hydrodynamic theory for this model also describes the fluctuations in a Kardar-Parisi-Zhang (KPZ) surface with a conserved species on it, or an active fluid membrane with a finite tension, without momentum conservation and a conserved species living on it. This implies the existence of stable fluctuating surfaces that are only logarithmically smoother or rougher than the Edward-Wilkinson surface at two dimensions (2D) can exist, in contrast to the 2D pure KPZ-like "rough" surfaces.

Phase separation of passive particles in active liquids

The transport properties of colloidal particles in active liquids have been studied extensively. It has led to a deeper understanding of the interactions between passive and active particles. However, the phase behavior of colloidal particles in active media has received little attention. Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles. Our study reveals dynamic clustering of colloids in active media due to an interplay of activity and attractive effective potential between the colloids. The strength of the effective potential is set by the size ratio of passive particles to the active ones. As the relative size of the passive particles increases, the effective potential becomes stronger and the average size of the clusters grows. The simulations reveal a macroscopic phase separation at sufficiently large size ratios. We will discuss the effect of density fluctuations of active particles on the nature of effective interactions between passive ones.

Spontaneous motion of a passive fluid droplet in an active microchannel

We numerically study the dynamics of a passive fluid droplet confined within a microchannel whose walls are covered with a thin layer of active gel. The latter represents a fluid of extensile material modelling, for example, a suspension of cytoskeletal filaments and molecular motors. Our results show that the layer is capable of producing a spontaneous flow triggering a rectilinear motion of the passive droplet. For a hybrid design (a single wall covered by the active layer), at the steady state the droplet attains an elliptical shape, resulting from an asymmetric saw-toothed structure of the velocity field. In contrast, if the active gel covers both walls, the velocity field exhibits a fully symmetric pattern considerably mitigating morphological deformations. We further show that the structure of the spontaneous flow in the microchannel can be controlled by the anchoring conditions of the active gel at the wall. These findings are also confirmed by selected 3D simulations. Our results may stimulate further research addressed to design novel microfludic devices whose functioning relies on the collective properties of active gels.

Geometrical control of interface patterning underlies active matter invasion

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

Motility-induced shear thickening in dense colloidal suspensions

Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. Here the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved Brownian dynamics simulations. First, the combined effect of activity and shear in the solid on the disordering transition of the suspension is analyzed. While both self-propulsion and shear destroy order and melt the system if critical values are exceeded, self-propulsion largely lowers the stress barrier needed to be overcome during the transition. We further explore the rheological response of the active sheared system once a steady state is reached. While passive suspensions show a solid-like behaviour, turning on particle motility fluidises the system. At low self-propulsion, the active suspension behaves in the steady state as a shear-thinning fluid. Increasing the self-propulsion changes the behaviour of the liquid from shear-thinning to shear-thickening. We attribute this to clustering in the sheared suspensions induced by motility. This new phenomenon of motility-induced shear thickening (MIST) can be used to tailor the rheological response of colloidal suspensions.

Spontaneous symmetry-breaking of the active cluster drives the directed movement and self-sustained oscillation of symmetric rod-like passive particles

Active particles without detailed balance can rectify their random motions to drive the directed movement or rotation of asymmetric passive obstacles. However, whether they can drive the directed movement of symmetric passive obstacles is still unclear. Here, we show that a rod-like passive particle which is fixed to move along the x-axis in an active bath can keep long-lived directed movement at nearly constant speed due to the spontaneous symmetry breaking of the neighboring active particle cluster. If the passive particle is further confined by a harmonic potential, it may undergo self-sustained periodic oscillation for an appropriate length of the passive particle and self-propelled velocity of active particles. The restoring force from the harmonic potential will trigger the velocity jump-off and thus lead to self-sustained periodic oscillation. Remarkably, the relationship between the velocity of the passive particle and the external force shows that the effective viscosity of the active bath may become negative in some regime. Finally, we develop a minimum 1D theoretical model to further probe the mechanism underlying the directed movement and self-sustained oscillation of the passive particle. Our findings reveal the effect of the moving boundary on the active bath and demonstrate a novel method to extract practical mechanical work from the active bath to propel microdevices.

Active Brownian particles in random and porous environments

The transport of active particles may occur in complex environments, in which it emerges from the interplay between the mobility of the active components and the quenched disorder of the environment. Here, we explore the structural and dynamical properties of active Brownian particles (ABPs) in random environments composed of fixed obstacles in three dimensions. We consider different arrangements of the obstacles. In particular, we consider two particular situations corresponding to experimentally realizable settings. First, we model pinning particles in (non-overlapping) random positions and, second, in a percolating gel structure and provide an extensive characterization of the structure and dynamics of ABPs in these complex environments. We find that the confinement increases the heterogeneity of the dynamics, with new populations of absorbed and localized particles appearing close to the obstacles. This heterogeneity has a profound impact on the motility induced phase separation exhibited by the particles at high activity, ranging from nucleation and growth in random disorder to a complex phase separation in porous environments.

The crucial role of adhesion in the transmigration of active droplets through interstitial orifices

Active fluid droplets are a class of soft materials exhibiting autonomous motion sustained by an energy supply. Such systems have been shown to capture motility regimes typical of biological cells and are ideal candidates as building-block for the fabrication of soft biomimetic materials of interest in pharmacology, tissue engineering and lab on chip devices. While their behavior is well established in unconstrained environments, much less is known about their dynamics under strong confinement. Here, we numerically study the physics of a droplet of active polar fluid migrating within a microchannel hosting a constriction with adhesive properties, and report evidence of a striking variety of dynamic regimes and morphological features, whose properties crucially depend upon droplet speed and elasticity, degree of confinement within the constriction and adhesiveness to the pore. Our results suggest that non-uniform adhesion forces are instrumental in enabling the crossing through narrow orifices, in contrast to larger gaps where a careful balance between speed and elasticity is sufficient to guarantee the transition. These observations may be useful for improving the design of artificial micro-swimmers, of interest in material science and pharmaceutics, and potentially for cell sorting in microfluidic devices.

Quasi-two-dimensional bacterial swimming around pillars: Enhanced trapping efficiency and curvature dependence

Microswimmers exhibit more diverse behavior in quasi-two dimensions than in three dimensions. Such behavior remains elusive due to the analytical difficulty of dealing with two parallel solid boundaries. The existence of additional obstacles in quasi-two dimensional systems further complicates the analysis. Combining experiments and hydrodynamic simulations, we investigate how the spatial dimension affects the interactions between microswimmers and obstacles. We fabricated microscopic pillars in quasi-two dimensions by etching glass coverslips and observed bacterial swimming among the pillars. Bacteria got trapped around the circular pillars and the trapping efficiency increased as the quasi-two-dimensionality was increased or as the curvature of the pillars was decreased. Numerical simulations of the simplest situation of a confined squirmer showed anomalous increase of hydrodynamic attractions, establishing that the enhanced interaction is a universal property of quasi-two-dimensional microhydrodynamics. We also demonstrated that the local curvature of the obstacle controls the trapping efficiency by experiments with elliptic pillars.

Frustrated 'run and tumble' of swimming Escherichia coli bacteria in nematic liquid crystals

In many situations, bacteria move in complex environments, as soils, oceans or the human gut-track, where carrier fluids show complex structures associated with non-Newtonian rheology. Many fundamental questions concerning the ability to navigate in such environments remain unsolved. Recently, it has been shown that the kinetics of bacterial motion in structured fluids as liquid crystals (LCs) is constrained by the orientational molecular order (or director field) and that novel spatio-temporal patterns arise. A question unaddressed so far is how bacteria change swimming direction in such an environment. In this work, we study the swimming mechanism of a single bacterium, Esherichia coli, constrained to move along the director field of a lyotropic chromonic liquid crystal confined to a planar cell. Here, the spontaneous 'run and tumble' motion of the bacterium gets frustrated: the elasticity of the LC prevents flagella from unbundling. Interestingly, to change direction, bacteria execute a reversal motion along the director field, driven by the relocation of a single flagellum, a 'frustrated tumble'. We characterize this phenomenon in detail experimentally, exploiting exceptional spatial and temporal resolution of bacterial and flagellar dynamics, using a two colour Lagrangian tracking technique. We suggest a possible mechanism accounting for these observations.

Coexistence of Active and Hydrodynamic Turbulence in Two-Dimensional Active Nematics

In active nematic liquid crystals, activity is able to drive chaotic spatiotemporal flows referred to as active turbulence. Active turbulence has been characterized through theoretical and experimental work as a low Reynolds number phenomenon. We show that, in two dimensions, the active forcing alone is able to trigger hydrodynamic turbulence leading to the coexistence of active and inertial turbulence. This type of flow develops for sufficiently active and extensile flow-aligning nematics. We observe that the combined effect of an extensile nematic and large values of the flow-aligning parameter leads to a broadening of the elastic energy spectrum that promotes a growth of kinetic energy able to trigger an inverse energy cascade.

Flocking in one dimension: Asters and reversals

We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate, and the temperature controlling the alignment shows a homogeneous disordered phase but no homogeneous ordered one, as well as two phases with localized dense structures. In the flocking phase, large ordered aggregates move ballistically and stochastically reverse their direction of motion. In what we termed the "aster" phase, dense immobile aggregates of opposite magnetization face each other, exchanging particles, without any net motion of the aggregates. Using a combination of numerical simulations and mean-field theory, we study the evolution of the shapes of the flocks, the statistics of their reversal times, and their coarsening dynamics. Solving exactly for the zero-temperature dynamics of an aster allows us to understand their coarsening, which shows extremal dynamics, while mean-field equations account for their shape.

Nonequilibrium dynamical structure factor of a dilute suspension of active particles in a viscoelastic fluid

In this work we investigate the dynamics of the number-density fluctuations of a dilute suspension of active particles in a linear viscoelastic fluid. We propose a model for the frequency-dependent diffusion coefficient of the active particles which captures the effect of rotational diffusion on the persistence of their self-propelled motion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, the linearized equations for the active suspension are derived, from which we calculate its dynamic structure factor and the corresponding intermediate scattering function. For a Maxwell-type rheological model, we find an intricate dependence of these functions on the parameters that characterize the viscoelasticity of the solvent and the activity of the particles, which can significantly deviate from those of an inert suspension of passive particles and of an active suspension in a Newtonian solvent. In particular, in some regions of the parameter space we uncover the emergence of oscillations in the intermediate scattering function at certain wave numbers which represent the hallmark of the nonequilibrium particle activity in the dynamical structure of the suspension and also encode the viscoelastic properties of the medium.

Novel form of collective movement by soil bacteria

Although migrations are essential for soil microorganisms to exploit scarce and heterogeneously distributed resources, bacterial mobility in soil remains poorly studied due to experimental limitations. In this study, time-lapse images collected using live microscopy techniques captured collective and coordinated groups of B. subtilis cells exhibiting "crowd movement". Groups of B. subtilis cells moved through transparent soil (nafion polymer with particle size resembling sand) toward plant roots and re-arranged dynamically around root tips in the form of elongating and retracting "flocks" resembling collective behaviour usually associated with higher organisms (e.g., bird flocks or fish schools). Genetic analysis reveals B. subtilis flocks are likely driven by the diffusion of extracellular signalling molecules (e.g., chemotaxis, quorum sensing) and may be impacted by the physical obstacles and hydrodynamics encountered in the soil like environment. Our findings advance understanding of bacterial migration through soil matrices and expand known behaviours for coordinated bacterial movement.

Asymptotics and Summation of the Effective Properties of Suspensions, Simple Liquids and Composites

We review the problem of summation for a very short truncation of a power series by means of special resummation techniques inspired by the field-theoretical renormalization group. Effective viscosity (EV) of active and passive suspensions is studied by means of a special algebraic renormalization approach applied to the first and second-order expansions in volume fractions of particles. EV of the 2D and 3D passive suspensions is analysed by means of various self-similar approximants such as iterated roots, exponential approximants, super-exponential approximants and root approximants. General formulae for all concentrations are derived. A brief introduction to the rheology of micro-swimmers is given. Microscopic expressions for the intrinsic viscosity of the active system of puller-like microswimmers are obtained. Special attention is given to the problem of the calculation of the critical indices and amplitudes of the EV and to the sedimentation rate in the vicinity of known critical points. Critical indices are calculated from the short truncation by means of minimal difference and minimal derivative conditions on the fixed points imposed directly on the critical properties. Accurate expressions are presented for the non-local diffusion coefficient of a simple liquid in the vicinity of a critical point. Extensions and corrections to the celebrated Kawasaki formula are discussed. We also discuss the effective conductivity for the classical analog of graphene and calculate the effective critical index for superconductivity dependent on the concentration of vacancies. Finally, we discuss the effective conductivity of a random 3D composite and calculate the superconductivity critical index of a random 3D composite.

Run-to-Tumble Variability Controls the Surface Residence Times of E. coli Bacteria

Motile bacteria are known to accumulate at surfaces, eventually leading to changes in bacterial motility and biofilm formation. We use a novel two-color, three-dimensional Lagrangian tracking technique to follow simultaneously the body and the flagella of a wild-type Escherichia coli. We observe long surface residence times and surface escape corresponding mostly to immediately antecedent tumbling. A motility model accounting for a large behavioral variability in run-time duration reproduces all experimental findings and gives new insights into surface trapping efficiency.

Bacterial active matter

Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.

Rectification and confinement of photokinetic bacteria in an optical feedback loop

Active particles can self-propel by exploiting locally available energy resources. When powered by light, these resources can be distributed with high resolution allowing spatio-temporal modulation of motility. Here we show that the random walks of light-driven bacteria are rectified when they swim in a structured light field that is obtained by a simple geometric transformation of a previous system snapshot. The obtained currents achieve an optimal value that we establish by general theoretical arguments. This optical feedback is used to gather and confine bacteria in high-density and high-activity regions that can be dynamically relocated and reconfigured. Moving away from the boundaries of these optically confined states, the density decays to zero in a few tens of micrometers, exhibiting steep exponential tails that suppress cell escape and ensure long-term stability. Our method is general and scalable, providing a versatile tool to produce localized and tunable active baths for microengineering applications and systematic studies of non-equilibrium phenomena in active systems.

 Light can be used to precisely modulate the speed of active particles in space and time. Here, the authors rectify and confine bacteria using an optical feedback loop that couples bacteria topast configurations.

Dynamic and mechanical evolution of an oil-water interface during bacterial biofilm formation

We present an experimental study combining particle tracking, active microrheology, and differential dynamic microscopy (DDM) to investigate the dynamics and rheology of an oil-water interface during biofilm formation by the bacteria Pseudomonas Aeruginosa PA14. The interface transitions from an active fluid dominated by the swimming motion of adsorbed bacteria at early age to an active viscoelastic system at late ages when the biofilm is established. The microrheology measurements using microscale magnetic rods indicate that the biofilm behaves as a viscoelastic solid at late age. The bacteria motility at the interface during the biofilm formation, which is characterized in the DDM measurements, evolves from diffusive motion at early age to constrained, quasi-localized motion at later age. Similarly, the mobility of passively moving colloidal spheres at the interface decreases significantly with increasing interface age and shows a dependence on sphere size after biofilm formation that is orders-of-magnitude larger than that expected in a homogeneous system in equilibrium. We attribute this anomalous size dependence to either length-scale-dependent rheology of the biofilm or widely differing effects of the bacteria activity on the motion of spheres of different sizes.

Rheology of bacterial superfluids in viscous environments

Viscous environments are ubiquitous in nature and in engineering applications, from mucus in lungs to oil recovery strategies in the earth's subsurface - and in all these environments, bacteria also thrive. The behavior of bacteria in viscous environments has been investigated for a single bacterium, but not for active suspensions. Dense populations of pusher-type bacteria are known to create superfluidic regimes where the effective viscosity of the entire suspension is reduced through collective motion, and the main purpose of this study is to investigate how a viscous environment will affect this behavior. Using a Couette rheometer, we measure shear stress as a function of the applied shear rate to define the effective viscosity of suspensions of Escherichia coli (E. coli), while varying both the bacterial density within the suspension and the viscosity of the suspending fluid. We document the remarkable observation that E. coli decreases the effective suspension viscosity to near-zero (superfluidic regime) for all solvent viscosities tested (1-17 mPa s). Specifically, we observe that the bacterial density needed to trigger this superfluidic regime and the maximum shear rate under which this regime can be sustained both decrease with increasing solvent viscosity. We find that the resulting rheograms can be well approximated by the Carreau-Yasuda law. Using this, we propose a constitutive model as a function of the solvent viscosity and the bacterial concentration only. This model captures the onset of the superfluidic regime and offers promising avenues for the modelling of flow of bacterial suspensions in viscous environments.

Transport and fluctuations in mass aggregation processes: Mobility-driven clustering

We calculate the bulk-diffusion coefficient and the conductivity in nonequilibrium conserved-mass aggregation processes on a ring. These processes involve chipping and fragmentation of masses, which diffuse on a lattice and aggregate with their neighboring masses on contact, and, under certain conditions, they exhibit a condensation transition. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility of masses, is greatly enhanced. The enhancement in the conductivity, in accordance with the Einstein relation, results in large mass fluctuations and can induce a mobility-driven clustering in the systems. Indeed, in a certain parameter regime, we show that the conductivity, along with the mass fluctuation, diverges beyond a critical density, thus characterizing the previously observed nonequilibrium condensation transition [Phys. Rev. Lett. 81, 3691 (1998)10.1103/PhysRevLett.81.3691] in terms of an instability in the conductivity. Notably, the bulk-diffusion coefficient remains finite in all cases. We find our analytic results in quite good agreement with simulations.

Bacterial activity hinders particle sedimentation

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and industrial processes. Here, we investigate sedimentation dynamics of passive particles in a fluid as a function of bacteria E. coli concentration. Results show that the presence of swimming bacteria significantly reduces the speed of the sedimentation front even in the dilute regime, in which the sedimentation speed is expected to be independent of particle concentration. Furthermore, bacteria increase the dispersion of the passive particles, which determines the width of the sedimentation front. For short times, particle sedimentation speed has a linear dependence on bacterial concentration. Mean square displacement data shows, however, that bacterial activity decays over long experimental (sedimentation) times. An advection-diffusion equation coupled to bacteria population dynamics seems to capture concentration profiles relatively well. A single parameter, the ratio of single particle speed to the bacteria flow speed can be used to predict front sedimentation speed.

Imaging the emergence of bacterial turbulence: Phase diagram and transition kinetics

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 Escherichia 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. 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 insights into interparticle interactions and transition kinetics of bacterial turbulence.

Heterogeneous bacterial swarms with mixed lengths

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming speeds. On the other hand, high fractions of long cells form a bottleneck for efficient swarming. Our results suggest a physical advantage for the spontaneous heterogeneity of bacterial swarm populations.

Viscoelastic control of spatiotemporal order in bacterial active matter

Active matter consists of units that generate mechanical work by consuming energy¹. Examples include living systems (such as assemblies of bacteria^2-5 and biological tissues^6,7), biopolymers driven by molecular motors^8-11 and suspensions of synthetic self-propelled particles^12-14. A central goal 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^12,14,15 or the temporal synchronization of individual oscillatory dynamics². The simultaneous control of spatial and temporal organization is more challenging and generally requires complex interactions, such as reaction-diffusion hierarchies¹⁶ or genetically engineered cellular circuits². Here we report a simple technique to simultaneously control the spatial and temporal self-organization of bacterial active matter. We confine dense active suspensions of Escherichia coli cells and manipulate a single macroscopic parameter-namely, the viscoelasticity of the suspending fluid- through the addition of purified genomic DNA. This reveals self-driven spatial and temporal organization in the form of a millimetre-scale rotating vortex with periodically oscillating global chirality of tunable frequency, reminiscent of a torsional pendulum. By combining experiments with an active-matter model, we explain this behaviour in terms of the interplay between active forcing and viscoelastic stress relaxation. Our findings provide insight into the influence of bacterial motile behaviour in complex fluids, which may be of interest in health- and ecology-related research, and demonstrate experimentally that rheological properties can be harnessed to control active-matter flows^17,18. We envisage that our millimetre-scale, tunable, self-oscillating bacterial vortex may be coupled to actuation systems to act a 'clock generator' capable of providing timing signals for rhythmic locomotion of soft robots and for programmed microfluidic pumping¹⁹, for example, by triggering the action of a shift register in soft-robotic logic devices²⁰.