Confinement stabilizes a bacterial suspension into a spiral vortex

Driven topological transitions in active nematic films

The topological properties of many materials are central to their behavior. In intrinsically out-of-equilibrium active materials, the dynamics of topological defects can be particularly important. In this paper, local manipulation of the order, dynamics, and topological properties of microtubule-based active nematic films is demonstrated in a joint experimental and simulation study. Hydrodynamic stresses created by magnetically actuated rotation of disk-shaped colloids in proximity to the films compete with internal stresses in the active nematic, influencing the local motion of +1/2 charge topological defects that are intrinsic to the nematic order in the spontaneously turbulent active films. Sufficiently large applied stresses drive the formation of +1 charge topological vortices through the merger of two +1/2 defects. The directed motion of the defects is accompanied by ordering of the vorticity and velocity of the active flows within the film that is qualitatively unlike the response of passive viscous films. Many features of the film's response to the stress are captured by lattice Boltzmann simulations, providing insight into the anomalous viscoelastic nature of the active nematic. The topological vortex formation is accompanied by a rheological instability in the film that leads to significant increase in the flow velocities. Comparison of the velocity profile in vicinity of the vortex with fluid-dynamics calculations provides an estimate of the film viscosity.

Active microfluidic transport in two-dimensional handlebodies

Unlike traditional nematic liquid crystals, which adopt ordered equilibrium configurations compatible with the topological constraints imposed by the boundaries, active nematics are intrinsically disordered because of their self-sustained internal flows. Controlling the flow patterns of active nematics remains a limiting step towards their use as functional materials. Here we show that confining a tubulin-kinesin active nematic to a network of connected annular microfluidic channels enables controlled directional flows and autonomous transport. In single annular channels, for narrow widths, the typically chaotic streams transform into well-defined circulating flows, whose direction or handedness can be controlled by introducing asymmetric corrugations on the channel walls. The dynamics is altered when two or three annular channels are interconnected. These more complex topologies lead to scenarios of synchronization, anti-correlation, and frustration of the active flows, and to the stabilisation of high topological singularities in both the flow field and the orientational field of the material. Controlling textures and flows in these microfluidic platforms opens unexplored perspectives towards their application in biotechnology and materials science.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Morphological transitions of active Brownian particle aggregates on porous walls

Motility-induced wall aggregation of Active Brownian Particles (ABPs) is a well-studied phenomenon. Here, we study the aggregation of ABPs on porous walls, which allows the particles to penetrate through at large motility. We show that the active aggregates undergo a morphological transition from a connected dense-phase to disconnected droplets with an increase in wall porosity and the particle self-motility, similar to wetting-dewetting transitions in equilibrium fluids. We show that both morphologically distinct states are stable, and independent of initial conditions at least in some parameter regions. Our analysis reveals that changes in wall porosity affect the intrinsic properties of the aggregates and changes the effective wall-aggregate interfacial tension, consistent with the appearance of the morphological transition. Accordingly, a close analysis of the density, as well as orientational distribution, indicates that the underlying reason for such morphological transitions is not necessarily specific to the systems with porous walls, and it can be possible to observe in a larger class of confined, active systems by tuning the properties of confining walls.

Pressure-driven changes to spontaneous flow in active nematic liquid crystals

We consider the effects of a pressure gradient on the spontaneous flow of an active nematic liquid crystal in a channel, subject to planar anchoring and no-slip conditions on the boundaries of the channel. We employ a model based on the Ericksen-Leslie theory of nematics, with an additional active stress accounting for the activity of the fluid. By directly solving the flow equation, we consider an asymptotic solution for the director angle equation for large activity parameter values and predict the possible values of the director angle in the bulk of the channel. Through a numerical solution of the full nonlinear equations, we examine the effects of pressure on the branches of stable and unstable equilibria, some of which are disconnected from the no-flow state. In the absence of a pressure gradient, solutions are either symmetric or antisymmetric about the channel midpoint; these symmetries are changed by the pressure gradient. Considering the activity-pressure state space allows us to predict qualitatively the extent of each solution type and to show, for large enough pressure gradients, that a branch of non-trivial director angle solutions exists for all activity values.

Squirmer rods as elongated microswimmers: flow fields and confinement

Microswimmers or active elements, such as bacteria and active filaments, have an elongated shape, which determines their individual and collective dynamics. There is still a need to identify what role long-range hydrodynamic interactions play in their fascinating dynamic structure formation. We construct rods of different aspect ratios using several spherical squirmer model swimmers. With the help of the mesoscale simulation method of multi-particle collision dynamics we analyze the flow fields of these squirmer rods both in a bulk fluid and in Hele-Shaw geometries of different slab widths. Based on the hydrodynamic multipole expansion either for bulk or confinement between two parallel plates, we categorize the different multipole contributions of neutral as well as pusher-type squirmer rods. We demonstrate how confinement alters the radial decay of the flow fields for a given force or source multipole moment compared to the bulk fluid.

Thin-film modeling of resting and moving active droplets

We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization in the form of a gradient dynamics supplemented with active stresses and fluxes. A wetting energy for a partially wetting liquid is incorporated allowing for motion of the liquid-solid-gas contact line. This gives a consistent basis for the description of drops of dense bacterial suspensions or compact aggregates of living cells on solid substrates. As example, we analyze the dynamics of two-dimensional active drops (i.e., ridges) and demonstrate how active forces compete with passive surface forces to shape droplets and drive their motion. In our simple two-dimensional scenario we find that defect structures within the polarization profile drastically influence the shape and motility of active droplets. Thus, we can observe a transition from resting to motile droplets via the elimination of defects in the polarization profile. Furthermore, droplet motility is modulated by strong active stresses. Contractile stresses even lead to topological changes, i.e., drop splitting, which is naturally encoded in the evolution equations.

Active noise experienced by a passive particle trapped in an active bath

We study the properties of active noise experienced by a passive particle harmonically trapped in an active bath. The active bath is either explicitly simulated by an ensemble of active Brownian particles or abstractly represented by an active colored noise in theory. Assuming the equivalence of the two descriptions of the active bath, the active noise in the simulation system, which is directly extracted by fitting theoretical predictions to simulation measurements, is shown to depend on the constraint suffered by the passive tracer. This scenario is in significant contrast to the case of thermal noise that is independent of external trap potentials. The constraint dependence of active noise arises from the fact that the persistent force on the passive particle from the active bath can be influenced by the particle relaxation dynamics. Moreover, due to the interplay between the active collisions and particle relaxation dynamics, the effective temperature of the passive tracer quantified as the ratio of fluctuation to dissipation increases as the constraint strengthens, while the average potential and kinetic energies of the passive particle both decrease.

Oscillating collective motion of active rotors in confinement

Due to its inherent out-of-equilibrium nature, active matter in confinement may exhibit collective behavior absent in unconfined systems. Extensive studies have indicated that hydrodynamic or steric interactions between active particles and boundary play an important role in the emergence of collective behavior. However, besides introducing external couplings at the single-particle level, the confinement also induces an inhomogeneous density distribution due to particle-position correlations, whose effect on collective behavior remains unclear. Here, we investigate this effect in a minimal chiral active matter composed of self-spinning rotors through simulation, experiment, and theory. We find that the density inhomogeneity leads to a position-dependent frictional stress that results from interrotor friction and couples the spin to the translation of the particles, which can then drive a striking spatially oscillating collective motion of the chiral active matter along the confinement boundary. Moreover, depending on the oscillation properties, the collective behavior has three different modes as the packing fraction varies. The structural origins of the transitions between the different modes are well identified by the percolation of solid-like regions or the occurrence of defect-induced particle rearrangement. Our results thus show that the confinement-induced inhomogeneity, dynamic structure, and compressibility have significant influences on collective behavior of active matter and should be properly taken into account.

Different-shaped micro-objects driven by active particle aggregations

The dynamics of passive micro-objects in an active bath has been receiving much attention. However, the influence of the shapes of micro-objects remains unclear. Here, we use 2D simulation to investigate the interaction between active Brownian particles and different-shaped passive micro-objects. We show that active particles accumulate around micro-objects and self-assemble into living aggregations at a high active velocity and high volume fraction. The shapes of micro-objects affect the distributions of the aggregations. In turn, the different distribution of aggregations influences the motion of micro-objects and induces abnormal diffusive behaviors. We further demonstrate that polar distributed aggregations at a high active velocity and the inhibition of the active bath at a low active velocity induce the counterintuitive anisotropic enhanced diffusion of rods, and the steric interaction between active particles induces the reverse translation-rotation coupled diffusion of chevrons.

Interface-mediated spontaneous symmetry breaking and mutual communication between drops containing chemically active particles

Symmetry breaking and the emergence of self-organized patterns is the hallmark of complexity. Here, we demonstrate that a sessile drop, containing titania powder particles with negligible self-propulsion, exhibits a transition to collective motion leading to self-organized flow patterns. This phenomenology emerges through a novel mechanism involving the interplay between the chemical activity of the photocatalytic particles, which induces Marangoni stresses at the liquid–liquid interface, and the geometrical confinement provided by the drop. The response of the interface to the chemical activity of the particles is the source of a significantly amplified hydrodynamic flow within the drop, which moves the particles. Furthermore, in ensembles of such active drops long-ranged ordering of the flow patterns within the drops is observed. We show that the ordering is dictated by a chemical communication between drops, i.e., an alignment of the flow patterns is induced by the gradients of the chemicals emanating from the active particles, rather than by hydrodynamic interactions.

Complex systems exhibit unique properties like spontaneous symmetry breaking and self-organization. Singh et al. show that catalytically active, non-propelling particles can induce steady vortical flows within a drop, as well as flow alignment between neighboring drops.

Polar pattern formation induced by contact following locomotion in a multicellular system

Biophysical mechanisms underlying collective cell migration of eukaryotic cells have been studied extensively in recent years. One mechanism that induces cells to correlate their motions is contact inhibition of locomotion, by which cells migrating away from the contact site. Here, we report that tail-following behavior at the contact site, termed contact following locomotion (CFL), can induce a non-trivial collective behavior in migrating cells. We show the emergence of a traveling band showing polar order in a mutant Dictyostelium cell that lacks chemotactic activity. We find that CFL is the cell-cell interaction underlying this phenomenon, enabling a theoretical description of how this traveling band forms. We further show that the polar order phase consists of subpopulations that exhibit characteristic transversal motions with respect to the direction of band propagation. These findings describe a novel mechanism of collective cell migration involving cell-cell interactions capable of inducing traveling band with polar order.

Constraint Dependence of Active Depletion Forces on Passive Particles

Using simulations and experiments, we demonstrate that the effective interaction between passive particles in an active bath substantially depends on an external constraint suffered by the passive particles. Particularly, the effective interaction between two free passive particles, which is directly measured in simulation, is qualitatively different from the one between two fixed particles. Moreover, we find that the friction experienced by the passive particles-a kinematic constraint-similarly influences the effective interaction. These remarkable features are in significant contrast to the equilibrium cases, and mainly arise from the accumulation of the active particles near the concave gap formed by the passive spheres. This constraint dependence not only deepens our understanding of the "active depletion force," but also provides an additional tool to tune the effective interactions in an active bath.

Emergence of self-organized multivortex states in flocks of active rollers

Active matter, both synthetic and biological, demonstrates complex spatiotemporal self-organization and the emergence of collective behavior. A coherent rotational motion, the vortex phase, is of great interest because of its ability to orchestrate well-organized motion of self-propelled particles over large distances. However, its generation without geometrical confinement has been a challenge. Here, we show by experiments and computational modeling that concentrated magnetic rollers self-organize into multivortex states in an unconfined environment. We find that the neighboring vortices more likely occur with the opposite sense of rotation. Our studies provide insights into the mechanism for the emergence of coherent collective motion on the macroscale from the coupling between microscale rotation and translation of individual active elements. These results may stimulate design strategies for self-assembled dynamic materials and microrobotics.

Active nematics with anisotropic friction: the decisive role of the flow aligning parameter

We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic liquid crystals. Within a flow-tumbling regime, however, we find that no such laning state is possible. Instead, the synergistic effects of friction anisotropy and flow tumbling can lead to the emergence of bound pairs of topological defects that align at an angle to the easy flow direction and navigate together throughout the domain. In addition to confirming the mechanism behind the laning states observed in experiments, our findings emphasise the role of the flow aligning parameter in the dynamics of active nematics.

Bacteria driving droplets

We confine a dense suspension of motile 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∼ 0.3 s, a long-time diffusion coefficient D∼ 0.5 μm² s^-1, and an average instantaneous speed V∼ 1.5 μm s^-1 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 coefficient and average speed increase with the bacterial concentration inside the drop, but are largely independent of the droplet size. By measuring the turbulent-like motion of the bacteria inside the drop, we demonstrate that the mean velocity of the bacteria near the bottom of the drop, which is separated from a glass substrate by a thin lubrication oil film, is antiparallel to the instantaneous velocity of the drop. This suggests that the driving mechanism is a slippery rolling of the drop over the substrate, caused by the collective motion of the bacteria. Our results show that microscopic organisms can transfer useful mechanical energy to their confining environment, opening the way to the assembly of mesoscopic motors composed of microswimmers.

A combined rheometry and imaging study of viscosity reduction in bacterial suspensions

Suspending self-propelled "pushers" in a liquid lowers its viscosity. We study how this phenomenon depends on system size in bacterial suspensions using bulk rheometry and particle-tracking rheoimaging. Above the critical bacterial volume fraction needed to decrease the viscosity to zero, [Formula: see text], large-scale collective motion emerges in the quiescent state, and the flow becomes nonlinear. We confirm a theoretical prediction that such instability should be suppressed by confinement. Our results also show that a recent application of active liquid-crystal theory to such systems is untenable.

Quorum-sensing active particles with discontinuous motility

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.

Defect dynamics in clusters of self-propelled rods in circular confinement

Rod-shaped active micro/nano-particles, such as bacterial and bipolar metallic micro/nano-motors, demonstrate novel collective phenomena far from the equilibrium state compared to passive particles. We apply a simulation approach --dissipative particle dynamics (DPD)-- to explore the collectively ordered states of self-propelled rods (SPRs). The SPRs are confined in a finite circular zone and repel each other when two rods touch each other. It is found that for a long enough rods system, the global vortex patterns, dynamic pattern oscillation between hedgehog pattern and vortex pattern, and hedgehog patterns are observed successively with increasing active force F_a. For the vortex pattern, the total interaction energy between the rods U is linear with active force F_a, i.e., U ∼ F_a . While the relation U ∼ F_a² is obtained for the hedgehog structure. It is observed that a new hedgehog pattern with one defect core is created by two ejections of polar cluster in opposite directions from the original hedgehog pattern, and then merges into one through the diffusion of the two aggregates, i.e., the creation and annihilation of topological charges.

Tuning the self-organization of confined active particles by the steepness of the trap

We consider the collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with small rotational fluctuations. They also interact with each other via soft, isotropic, repulsive potentials. The particles are confined in a circular trap. The steepness of the trap is tuneable. The average packing fraction of the particles is low. When the trap is steep, particles flock along its boundary. They form a polar cluster that spreads over the boundary. The cluster is not spatially ordered. We show that when the steepness is decreased beyond a threshold value, the cluster becomes round and compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order. We investigate the kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the cluster needs to roll around its centre of mass to be spatially ordered. We have studied the stability of the order when the trap is suddenly switched off. We find that for the particles with velocity alignment interaction, the decay of the spatial order is much slower than the particles without the alignment interaction.

Magnetotactic bacteria in a droplet self-assemble into a rotary motor

From intracellular protein trafficking to large-scale motion of animal groups, the physical concepts driving the self-organization of living systems are still largely unraveled. Self-organization of active entities, leading to novel phases and emergent macroscopic properties, recently shed new light on these complex dynamical processes. Here we show that under the application of a constant magnetic field, motile magnetotactic bacteria confined in water-in-oil droplets self-assemble into a rotary motor exerting a torque on the external oil phase. A collective motion in the form of a large-scale vortex, reversable by inverting the field direction, builds up in the droplet with a vorticity perpendicular to the magnetic field. We study this collective organization at different concentrations, magnetic fields and droplet radii and reveal the formation of two torque-generating areas close to the droplet interface. We characterize quantitatively the mechanical energy extractable from this new biological and self-assembled motor.

Active matter invasion

Biologically active materials such as bacterial biofilms and eukaryotic cells thrive in confined micro-spaces. Here, we show through numerical simulations that confinement can serve as a mechanical guidance to achieve distinct modes of collective invasion when combined with growth dynamics and the intrinsic activity of biological materials. We assess the dynamics of the growing interface and classify these collective modes of invasion based on the activity of the constituent particles of the growing matter. While at small and moderate activities the active material grows as a coherent unit, we find that blobs of active material collectively detach from the cohort above a well-defined activity threshold. We further characterise the mechanical mechanisms underlying the crossovers between different modes of invasion and quantify their impact on the overall invasion speed.

Thrust and Power Output of the Bacterial Flagellar Motor: A Micromagnetic Tweezers Approach

One of the most common swimming strategies employed by microorganisms is based on the use of rotating helical filaments, called flagella, that are powered by molecular motors. Determining the physical properties of this propulsive system is crucial to understanding the behavior of these organisms. Furthermore, the ability to dynamically monitor the activity of the flagellar motor is a valuable indicator of the overall energetics of the cell. In this work, inherently magnetic bacteria confined in micromagnetic CoFe traps are used to directly and noninvasively determine the flagellar thrust force and swimming speed of motile cells. The technique permits determination of the ratio of propulsive force/swimming speed (the hydrodynamic resistance) and the power output of the flagellar motor for individual cells over extended time periods. Cells subjected to ultraviolet radiation are observed to experience exponential decays in power output as a function of exposure time. By noninvasively measuring thrust, velocity, and power output over time at a single-cell level, this technique can serve as the foundation for fundamental studies of bacterial hydrodynamics and also provides a novel, to our knowledge, tether-free probe of single-cell energetics over time.

Direct-forcing fictitious domain method for simulating non-Brownian active particles

We present a direct-forcing fictitious domain method for simulating non-Brownian squirmer particles with both the hydrodynamic interactions and collisions being fully resolved. In this method, we solve the particle motion by distributing collocation points inside the particle interior domain that overlay upon a fixed Eulerian mesh. The fluid motions, including those of the "fictitious fluids" being extended into the particle, are solved on the entire computation domain. Pseudo-body forces are used to enforce the fictitious fluids to follow the particle movement. A direct-forcing approach is employed to map physical variables between the overlaid meshes, which does not require additional iterations to achieve convergence. We perform a series of numerical studies at both small and finite Reynolds numbers. First, accuracy of the algorithm is examined in studying benchmark problems of a free-swimming squirmer and two side-by-side squirmers. Then we investigate statistic properties of the quasi-two-dimensional collective dynamics for a monolayer of squirmer particles that are confined on a surface immersed in a bulk flow. Finally, we explore the physical mechanisms of how a freely moving short cylinder interacts with a monolayer of active particles, and find out that the cylinder movement is dominated by collision. We demonstrate that a more directional migration of cylinder can be resultant from an inhomogeneous distribution of active particles around the cylinder that has an anisotropic shape.

Traveling band formation in feedback-driven colloids

Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.

Dynamic response and hydrodynamics of polarized crowds

Modeling crowd motion is central to situations as diverse as risk prevention in mass events and visual effects rendering in the motion picture industry. The difficulty of performing quantitative measurements in model experiments has limited our ability to model pedestrian flows. We use tens of thousands of road-race participants in starting corrals to elucidate the flowing behavior of polarized crowds by probing its response to boundary motion. We establish that speed information propagates over system-spanning scales through polarized crowds, whereas orientational fluctuations are locally suppressed. Building on these observations, we lay out a hydrodynamic theory of polarized crowds and demonstrate its predictive power. We expect this description of human groups as active continua to provide quantitative guidelines for crowd management.

Orbiting of Flagellated Bacteria within a Thin Fluid Film around Micrometer-Sized Particles

Bacterial motility under confinement is relevant to both environmental control and the spread of infection. Here, we report observations on Escherichia coli, Enterobacter sp., Pseudomonas aeruginosa, and Bacillus subtilis when they are confined within a thin layer of water around dispersed micrometer-sized particles sprinkled over a semisolid agar gel. In this setting, E. coli and Enterobacteria orbit around the dispersed particles. The liquid layer is shaped like a shallow tent with its height at the center set by the seeding particle, and the meniscus profile set by the strong surface tension of water. The tent-shaped confinement and the left handedness of the flagellar filaments result in exclusively clockwise circular trajectories. The thin fluid layer is resilient because of a balance between evaporation and reinforcement of fluid that permeated out of the agar. The latter is driven by the Laplace pressure caused by the concave meniscus. In short, we explain the physical mechanism of a convenient method to entrap bacteria within localized thin fluid film near a permeable surface.

Aggregation dynamics of active rotating particles in dense passive media

Active matter systems are able to exhibit emergent non-equilibrium behavior due to activity-induced effective interactions between the active particles. Here we study the aggregation and dynamical behavior of active rotating particles, spinners, embedded in 2D passive colloidal monolayers. Using both experiments and simulations we observe aggregation of active particles or spinners whose behavior resembles classical 2D Cahn-Hilliard coarsening. The aggregation behavior and spinner attraction depend on the mechanical properties of the passive monolayer and the activity of spinners. Spinner aggregation only occurs when the passive monolayer behaves elastically and when the spinner activity exceeds a minimum activity threshold. Interestingly, for the spinner concentrations investigated here, the spinner concentration does not seem to change the dynamics of the aggregation behavior. There is a characteristic cluster size which maximizes spinner aggregation by minimizing the drag through the passive monolayer and maximizing the stress applied on the passive medium. We also show a ternary mixture of passive particles and co-rotating and counter-rotating spinners that aggregate into clusters of co and counter-rotating spinners respectively.

Advances in Biological Liquid Crystals

Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.

Self-organization of swimmers drives long-range fluid transport in bacterial colonies

Motile subpopulations in microbial communities are believed to be important for dispersal, quest for food, and material transport. Here, we show that motile cells in sessile colonies of peritrichously flagellated bacteria can self-organize into two adjacent, centimeter-scale motile rings surrounding the entire colony. The motile rings arise from spontaneous segregation of a homogeneous swimmer suspension that mimics a phase separation; the process is mediated by intercellular interactions and shear-induced depletion. As a result of this self-organization, cells drive fluid flows that circulate around the colony at a constant peak speed of ~30 µm s⁻¹, providing a stable and high-speed avenue for directed material transport at the macroscopic scale. Our findings present a unique form of bacterial self-organization that influences population structure and material distribution in colonies.

Motile and non-motile subpopulations often coexist in bacterial communities. Here, Xu et al. show that motile cells in colonies of common flagellated bacteria can self-organize into two adjacent motile rings, driving stable flows of fluid and materials around the colony.

Rotational motion of a camphor disk in a circular region

In a two-dimensional axisymmetric system, the system symmetry allows rotational or oscillatory motion as stable stationary motion for a symmetric self-propelled particle. In the present paper, we studied the motion of a camphor disk confined in a two-dimensional circular region. By reducing the mathematical model describing the dynamics of the motion of a camphor disk and the concentration field of camphor molecules on a water surface, we analyzed the reduced equations around a bifurcation point where the rest state at the center of the system becomes unstable. As a result, we found that rotational motion is stably realized through the double-Hopf bifurcation from the rest state. The theoretical results were confirmed by numerical calculation and corresponded well to the experimental results.

Self-organized dynamics and the transition to turbulence of confined active nematics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of [Formula: see text] defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.

Nonideal rheology of semidilute bacterial suspensions

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, ending 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 oscillates with large amplitudes, when a constant shear rate is imposed. This oscillation disappears for large shear rates in a continuous or discontinuous transition, depending on if the aligning is polar or axial, respectively. For pusher swimmers these nonlinear effects can produce an increase on the shear stress, contrary to the prediction of a viscosity reduction made for the dilute regime with the ideal gas approximation.

Sparse Game Changers Restore Collective Motion in Panicked Human Crowds

Using a dynamic variant of the Vicsek model, we show that the emergence of disorder from an orderly moving human crowd is a nonequilibrium first-order phase transition. We also show that this transition can be reversed by modifying the dynamics of a few agents, deemed as game changers. Surprisingly, the optimal placement of these game changers is found to be in regions of maximum local crowd speed. The presence of such game changers is effective owing to the discontinuous nature of the underlying phase transition. Thus our generic approach provides strategies to (i) delay crowd crush and (ii) design safe evacuation procedures, two aspects that are of paramount importance in maintaining safety of mass gatherings of people.

Homogeneous and heterogeneous populations of active rods in two-dimensional channels

Active swarms, consisting of individual agents which consume energy to move or produce work, are known to generate a diverse range of collective behaviors. Many examples of active swarms are biological in nature (e.g., fish shoals and bird flocks) and have been modeled extensively by numerical simulations. Such simulations of swarms usually assume that the swarm is homogeneous; that is, every agent has exactly the same dynamical properties. However, many biological swarms are highly heterogeneous, such as multispecies communities of micro-organisms in soil, and individual species may have a wide range of different physical properties. Here we explore heterogeneity by developing a simple model for the dynamics of a swarm of motile heterogeneous rodlike bacteria in the absence of hydrodynamic effects. Using molecular dynamics simulations of active rods confined within a two-dimensional rectangular channel, we first explore the case of homogeneous swarms and show that the key parameter governing both dynamics is ratio of the motility force to the steric force. Next we explore heterogeneous or mixed swarms in which the constituent self-propelled rods have a range of motilities and steric interactions. Our results show that the confining boundaries play a strong role in driving the segregation of mixed populations.

Biomechanics of Tetrahymena escaping from a dead end

Understanding the behaviours of swimming microorganisms in various environments is important for understanding cell distribution and growth in nature and industry. However, cell behaviour in complex geometries is largely unknown. In this study, we used Tetrahymena thermophila as a model microorganism and experimentally investigated cell behaviour between two flat plates with a small angle. In this configuration, the geometry provided a ‘dead end' line where the two flat plates made contact. The results showed that cells tended to escape from the dead end line more by hydrodynamics than by a biological reaction. In the case of hydrodynamic escape, the cell trajectories were symmetric as they swam to and from the dead end line. Near the dead end line, T. thermophila cells were compressed between the two flat plates while cilia kept beating with reduced frequency; those cells again showed symmetric trajectories, although the swimming velocity decreased. These behaviours were well reproduced by our computational model based on biomechanics. The mechanism of hydrodynamic escape can be understood in terms of the torque balance induced by lubrication flow. We therefore conclude that a cell's escape from the dead end was assisted by hydrodynamics. These findings pave the way for understanding cell behaviour and distribution in complex geometries.

Nutrient Transport Driven by Microbial Active Carpets

We demonstrate that active carpets of bacteria or self-propelled colloids generate coherent flows towards the substrate, and propose that these currents provide efficient pathways to replenish nutrients that feed back into activity. A full theory is developed in terms of gradients in the active matter density and velocity, and applied to bacterial turbulence, topological defects and clustering. Currents with complex spatiotemporal patterns are obtained, which are tunable through confinement. Our findings show that diversity in carpet architecture is essential to maintain biofunctionality.

Geometric Effect for Biological Reactors and Biological Fluids

As expressed "God made the bulk; the surface was invented by the devil" by W. Pauli, the surface has remarkable properties because broken symmetry in surface alters the material properties. In biological systems, the smallest functional and structural unit, which has a functional bulk space enclosed by a thin interface, is a cell. Cells contain inner cytosolic soup in which genetic information stored in DNA can be expressed through transcription (TX) and translation (TL). The exploration of cell-sized confinement has been recently investigated by using micron-scale droplets and microfluidic devices. In the first part of this review article, we describe recent developments of cell-free bioreactors where bacterial TX-TL machinery and DNA are encapsulated in these cell-sized compartments. Since synthetic biology and microfluidics meet toward the bottom-up assembly of cell-free bioreactors, the interplay between cellular geometry and TX-TL advances better control of biological structure and dynamics in vitro system. Furthermore, biological systems that show self-organization in confined space are not limited to a single cell, but are also involved in the collective behavior of motile cells, named active matter. In the second part, we describe recent studies where collectively ordered patterns of active matter, from bacterial suspensions to active cytoskeleton, are self-organized. Since geometry and topology are vital concepts to understand the ordered phase of active matter, a microfluidic device with designed compartments allows one to explore geometric principles behind self-organization across the molecular scale to cellular scale. Finally, we discuss the future perspectives of a microfluidic approach to explore the further understanding of biological systems from geometric and topological aspects.

Swimming bacteria power microspin cycles

Dense suspensions of swimming bacteria are living fluids, an archetype of active matter. For example, Bacillus subtilis confined within a disc-shaped region forms a persistent stable vortex that counterrotates at the periphery. Here, we examined Escherichia coli under similar confinement and found that these bacteria, instead, form microspin cycles: a single vortex that periodically reverses direction on time scales of seconds. Using experimental perturbations of the confinement geometry, medium viscosity, bacterial length, density, and chemotaxis pathway, we show that morphological alterations of the bacteria transition a stable vortex into a periodically reversing one. We develop a mathematical model based on single-cell biophysics that quantitatively recreates the dynamics of these vortices and predicts that density gradients power the reversals. Our results define how microbial physics drives the active behavior of dense bacterial suspensions and may allow one to engineer novel micromixers for biomedical and other microfluidic applications.

Magnetic Active Matter Based on Helical Propulsion

Micro- and nanomotors are nonliving micro- and nanoparticles that are rendered motile by supplying energy from external sources, for example, through asymmetric chemical reactions or the application of electric, magnetic, optical, or acoustic fields. Their study is interesting for two reasons. First, nanomotors can impact future biomedical practices, where one envisions intelligent multifunctional nanomachines swarming toward a diseased site and delivering therapeutics with high accuracy. The second motivation stems from the prevalence of self-powered systems in nature, ranging from intracellular transport to human migration, which are nonequilibrium phenomena yet to be completely understood. Nanomotors provide a promising route toward the study of complex active matter phenomena with a well-defined and possibly reduced set of variables. Among different ways of powering nanomotors, magnetic field deserves a special mention because of its inherent biocompatibility, minimal dependence on properties of the surrounding medium, and remote powering mechanism. In particular, magnetically actuated propellers (MAPs), which are helical structures driven by rotating fields in fluids and gels, have been demonstrated to be highly suitable for various microfluidic and biotechnology applications. Unfortunately, this method of actuation requires direct application of mechanical torque by the applied field, implying that the system is driven and therefore cannot be considered self-propelled. To overcome this fundamental limitation, we discuss an alternate magnetic drive where the MAPs are powered by oscillating (not rotating) magnetic fields. This technique induces motility in the form of back-and-forth motion but allows the directionality to be unspecified, and therefore, it represents a zero-force, zero-torque active matter where the nanomotors behave effectively as self-propelled entities. The MAPs show enhanced diffusivity compared with their passive counterparts, and their motility can be tuned by altering the external magnetic drive, which establishes the suitability of the MAPs as model active particles. Enhancement of the diffusivity depends on the thermal noise as well as the inherent asymmetries of the individual motors, which could be well-understood through numerical simulations. In the presence of small direct-current fields and interactions with the surface, the swimmers can be maneuvered and subsequently positioned in an independent manner. Next, we discuss experimental results pertaining to the collective dynamics of these helical magnetic nanoswimmers. We have studied nonmagnetic tracer beads suspended in a medium containing many swimmers and found the diffusivity of the beads to increase under magnetic actuation, akin to measurements performed in dense bacterial suspensions. In summary, we envision that rendering the system of MAPs active will not only provide a new model system to investigate fundamental nonequilibrium phenomena but also play a vital role in the development of intelligent theranostic probes for futuristic biomedical applications.

Engineering bacterial vortex lattice via direct laser lithography

A suspension of swimming bacteria is possibly the simplest realization of active matter, i.e. a class of systems transducing stored energy into mechanical motion. Collective swimming of hydrodynamically interacting bacteria resembles turbulent flow. This seemingly chaotic motion can be rectified by a geometrical confinement. Here we report on self-organization of a concentrated suspension of motile bacteria Bacillus subtilis constrained by two-dimensional (2D) periodic arrays of microscopic vertical pillars. We show that bacteria self-organize into a lattice of hydrodynamically bound vortices with a long-range antiferromagnetic order controlled by the pillars’ spacing. The patterns attain their highest stability and nearly perfect order for the pillar spacing comparable with an intrinsic vortex size of an unconstrained bacterial turbulence. We demonstrate that the emergent antiferromagnetic order can be further manipulated and turned into a ferromagnetic state by introducing chiral pillars. This strategy can be used to control a wide class of active 2D systems.

Geometrically confined suspensions of swimming bacteria can self-organize into an ordered state. Here, the authors use tiny pillars to trigger organization of bacterial motion into a stable lattice of vortices with a long-range antiferromagnetic order and control vortex direction through pillar chirality.

Sounds and hydrodynamics of polar active fluids

Spontaneously flowing liquids have been successfully engineered from a variety of biological and synthetic self-propelled units^1-11. Together with their orientational order, wave propagation in such active fluids has remained a subject of intense theoretical studies^12-17. However, the experimental observation of this phenomenon has remained elusive. Here, we establish and exploit the propagation of sound waves in colloidal active materials with broken rotational symmetry. We demonstrate that two mixed modes, coupling density and velocity fluctuations, propagate along all directions in colloidal-roller fluids. We then show how the six material constants defining the linear hydrodynamics of these active liquids can be measured from their spontaneous fluctuation spectrum, while being out of reach of conventional rheological methods. This active-sound spectroscopy is not specific to synthetic active materials and could provide a quantitative hydrodynamic description of herds, flocks and swarms from inspection of their large-scale fluctuations^18-21.

Active nematics

Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.

Insensitivity of active nematic liquid crystal dynamics to topological constraints

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

Active Suspensions have Nonmonotonic Flow Curves and Multiple Mechanical Equilibria

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 E. Coli effectively behaves, at steady-state, as a negative viscosity fluid and reach a quantitative agreement with experimental measurements. Our theoretical analysis further shows that a negative apparent viscosity is due to a nonmonotonic local velocity profile, and it is associated with a nonmonotonic stress versus strain rate flow curve. This implies that fixed stress and fixed strain rate ensembles are not equivalent for active fluids.

Manipulation of emergent vortices in swarms of magnetic rollers

Active colloids are an emergent class of out-of-equilibrium materials demonstrating complex collective phases and tunable functionalities. Microscopic particles energized by external fields exhibit a plethora of fascinating collective phenomena, yet mechanisms of control and manipulation of active phases often remains lacking. Here we report the emergence of unconfined macroscopic vortices in a system of ferromagnetic rollers energized by a vertical alternating magnetic field and elucidate the complex nature of a magnetic roller-vortex interactions with inert scatterers. We demonstrate that active self-organized vortices have an ability to spontaneously switch the direction of rotation and move across the surface. We reveal the capability of certain non-active particles to pin the vortex and manipulate its dynamics. Building on our findings, we demonstrate the potential of magnetic roller vortices to effectively capture and transport inert particles at the microscale.

Maximum in density heterogeneities of active swimmers

Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.

Confined Flow: Consequences and Implications for Bacteria and Biofilms

Bacteria overwhelmingly live in geometrically confined habitats that feature small pores or cavities, narrow channels, or nearby interfaces. Fluid flows through these confined habitats are ubiquitous in both natural and artificial environments colonized by bacteria. Moreover, these flows occur on time and length scales comparable to those associated with motility of bacteria and with the formation and growth of biofilms, which are surface-associated communities that house the vast majority of bacteria to protect them from host and environmental stresses. This review describes the emerging understanding of how flow near surfaces and within channels and pores alters physical processes that control how bacteria disperse, attach to surfaces, and form biofilms. This understanding will inform the development and deployment of technologies for drug delivery, water treatment, and antifouling coatings and guide the structuring of bacterial consortia for production of chemicals and pharmaceuticals.