Fluid dynamics of bacterial turbulence

Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer

We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. The particles predominantly swim normal to the free film surface with only a small component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by i) the upward pushing force of the swimmers onto the liquid-gas interface, ii) the solutal Marangoni force due to gradients in the swimmer concentration, and iii) the rotational diffusion of the swimmers together with the in-plane active motion. After reviewing and extending the analysis of the linear stability of the uniform state, we analyse the fully nonlinear dynamic equations and show that point-like swimmers, which only interact via long-wave deformations of the liquid film, self-organise in highly regular (standing, travelling, and modulated waves) and various irregular patterns.

Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles

Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation, a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.

Active Curved Polymers Form Vortex Patterns on Membranes

Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring. We model FtsZ polymers as active particles moving along chiral, circular paths by Brownian dynamics simulations and a Boltzmann approach. Our two conceptually different methods point to a generic phase behavior. At intermediate particle densities, we find self-organization into vortex structures including closed rings. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.

Vortex with fourfold defect lines in a simple model of self-propelled particles

We study the formation of a vortex with fourfold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observe five other regimes in the system: a homogeneous gaseous phase, band structures, moving clumps, moving clusters, and vibrating rings. All six regimes emerge from controlling the strength of noise and from the contribution of repulsion and alignment interactions. We study the shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. We derive hydrodynamical equations with an introduction of the "small deviation" technique to describe the vortex phase. The method is applicable to other systems as well. Finally, we compare the theory with the results of both computer simulations and an experiment using Quincke rotors. A good agreement between the three is observed.

Ferromagnetic and antiferromagnetic order in bacterial vortex lattices

Despite their inherent non-equilibrium nature1, living systems can self-organize in highly ordered collective states2,3 that share striking similarities with the thermodynamic equilibrium phases4,5 of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies6,7, microbial suspensions8,9 and tissues10 to the coherent macro-scale dynamics in schools of fish11 and flocks of birds12. Yet, the generic mathematical principles that govern the emergence of structure in such artificial13 and biological6-9,14 systems are elusive. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Here, we connect these two previously disparate regimes: Through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct phases of ferro- and antiferromagnetic order. The preferred phase can be controlled by tuning the vortex coupling through changes of the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents15,16, reminiscent of those in quantum systems17-19. Our experimental observations can be rationalized in terms of a generic lattice field theory, suggesting that bacterial spin networks belong to the same universality class as a wide range of equilibrium systems.

Rapid expulsion of microswimmers by a vortical flow

Interactions of microswimmers with their fluid environment are exceptionally complex. Macroscopic shear flow alters swimming trajectories in a highly nontrivial way and results in dramatic reduction of viscosity and heterogeneous bacterial distributions. Here we report on experimental and theoretical studies of rapid expulsion of microswimmers, such as motile bacteria, by a vortical flow created by a rotating microparticle. We observe a formation of a macroscopic depletion area in a high-shear region, in the vicinity of a microparticle. The rapid migration of bacteria from the shear-rich area is caused by a vortical structure of the flow rather than intrinsic random fluctuations of bacteria orientations, in stark contrast to planar shear flow. Our mathematical model reveals that expulsion is a combined effect of motility and alignment by a vortical flow. Our findings offer a novel approach for manipulation of motile microorganisms and shed light on bacteria–flow interactions.

The control of microswimmers such as bacteria is important for emerging applications of active bioinspired materials. Here, the authors demonstrate the use of vortical shear to expel suspended motile bacteria from the vicinity of a rotating microparticle.

Role of Particle Focusing in Resistive-Pulse Technique: Direction-Dependent Velocity in Micropores

Passage time through single micropores is an important parameter used to quantify the surface charge and zeta potential of particles. In the resistive-pulse technique, the measured time of pressure- or electric-field-induced translocation is assumed to be direction independent. This assumption is supported by the low velocities of the particles and the supporting fluid such that the transport reversibility known for Stokes flow is expected to apply. In this article, we present examples of micropores in which passage time of ∼400 nm diameter particles becomes direction-dependent; that is, the particles' translocation times from left to right and right to left are different. These pores are characterized by an undulating inner diameter such that at least one wider zone called a cavity separates two narrower regions of different lengths. We propose that the observed direction-dependence of the translocation velocity is caused by an asymmetric efficiency of particle focusing toward the pore axis, which leads to a direction-dependent set of particle trajectories. The reported pores present the simplest system in which time-broken symmetry has been observed. The results are of importance for sensing of particles and molecules by the resistive-pulse technique since pores used for detection are often characterized by finite roughness or noncylindrical shape. This article also points to the role of particle focusing in the magnitude and distribution of the translocation times.

Architectural transitions in Vibrio cholerae biofilms at single-cell resolution

Many bacterial species colonize surfaces and form dense 3D structures, known as biofilms, which are highly tolerant to antibiotics and constitute one of the major forms of bacterial biomass on Earth. Bacterial biofilms display remarkable changes during their development from initial attachment to maturity, yet the cellular architecture that gives rise to collective biofilm morphology during growth is largely unknown. Here, we use high-resolution optical microscopy to image all individual cells in Vibrio cholerae biofilms at different stages of development, including colonies that range in size from 2 to 4,500 cells. From these data, we extracted the precise 3D cellular arrangements, cell shapes, sizes, and global morphological features during biofilm growth on submerged glass substrates under flow. We discovered several critical transitions of the internal and external biofilm architectures that separate the major phases of V. cholerae biofilm growth. Optical imaging of biofilms with single-cell resolution provides a new window into biofilm formation that will prove invaluable to understanding the mechanics underlying biofilm development.

Live from under the lens: exploring microbial motility with dynamic imaging and microfluidics

Motility is one of the most dynamic features of the microbial world. The ability to swim or crawl frequently governs how microorganisms interact with their physical and chemical environments, and underpins a myriad of microbial processes. The ability to resolve temporal dynamics through time-lapse video microscopy and the precise control of the physicochemical microenvironment afforded by microfluidics offer powerful new opportunities to study the many motility adaptations of microorganisms and thereby further our understanding of their ecology. In this Review, we outline recent insights into the motility strategies of microorganisms brought about by these techniques, including the hydrodynamic signature of microorganisms, their locomotion mechanics, chemotaxis, their motility near and on surfaces, swimming in moving fluids and motility in dense microbial suspensions.

Collective chemotaxis and segregation of active bacterial colonies

Still recently, bacterial fluid suspensions have motivated a lot of works, both experimental and theoretical, with the objective to understand their collective dynamics from universal and simple rules. Since some species are active, most of these works concern the strong interactions that these bacteria exert on a forced flow leading to instabilities, chaos and turbulence. Here, we investigate the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction. We propose a simple model to understand and quantify the physical properties of these living organisms which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.

Activity induces traveling waves, vortices and spatiotemporal chaos in a model actomyosin layer

Inspired by the actomyosin cortex in biological cells, we investigate the spatiotemporal dynamics of a model describing a contractile active polar fluid sandwiched between two external media. The external media impose frictional forces at the interface with the active fluid. The fluid is driven by a spatially-homogeneous activity measuring the strength of the active stress that is generated by processes consuming a chemical fuel. We observe that as the activity is increased over two orders of magnitude the active polar fluid first shows spontaneous flow transition followed by transition to oscillatory dynamics with traveling waves and traveling vortices in the flow field. In the flow-tumbling regime, the active polar fluid also shows transition to spatiotemporal chaos at sufficiently large activities. These results demonstrate that level of activity alone can be used to tune the operating point of actomyosin layers with qualitatively different spatiotemporal dynamics.

Multiscale flow in an electro-hydrodynamically driven oil-in-oil emulsion

Efficient mixing strategies in a fluid involve generation of multi-scale flows which are strongly suppressed in highly viscous systems. In this work, we report a novel form of multi-scale flow, driven by an external electric field, in a highly viscous (η∼ 1 Pa s) oil-in-oil emulsion system consisting of micron-size droplets. This electro-hydrodynamic flow leads to dynamical organization at spatial scales much larger than that of the individual droplets. We characterize the dynamics associated with these structures by measuring the time variation of the bulk Reynolds stress in a rheometer, as well as through a micro-scale rheometric measurement by probing the spectrum of fluctuations of a thin fiber cantilever driven by these flows. The results display scale invariance in the energy spectra over three decades with a power law reminiscent of turbulent convection. We also demonstrate the mixing efficiency in such micro-scale systems.

Stabilization of active matter by flow-vortex lattices and defect ordering

Active systems, from bacterial suspensions to cellular monolayers, are continuously driven out of equilibrium by local injection of energy from their constituent elements and exhibit turbulent-like and chaotic patterns. Here we demonstrate both theoretically and through numerical simulations, that the crossover between wet active systems, whose behaviour is dominated by hydrodynamics, and dry active matter where any flow is screened, can be achieved by using friction as a control parameter. Moreover, we discover unexpected vortex ordering at this wet-dry crossover. We show that the self organization of vortices into lattices is accompanied by the spatial ordering of topological defects leading to active crystal-like structures. The emergence of vortex lattices, which leads to the positional ordering of topological defects, suggests potential applications in the design and control of active materials.

Density Shock Waves in Confined Microswimmers

Motile and driven particles confined in microfluidic channels exhibit interesting emergent behavior, from propagating density bands to density shock waves. A deeper understanding of the physical mechanisms responsible for these emergent structures is relevant to a number of physical and biomedical applications. Here, we study the formation of density shock waves in the context of an idealized model of microswimmers confined in a narrow channel and subject to a uniform external flow. Interestingly, these density shock waves exhibit a transition from "subsonic" with compression at the back to "supersonic" with compression at the front of the population as the intensity of the external flow increases. This behavior is the result of a nontrivial interplay between hydrodynamic interactions and geometric confinement, and it is confirmed by a novel quasilinear wave model that properly captures the dependence of the shock formation on the external flow. These findings can be used to guide the development of novel mechanisms for controlling the emergent density distribution and the average population speed, with potentially profound implications on various processes in industry and biotechnology, such as the transport and sorting of cells in flow channels.

Swimming in a crystal

We study catalytic Janus particles and Escherichia coli bacteria swimming in a two-dimensional colloidal crystal. The Janus particles orbit individual colloids and hop between colloids stochastically, with a hopping rate that varies inversely with fuel (hydrogen peroxide) concentration. At high fuel concentration, these orbits are stable for 100s of revolutions, and the orbital speed oscillates periodically as a result of hydrodynamic, and possibly also phoretic, interactions between the swimmer and the six neighbouring colloids. Motile E. coli bacteria behave very differently in the same colloidal crystal: their circular orbits on plain glass are rectified into long, straight runs, because the bacteria are unable to turn corners inside the crystal.

Shape matters: Near-field fluid mechanics dominate the collective motions of ellipsoidal squirmers

Microswimmers show a variety of collective motions. Despite extensive study, questions remain regarding the role of near-field fluid mechanics in collective motion. In this paper, we describe precisely the Stokes flow around hydrodynamically interacting ellipsoidal squirmers in a monolayer suspension. The results showed that various collective motions, such as ordering, aggregation, and whirls, are dominated by the swimming mode and the aspect ratio. The collective motions are mainly induced by near-field fluid mechanics, despite Stokes flow propagation over a long range. These results emphasize the importance of particle shape in collective motion.

New class of turbulence in active fluids

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier-Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such "living fluids" that is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308-14313]. This introduces a cubic nonlinearity, related to the Toner-Tu theory of flocking, which can interact with the quadratic Navier-Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

Clustering and phase behaviour of attractive active particles with hydrodynamics

We simulate clustering, phase separation and hexatic ordering in a monolayered suspension of active squirming disks subject to an attractive Lennard-Jones-like pairwise interaction potential, taking hydrodynamic interactions between the particles fully into account. By comparing the hydrodynamic case with counterpart simulations for passive and active Brownian particles, we elucidate the relative roles of self-propulsion, interparticle attraction, and hydrodynamic interactions in determining clustering and phase behaviour. Even in the presence of an attractive potential, we find that hydrodynamic interactions strongly suppress the motility induced phase separation that might a priori have been expected in a highly active suspension. Instead, we find only a weak tendency for the particles to form stringlike clusters in this regime. At lower activities we demonstrate phase behaviour that is broadly equivalent to that of the counterpart passive system at low temperatures, characterized by regimes of gas-liquid, gas-solid and liquid-solid phase coexistence. In this way, we suggest that a dimensionless quantity representing the level of activity relative to the strength of attraction plays the role of something like an effective non-equilibrium temperature, counterpart to the (dimensionless) true thermodynamic temperature in the passive system. However there are also some important differences from the equilibrium case, most notably with regards the degree of hexatic ordering, which we discuss carefully.

Celebrating Soft Matter's 10th Anniversary: Cell division: a source of active stress in cellular monolayers

We introduce the notion of cell division-induced activity and show that the cell division generates extensile forces and drives dynamical patterns in cell assemblies. Extending the hydrodynamic models of lyotropic active nematics we describe turbulent-like velocity fields that are generated by the cell division in a confluent monolayer of cells. We show that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by our modeling approach. Division-induced activity acts together with intrinsic activity of the cells in extensile and contractile cell assemblies to change the flow and director patterns and the density of topological defects. Finally we model the evolution of the boundary of a cellular colony and compare the fingering instabilities induced by cell division to experimental observations on the expansion of MDCK cell cultures.

Swarming bacteria migrate by Lévy Walk

Individual swimming bacteria are known to bias their random trajectories in search of food and to optimize survival. The motion of bacteria within a swarm, wherein they migrate as a collective group over a solid surface, is fundamentally different as typical bacterial swarms show large-scale swirling and streaming motions involving millions to billions of cells. Here by tracking trajectories of fluorescently labelled individuals within such dense swarms, we find that the bacteria are performing super-diffusion, consistent with Lévy walks. Lévy walks are characterized by trajectories that have straight stretches for extended lengths whose variance is infinite. The evidence of super-diffusion consistent with Lévy walks in bacteria suggests that this strategy may have evolved considerably earlier than previously thought.

Turbulence of swarming sperm

Collective motion of self-sustained swarming flows has recently provided examples of small-scale turbulence arising where viscous effects are dominant. We report the first observation of universal enstrophy cascade in concentrated swarming sperm consistent with a body of evidence built from various independent measurements. We found a well-defined k^{-3} power-law decay of a velocity field power spectrum and relative dispersion of small beads consistent with theoretical predictions in 2D turbulence. Concentrated living sperm displays long-range, correlated whirlpool structures of a size that provides an integral scale of turbulence. We propose a consistent explanation for this quasi-2D turbulence based on self-structured laminated flow forced by steric interactions and alignment, a state of active matter that we call "swarming liquid crystal." We develop scaling arguments consistent with this interpretation.

Flexibility of bacterial flagella in external shear results in complex swimming trajectories

Many bacteria use rotating helical flagella in swimming motility. In the search for food or migration towards a new habitat, bacteria occasionally unbundle their flagellar filaments and tumble, leading to an abrupt change in direction. Flexible flagella can also be easily deformed by external shear flow, leading to complex bacterial trajectories. Here, we examine the effects of flagella flexibility on the navigation of bacteria in two fundamental shear flows: planar shear and Poiseuille flow realized in long channels. On the basis of slender body elastodynamics and numerical analysis, we discovered a variety of non-trivial effects stemming from the interplay of self-propulsion, elasticity and shear-induced flagellar bending. We show that in planar shear flow the bacteria execute periodic motion, whereas in Poiseuille flow, they migrate towards the centre of the channel or converge towards a limit cycle. We also find that even a small amount of random reorientation can induce a strong response of bacteria, leading to overall non-periodic trajectories. Our findings exemplify the sensitive role of flagellar flexibility and shed new light on the navigation of bacteria in complex shear flows.

Turning Bacteria Suspensions into Superfluids

The rheological response under simple shear of an active suspension of Escherichia coli is determined in a large range of shear rates and concentrations. The effective viscosity and the time scales characterizing the bacterial organization under shear are obtained. In the dilute regime, we bring evidence for a low-shear Newtonian plateau characterized by a shear viscosity decreasing with concentration. In the semidilute regime, for particularly active bacteria, the suspension displays a "superfluidlike" transition where the viscous resistance to shear vanishes, thus showing that, macroscopically, the activity of pusher swimmers organized by shear is able to fully overcome the dissipative effects due to viscous loss.

Self-propelled rods exhibit a phase-separated state characterized by the presence of active stresses and the ejection of polar clusters

We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns-contrary to what has been suggested-vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region-which we call aggregate-which is surrounded by a disordered gas. Active stresses build inside aggregates as a result of the combined effect of local orientational order and active forces. This leads to the most distinctive feature of these aggregates: constant ejection of polar clusters of SPR. This novel phase-separated state represents a novel state of matter characterized by large fluctuations in volume and shape, related to mass ejection, and exhibits positional as well as orientational local order. SPR systems display new physics unseen in other active matter systems.

Physics of microswimmers--single particle motion and collective behavior: a review

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells

We investigate a new form of collective dynamics displayed by Thiovulum majus, one of the fastest-swimming bacteria known. Cells spontaneously organize on a surface into a visually striking two-dimensional hexagonal lattice of rotating cells. As each constituent cell rotates its flagella, it creates a tornadolike flow that pulls neighboring cells towards and around it. As cells rotate against their neighbors, they exert forces on one another, causing the crystal to rotate and cells to reorganize. We show how these dynamics arise from hydrodynamic and steric interactions between cells. We derive the equations of motion for a crystal, show that this model explains several aspects of the observed dynamics, and discuss the stability of these active crystals.

Circularly confined microswimmers exhibit multiple global patterns

Geometric confinement plays an important role in the dynamics of natural and synthetic microswimmers from bacterial cells to self-propelled particles in high-throughput microfluidic devices. However, little is known about the effects of geometric confinement on the emergent global patterns in such self-propelled systems. Recent experiments on bacterial cells report that, depending on the cell concentration, cells either spontaneously organize into vortical motion in thin cylindrical and spherical droplets or aggregate at the inner boundary of the droplets. Our goal in this paper is to investigate, in the context of an idealized physical model, the interplay between geometric confinement and level of flagellar activity on the emergent collective patterns. We show that decreasing flagellar activity induces a hydrodynamically triggered transition in confined microswimmers from swirling to global circulation (vortex) to boundary aggregation and clustering. These results highlight that the complex interplay between confinement, flagellar activity, and hydrodynamic flows in concentrated suspensions of microswimmers could lead to a plethora of global patterns that are difficult to predict from geometric consideration alone.

Hydrodynamics of a self-actuated bacterial carpet using microscale particle image velocimetry

Microorganisms can effectively generate propulsive force at the microscale where viscous forces overwhelmingly dominate inertia forces; bacteria achieve this task through flagellar motion. When swarming bacteria, cultured on agar plates, are blotted onto the surface of a microfabricated structure, a monolayer of bacteria forms what is termed a "bacterial carpet," which generates strong flows due to the combined motion of their freely rotating flagella. Furthermore, when the bacterial carpet coated microstructure is released into a low Reynolds number fluidic environment, the propulsive force of the bacterial carpet is able to give the microstructure motility. In our previous investigations, we demonstrated motion control of these bacteria powered microbiorobots (MBRs). Without any external stimuli, MBRs display natural rotational and translational movements on their own; this MBR self-actuation is due to the coordination of flagella. Here, we investigate the flow fields generated by bacterial carpets, and compare this flow to the flow fields observed in the bulk fluid at a series of locations above the bacterial carpet. Using microscale particle image velocimetry, we characterize the flow fields generated from the bacterial carpets of MBRs in an effort to understand their propulsive flow, as well as the resulting pattern of flagella driven self-actuated motion. Comparing the velocities between the bacterial carpets on fixed and untethered MBRs, it was found that flow velocities near the surface of the microstructure were strongest, and at distances far above, the surface flow velocities were much smaller.

Impact of hydrodynamics on effective interactions in suspensions of active and passive matter

Passive particles exhibit unique properties when immersed in an active bath of self-propelling entities. In particular, an effective attraction can appear between particles that repel each other when in a passive solution. Here we numerically study the effect of hydrodynamics on an active-passive hybrid system, where we observe qualitative differences as compared to simulations with excluded volume effects alone. The results shed light on an existing discrepancy in pair lifetimes between simulation and experiment, due to the hydrodynamically enhanced stability of coupled passive particles.

Antibiotic-induced anomalous statistics of collective bacterial swarming

Under sublethal antibiotics concentrations, the statistics of collectively swarming Bacillus subtilis transitions from normal to anomalous, with a heavy-tailed speed distribution and a two-step temporal correlation of velocities. The transition is due to changes in the properties of the bacterial motion and the formation of a motility-defective subpopulation that self-segregates into regions. As a result, both the colonial expansion and the growth rate are not affected by antibiotics. This phenomenon suggests a new strategy bacteria employ to fight antibiotic stress.

Green Algae as Model Organisms for Biological Fluid Dynamics

In the past decade the volvocine green algae, spanning from the unicellular Chlamydomonas to multicellular Volvox, have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 μm to several millimetres), their geometric regularity, the ease with which they can be cultured and the availability of many mutants that allow for connections between molecular details and organism-level behavior. This review summarizes these recent developments and highlights promising future directions in the study of biological fluid dynamics, especially in the context of evolutionary biology, that can take advantage of these remarkable organisms.

Vortex arrays and mesoscale turbulence of self-propelled particles

Inspired by the Turing mechanism for pattern formation, we propose a simple self-propelled particle model with short-range alignment and antialignment at larger distances. It is able to produce orientationally ordered states, periodic vortex patterns, and mesoscale turbulence, which resembles observations in dense suspensions of swimming bacteria. The model allows a systematic derivation and analysis of a kinetic theory as well as hydrodynamic equations for density and momentum fields. A phase diagram with regions of pattern formation as well as orientational order is obtained from a linear stability analysis of these continuum equations. Microscopic Langevin simulations of self-propelled particles are in agreement with these findings.

Active nematic materials with substrate friction

Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, first, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.

Vorticity, defects and correlations in active turbulence

We describe a numerical investigation of a continuum model of an active nematic, concentrating on the regime of active turbulence. Results are presented for the effect of three parameters, activity, elastic constant and rotational diffusion constant, on the order parameter and flow fields. Defects and distortions in the director field act as sources of vorticity, and thus vorticity is strongly correlated to the director field. In particular, the characteristic length of decay of vorticity and order parameter correlations is controlled by the defect density. By contrast, the decay of velocity correlations is determined by a balance between activity and dissipation. We highlight the role of microscopic flow generation mechanisms in determining the flow patterns and characteristic scales of active turbulence and contrast the behaviour of extensile and contractile active nematics.

Interfacial mechanisms in active emulsions

Active emulsions, i.e., emulsions whose droplets perform self-propelled motion, are of tremendous interest for mimicking collective phenomena in biological populations such as phytoplankton and bacterial colonies, but also for experimentally studying rheology, pattern formation, and phase transitions in systems far from thermal equilibrium. For fuelling such systems, molecular processes involving the surfactants which stabilize the emulsions are a straightforward concept. We outline and compare two different types of reactions, one which chemically modifies the surfactant molecules, the other which transfers them into a different colloidal state. While in the first case symmetry breaking follows a standard linear instability, the second case turns out to be more complex. Depending on the dissolution pathway, there is either an intrinsically nonlinear instability, or no symmetry breaking at all (and hence no locomotion).

Tangling of tethered swimmers: interactions between two nematodes

The tangling of two tethered microswimming worms serving as the ends of "active strings" is investigated experimentally and modeled analytically. C. elegans nematodes of similar size are caught by their tails using micropipettes and left to swim and interact at different separations over long times. The worms are found to tangle in a reproducible and statistically predictable manner, which is modeled based on the relative motion of the worm heads. Our results provide insight into the intricate tangling interactions present in active biological systems.

Freezing and thawing of artificial ice by thermal switching of geometric frustration in magnetic flux lattices

The problem of an ensemble of repulsive particles on a potential-energy landscape is common to many physical systems and has been studied in multiple artificial playgrounds. However, the latter usually involve fixed energy landscapes, thereby impeding in situ investigations of the particles' collective response to controlled changes in the landscape geometry. Here, we experimentally realize a system in which the geometry of the potential-energy landscape can be switched using temperature as the control knob. This realization is based on a high-temperature superconductor in which we engineer a nanoscale spatial modulation of the superconducting condensate. Depending on the temperature, the flux quanta induced by an applied magnetic field see either a geometrically frustrated energy landscape that favours an ice-like flux ordering, or an unfrustrated landscape that yields a periodic flux distribution. This effect is reflected in a dramatic change in the superconductor's magneto-transport. The thermal switching of the energy landscape geometry opens new opportunities for the study of ordering and reorganization in repulsive particle manifolds.

Deformable microswimmer in a swirl: capturing and scattering dynamics

Inspired by the classical Kepler and Rutherford problem, we investigate an analogous setup in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First, we identify new steady bound states in the swirl flow and analyze their stability. Second, we study the dynamics of a self-propelled swimmer heading towards the vortex center, and we observe the subsequent capturing and scattering dynamics. We distinguish between two major types of swimmers, those that tend to elongate perpendicularly to the propulsion direction and those that pursue a parallel elongation. While the first ones can get caught by the swirl, the second ones were always observed to be scattered, which proposes a promising escape strategy. This offers a route to design artificial microswimmers that show the desired behavior in complicated flow fields. It should be straightforward to verify our results in a corresponding quasi-two-dimensional experiment using self-propelled droplets on water surfaces.

Flagella-induced transitions in the collective behavior of confined microswimmers

Bacteria are usually studied in free-swimming planktonic state or in sessile biofilm state. However, little is known about intermediate states where variability in the environmental conditions and/or energy supply to the flagellar propulsive system alter flagellar activity. In this Rapid Communication, we propose an idealized physical model to investigate the effects of flagellar activity on the hydrodynamic interactions among a population of microswimmers. We show that decreasing flagellar activity induces a hydrodynamically triggered transition in confined microswimmers from turbulentlike swimming to aggregation and clustering. These results suggest that the interplay between flagellar activity and hydrodynamic interactions provides a physical mechanism for coordinating collective behaviors in confined bacteria, with potentially profound implications on processes such as molecular diffusion and transport of oxygen and nutrients that mediate transitions in the bacteria physiological state.

Large-scale chaos and fluctuations in active nematics

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Fluid flows created by swimming bacteria drive self-organization in confined suspensions

Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatiotemporal patterns on scales that are large compared with those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we use the recent discovery of a spiral-vortex state in confined suspensions of Bacillus subtilis to study this issue in detail. Those experiments showed that if the radius of confinement in a thin cylindrical chamber is below a critical value, the suspension will spontaneously form a steady single-vortex state encircled by a counter-rotating cell boundary layer, with spiral cell orientation within the vortex. Left unclear, however, was the flagellar orientation, and hence the cell swimming direction, within the spiral vortex. Here, using a fast simulation method that captures oriented cell-cell and cell-fluid interactions in a minimal model of discrete particle systems, we predict the striking, counterintuitive result that in the presence of collectively generated fluid motion, the cells within the spiral vortex actually swim upstream against those flows. This prediction is then confirmed by the experiments reported here, which include measurements of flagella bundle orientation and cell tracking in the self-organized state. These results highlight the complex interplay between cell orientation and hydrodynamic flows in concentrated suspensions of microorganisms.

Self-induced polar order of active Brownian particles in a harmonic trap

Hydrodynamically interacting active particles in an external harmonic potential form a self-assembled fluid pump at large enough Péclet numbers. Here, we give a quantitative criterion for the formation of the pump and show that particle orientations align in the self-induced flow field in surprising analogy to ferromagnetic order where the active Péclet number plays the role of inverse temperature. The particle orientations follow a Boltzmann distribution Φ(p) ∼ exp(Ap(z)) where the ordering mean field A scales with the active Péclet number and polar order parameter. The mean flow field in which the particles' swimming directions align corresponds to a regularized Stokeslet with strength proportional to swimming speed. Analytic mean-field results are compared with results from Brownian dynamics simulations with hydrodynamic interactions included and are found to capture the self-induced alignment very well.

Globally aligned states and hydrodynamic traffic jams in confined suspensions of active asymmetric particles

Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including coherent polarized density waves with global alignment, persistent counterrotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.

Actomyosin contractility rotates the cell nucleus

The cell nucleus functions amidst active cytoskeletal filaments, but its response to their contractile stresses is largely unexplored. We study the dynamics of the nuclei of single fibroblasts, with cell migration suppressed by plating onto micro-fabricated patterns. We find the nucleus undergoes noisy but coherent rotational motion. We account for this observation through a hydrodynamic approach, treating the nucleus as a highly viscous inclusion residing in a less viscous fluid of orientable filaments endowed with active stresses. Lowering actin contractility selectively by introducing blebbistatin at low concentrations drastically reduced the speed and coherence of the angular motion of the nucleus. Time-lapse imaging of actin revealed a correlated hydrodynamic flow around the nucleus, with profile and magnitude consistent with the results of our theoretical approach. Coherent intracellular flows and consequent nuclear rotation thus appear to be an intrinsic property of cells.

Living liquid crystals

Collective motion of self-propelled organisms or synthetic particles, often termed "active fluid," has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and interactions among the moving units and the medium lead to complex dynamics. Here, we introduce a class of active matter--living liquid crystals (LLCs)--that combines living swimming bacteria with a lyotropic liquid crystal. The physical properties of LLCs can be controlled by the amount of oxygen available to bacteria, by concentration of ingredients, or by temperature. Our studies reveal a wealth of intriguing dynamic phenomena, caused by the coupling between the activity-triggered flow and long-range orientational order of the medium. Among these are (i) nonlinear trajectories of bacterial motion guided by nonuniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a nonflowing uniform state into a flowing one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence-enabled visualization of microflow generated by the nanometers-thick bacterial flagella. Unlike their isotropic counterpart, the LLCs show collective dynamic effects at very low volume fraction of bacteria, on the order of 0.2%. Our work suggests an unorthodox design concept to control and manipulate the dynamic behavior of soft active matter and opens the door for potential biosensing and biomedical applications.

Controlling active self-assembly through broken particle-shape symmetry

Many structural properties of conventional passive materials are known to arise from the symmetries of their microscopic constituents. By contrast, it is largely unclear how the interplay between particle shape and self-propulsion controls the meso- and macroscale behavior of active matter. Here we use large-scale simulations of homo- and heterogeneous self-propelled particle systems to identify generic effects of broken particle-shape symmetry on collective motion. We find that even small violations of fore-aft symmetry lead to fundamentally different collective behaviors, which may facilitate demixing of differently shaped species as well as the spontaneous formation of stable microrotors. These results suggest that variation of particle shape yields robust physical mechanisms to control self-assembly of active matter, with possibly profound implications for biology and materials design.

Structure and dynamics of self-assembling colloidal monolayers in oscillating magnetic fields

Many fascinating phenomena such as large-scale collective flows, enhanced fluid mixing, and pattern formation have been observed in so-called active fluids, which are composed of particles that can absorb energy and dissipate it into the fluid medium. For active particles immersed in liquids, fluid-mediated viscous stresses can play an important role on the emergence of collective behavior. Here, we experimentally investigate their role in the dynamics of self-assembling magnetically driven colloidal particles which can rapidly form organized hexagonal structures. We find that viscous stresses reduce hexagonal ordering, generate smaller clusters, and significantly decrease the rate of cluster formation, all while holding the system at constant number density. Furthermore, we show that time and length scales of cluster formation depend on the Mason number (Mn), or ratio of viscous to magnetic forces, scaling as t∝Mn and L∝Mn(-1/2). Our results suggest that viscous stresses hinder collective behavior in a self-assembling colloidal system.

Active matter ratchets with an external drift

When active matter particles such as swimming bacteria are placed in an asymmetric array of funnels, it has been shown that a ratchet effect can occur even in the absence of an external drive. Here we examine active ratchets for two-dimensional arrays of funnels or L shapes where there is also an externally applied dc drive or drift. We show that for certain conditions the ratchet effect can be strongly enhanced and it is possible to have conditions under which run-and-tumble particles with one run length move in the opposite direction from particles with a different run length. For the arrays of L shapes, we find that the application of a drift force can enhance a transverse rectification in the direction perpendicular to the drift. When particle-particle steric interactions are included, we find that the ratchet effects can be either enhanced or suppressed depending on barrier geometry, particle run length, and particle density.