Dynamics-dependent density distribution in active suspensions

Active interface bulging in Bacillus subtilis swarms promotes self-assembly and biofilm formation

Microbial communities such as biofilms are commonly found at interfaces. However, it is unclear how the physical environment of interfaces may contribute to the development and behavior of surface-associated microbial communities. Combining multimode imaging, single-cell tracking, and numerical simulations, here, we found that activity-induced interface bulging promotes colony biofilm formation in Bacillus subtilis swarms presumably via segregation and enrichment of sessile cells in the bulging area. Specifically, the diffusivity of passive particles is ~50% lower inside the bulging area than elsewhere, which enables a diffusion-trapping mechanism for self-assembly and may account for the enrichment of sessile cells. We also uncovered a quasilinear relation between cell speed and surface-packing density that underlies the process of active interface bulging. Guided by the speed-density relation, we demonstrated reversible formation of liquid bulges by manipulating the speed and local density of cells with light. Over the course of development, the active bulges turned into striped biofilm structures, which eventually give rise to a large-scale ridge pattern. Our findings reveal a unique physical mechanism of biofilm formation at air-solid interface, which is pertinent to engineering living materials and directed self-assembly in active fluids.

Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli

We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.

Sizing multimodal suspensions with differential dynamic microscopy

Differential dynamic microscopy (DDM) can be used to extract the mean particle size from videos of suspensions. However, many suspensions have multimodal particle size distributions, for which a single 'mean' is not a sufficient description. After clarifying how different particle sizes contribute to the signal in DDM, we show that standard DDM analysis can extract the mean sizes of two populations in a bimodal suspension given prior knowledge of the sample's bimodality. Further, the use of the CONTIN algorithm obviates the need for such prior knowledge. Finally, we show that by selectively analysing portions of the DDM images, we can size a trimodal suspension where the large particles would otherwise dominate the signal, again without prior knowledge of the trimodality.

Orientation-Dependent Propulsion of Active Brownian Spheres: From Self-Advection to Programmable Cluster Shapes

Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the particles, become increasingly popular. In this Letter, we investigate systems of interacting active Brownian spheres in two spatial dimensions with orientation-dependent propulsion using analytical modeling and Brownian dynamics simulations. It is found that the orientation dependence leads to self-advection, circulating currents, and programmable cluster shapes.

Microswimmers under the spotlight: interplay between agents with different levels of activity

The ability of active matter to assemble into reconfigurable nonequilibrium structures has drawn considerable interest in recent years. We investigate how active fluids respond to spatial light patterns through simulations and experiments on light-activated self-propelled colloidal particles. We examine the processes of inverse templated assembly, which involves creating a region without active particles through a bright pattern, and templated assembly, which promotes the formation of dense particle regions through a dark pattern. We identify scaling relations for the characteristic times for both processes that quantify the interplay between the dimension of the applied pattern and the intrinsic properties of the active fluid. We also explore the assembly mechanism and dynamics of large clusters and show how assembly and inverse assembly can be combined to create any arbitrarily complex template. In addition to providing protocols for templated assembly via light patterning, our results demonstrate how the local packing fraction can be fine-tuned by modulation of the light intensity. The protocol so obtained exceeds the capabilities of conventional assembly strategies, in which packing fraction is dictated by thermodynamics, and opens the door to arbitrarily precise and programmable nonequilibrium assembly strategies in active matter.

Spatial Patterning of Micromotor Aggregation and Flux

Using a spatially varying light pattern with light activated semi-conductor based magnetic TiO2 micromotors, we study the difference in micromotor flux between illuminated and non-illuminated regions in the presence and absence of an applied magnetic field. We find that the magnetic field enhances the flux of the motors which we attribute to a straightening of the micromotor trajectories which decreases the time they spend in the illuminated region. We also demonstrate spatially patterned light-induced aggregation of the micromotors and study its time evolution at various micromotor concentrations. Although light induced aggregation has been observed previously, spatial patterning of aggregation demonstrates a further means of control which could be relevant to swarm control or self-assembly applications. Overall, these results draw attention to the effect of trajectory shape on the flux of active colloids as well as the concentration dependence of aggregation and its time dependence within a spatially patterned region, which is not only pertinent to self-assembly and swarm control, but also provides insight into the behavior of active matter systems with spatially varying activity levels.

Colloidal transport by light induced gradients of active pressure

Active fluids, like all other fluids, exert mechanical pressure on confining walls. Unlike equilibrium, this pressure is generally not a function of the fluid state in the bulk and displays some peculiar properties. For example, when activity is not uniform, fluid regions with different activity may exert different pressures on the container walls but they can coexist side by side in mechanical equilibrium. Here we show that by spatially modulating bacterial motility with light, we can generate active pressure gradients capable of transporting passive probe particles in controlled directions. Although bacteria swim faster in the brighter side, we find that bacteria in the dark side apply a stronger pressure resulting in a net drift motion that points away from the low activity region. Using a combination of experiments and numerical simulations, we show that this drift originates mainly from an interaction pressure term that builds up due to the compression exerted by a layer of polarized cells surrounding the slow region. In addition to providing new insights into the generalization of pressure for interacting systems with non-uniform activity, our results demonstrate the possibility of exploiting active pressure for the controlled transport of microscopic objects.

Confined active matter in external fields

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field normal to the walls, particles rotate to align with the field and accumulate in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement.

The landscape of micron-scale particles including microplastics in human enclosed body fluids

Exogenous microparticles including microplastics are novel pollutants that could persist in the environment with potential health effects, while crucial data on their exposure in humans are still lacking. To understand the panorama of microparticles including microplastics exposure and distribution characteristics in different kinds of body fluids. A non-targeted microparticle internal exposure landscape analysis was done in thirteen kinds of human enclosed body fluids covering eight body systems. Totally 104 patients aged 24-96 years with an average age of 56 years were included in this study. After sample digestion, non-soluble microparticles were detected and identified with one Raman Microspectroscope under a strict quality control-particle detection system. Totally 702 microparticles with size ranging from 2.15 to 103.27 µm were detected in samples. Microparticles were identified into 84 substances or 66 molecules, most of which were firstly reported inside human body. Nine kinds of microplastics were originally reported in human body fluids with their size ranging from 19.66 to 103.27 µm. Microparticles exposure was unexpectedly high inside the human body despite the protection of biological barriers and membranes, raising awareness of the impact of particle pollution on sustainable development.

Differential dynamic microscopy for the characterisation of motility in biological systems

Differential Dynamic Microscopy (DDM) is a relatively new technique which measures the dynamics of suspended particles using a dynamic light scattering formalism. Videos are recorded using standard light microscopy at moderate frame rates, and fluctuations in pixel intensity are measured as a function of time. As only pixel intensity is analysed, it is not necessary to resolve individual particles. This allows for low magnifications and wide fields of view, and therefore dynamics can be measured on tens of thousands of scattering objects, providing robust statistics. A decade ago the technique was successfully applied to measure bacterial motility. Since then, it has been applied to a range of motile systems, but has not yet reached the wider biological community. This perspective reviews the work done so far, and provides the basic background to enable the broader application of this promising technique.

Rectification and confinement of photokinetic bacteria in an optical feedback loop

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

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

Dynamics of active particles with space-dependent swim velocity

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

Optimization of an active heat engine

Optimization of heat engines at the microscale has applications in biological and artificial nanotechnology and stimulates theoretical research in nonequilibrium statistical physics. Here we consider noninteracting overdamped particles confined by an external harmonic potential, in contact with either a thermal reservoir or a stochastic self-propulsion force (active Ornstein-Uhlenbeck model). A cyclical machine is produced by periodic variation of the parameters of the potential and of the noise. An exact mapping between the passive and the active model allows us to define the effective temperature T_{eff}(t), which is meaningful for the thermodynamic performance of the engine. We show that T_{eff}(t) is different from all other known active temperatures, typically used in static situations. The mapping allows us to optimize the active engine, regardless of the values of the persistence time or self-propulsion velocity. In particular, through linear irreversible thermodynamics (small amplitude of the cycle), we give an explicit formula for the optimal cycle period and phase delay (between the two modulated parameters, stiffness and temperature) achieving maximum power with Curzon-Ahlborn efficiency. In the quasistatic limit, the formula for T_{eff}(t) simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency. A point, which has been overlooked in recent literature, is made about the difficulty in defining efficiency without a consistent definition of effective temperature.

Statistical mechanics of active Ornstein-Uhlenbeck particles

We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.

Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.

Photo-bioconvection: towards light control of flows in active suspensions

The persistent motility of individual constituents in microbial suspensions represents a prime example of the so-called active matter systems. Cells consume energy, exert forces and move, overall releasing the constraints of equilibrium statistical mechanics of passive elements and allowing for complex spatio-temporal patterns to emerge. Moreover, when subject to physico-chemical stimuli their collective behaviour often drives large-scale instabilities of a hydrodynamic nature, with implications for biomixing in natural environments and incipient industrial applications. In turn, our ability to exert external control of these driving stimuli could be used to govern the emerging patterns. Light, being easily manipulable and, at the same time, an important stimulus for a wide variety of microorganisms, is particularly well suited to this end. In this paper, we will discuss the current state, developments and some of the emerging advances in the fundamentals and applications of light-induced bioconvection with a focus on recent experimental realizations and modelling efforts. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Feedback-controlled active brownian colloids with space-dependent rotational dynamics

The non-thermal nature of self-propelling colloids offers new insights into non-equilibrium physics. The central mathematical model to describe their trajectories is active Brownian motion, where a particle moves with a constant speed, while randomly changing direction due to rotational diffusion. While several feedback strategies exist to achieve position-dependent velocity, the possibility of spatial and temporal control over rotational diffusion, which is inherently dictated by thermal fluctuations, remains untapped. Here, we decouple rotational diffusion from thermal fluctuations. Using external magnetic fields and discrete-time feedback loops, we tune the rotational diffusivity of active colloids above and below its thermal value at will and explore a rich range of phenomena including anomalous diffusion, directed transport, and localization. These findings add a new dimension to the control of active matter, with implications for a broad range of disciplines, from optimal transport to smart materials.

Active colloidal systems can serve as an enabling platform to study complex out-of-equilibrium physical phenomena. Using a magnetic control with a feedback loop, here the authors program the dynamics of active Brownian particles by updating their rotational diffusion coefficient depending on their locations.

Reverse osmotic effect in active matter

In nonequilibrium active matter systems, a spatial variation in activity can lead to a spatial variation in concentration of active particles satisfying, at steady state, the condition nU=const [Schnitzer, Phys. Rev. E 48, 2553 (1993)1063-651X10.1103/PhysRevE.48.2553; Tailleur and Cates, Phys. Rev. Lett. 100, 218103 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.218103], where n is the number density and U is the active (swim) speed. We show that this condition holds even when the variation is abrupt and when thermal Brownian motion is present provided that the Péclet number is large. This spatial variation in swim speed and concentration produces a fluid pressure distribution that drives a reverse osmotic flow-fluid flows from regions of high concentration to low.

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.

Run-and-tumble motion in one dimension with space-dependent speed

We consider a particle performing run-and-tumble dynamics with space-dependent speed. The model has biological relevance as it describes motile bacteria or cells in heterogeneous environments. We give exact expression for the probability density function in the case of free motion in unbounded space. We then analyze the case of a particle moving in a confined interval in the presence of partially absorbing boundaries, reporting the probability density in the Laplace (time) domain and the mean time to absorption. We also discuss the relaxation to the steady state in the case of confinement with reflecting boundaries and drift effects due to direction-dependent tumbling rates, modeling taxis phenomena of cells. The case of diffusive particles with spatially variable diffusivity is obtained as a limiting case.

Ramifications of disorder on active particles in one dimension

The effects of quenched disorder on a single and many active run-and-tumble particles are studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to nondisordered systems.

Dynamic optical rectification and delivery of active particles

We use moving light patterns to control the motion of Escherichia coli bacteria whose motility is photo-activated. Varying the pattern speed controls the magnitude and direction of the bacterial flux, and therefore the accumulation of cells in up- and down-stream reservoirs. We validate our results with two-dimensional simulations and a 1-dimensional analytic model, and use these to explore parameter space. We find that cell accumulation is controlled by a competition between directed flux and undirected, stochastic transport. Our results point to a number of design principles for using moving light patterns and light-activated micro-swimmers in a range of practical applications.

Propagating density spikes in light-powered motility-ratchets

Combining experiments and computer simulations, we use a spatially periodic and flashing light-field to direct the motion of phototactic active colloids. Here, the colloids self-organize into a density spike pattern, which resembles a shock wave and propagates over long distances, almost without dispersing. The underlying mechanism involves a synchronization of the colloids with the light-field, so that particles see the same intensity gradient each time the light-pattern is switched on, but no gradient in between (for example). This creates pulsating transport whose strength and direction can be controlled via the flashing protocol and the self-propulsion speed of the colloids. Our results might be useful for drug delivery applications and can be used to segregate active colloids by their speed.