Tuning the motility and directionality of self-propelled colloids

Counterfactual rewards promote collective transport using individually controlled swarm microrobots

Swarm robots offer fascinating opportunities to perform complex tasks beyond the capabilities of individual machines. Just as a swarm of ants collectively moves large objects, similar functions can emerge within a group of robots through individual strategies based on local sensing. However, realizing collective functions with individually controlled microrobots is particularly challenging because of their micrometer size, large number of degrees of freedom, strong thermal noise relative to the propulsion speed, and complex physical coupling between neighboring microrobots. Here, we implemented multiagent reinforcement learning (MARL) to generate a control strategy for up to 200 microrobots whose motions are individually controlled by laser spots. During the learning process, we used so-called counterfactual rewards that automatically assign credit to the individual microrobots, which allows fast and unbiased training. With the help of this efficient reward scheme, swarm microrobots learn to collectively transport a large cargo object to an arbitrary position and orientation, similar to ant swarms. We show that this flexible and versatile swarm robotic system is robust to variations in group size, the presence of malfunctioning units, and environmental noise. In addition, we let the robot swarms manipulate multiple objects simultaneously in a demonstration experiment, highlighting the benefits of distributed control and independent microrobot motion. Control strategies such as ours can potentially enable complex and automated assembly of mobile micromachines, programmable drug delivery capsules, and other advanced lab-on-a-chip applications.

Response of chemically active dimer motor in phase-separating binary fluid mixture: Motility regulation and self-aggregation

The design of synthetic chemically powered nanomotors often considers the fuel and product to be miscible. The propulsion properties of such motors can be altered if the binary fluid consisting of fuel and product is phase separating. The dynamical properties of a dimer motor in a phase-separating binary mixture are discussed. Depending on the strength of phase separation and the activity of the dimer, the single-motor propulsion velocity either decreases or reverses its direction. The velocity reversal is shown to be related to the generated fluid flow around the motor. The collective dynamics of the motors in such phase-separating fluid results in the formation of self-assembled structures.

Spatiotemporal control of structure and dynamics in a polar active fluid

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.

Motility-Induced Clustering of Active Particles under Soft Confinement

We investigate the structural and dynamic properties of active Brownian particles (APs) confined within a soft annulus-shaped channel. Depending on the strength of the confinement and the Péclet number, we observe a novel reentrant behavior that is not present in unconfined systems. Our findings are substantiated by numerical simulations and analytical considerations, revealing that this behavior arises from the strong coupling between the Péclet number and the effective confining dimensionality of the APs. Our work highlights the peculiarities of soft boundaries for APs and how clogging can be avoided under such conditions.

Environmental memory boosts group formation of clueless individuals

The formation of groups of interacting individuals improves performance and fitness in many decentralised systems, from micro-organisms to social insects, from robotic swarms to artificial intelligence algorithms. Often, group formation and high-level coordination in these systems emerge from individuals with limited information-processing capabilities implementing low-level rules of communication to signal to each other. Here, we show that, even in a community of clueless individuals incapable of processing information and communicating, a dynamic environment can coordinate group formation by transiently storing memory of the earlier passage of individuals. Our results identify a new mechanism of indirect coordination via shared memory that is primarily promoted and reinforced by dynamic environmental factors, thus overshadowing the need for any form of explicit signalling between individuals. We expect this pathway to group formation to be relevant for understanding and controlling self-organisation and collective decision making in both living and artificial active matter in real-life environments.

Collective foraging of active particles trained by reinforcement learning

Collective self-organization of animal groups is a recurring phenomenon in nature which has attracted a lot of attention in natural and social sciences. To understand how collective motion can be achieved without the presence of an external control, social interactions have been considered which regulate the motion and orientation of neighbors relative to each other. Here, we want to understand the motivation and possible reasons behind the emergence of such interaction rules using an experimental model system of light-responsive active colloidal particles (APs). Via reinforcement learning (RL), the motion of particles is optimized regarding their foraging behavior in presence of randomly appearing food sources. Although RL maximizes the rewards of single APs, we observe the emergence of collective behaviors within the particle group. The advantage of such collective strategy in context of foraging is to compensate lack of local information which strongly increases the robustness of the resulting policy. Our results demonstrate that collective behavior may not only result on the optimization of behaviors on the group level but may also arise from maximizing the benefit of individuals. Apart from a better understanding of collective behaviors in natural systems, these results may also be useful in context of the design of autonomous robotic systems.

Dynamical Pattern Formation without Self-Attraction in Quorum-Sensing Active Matter: The Interplay between Nonreciprocity and Motility

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a mechanism for dynamical pattern formation that does not rely on the standard route of intraspecies effective attractive interactions. Instead, our results reveal a highly dynamical phase of chasing bands induced only by the combined effects of self-propulsion and nonreciprocity in the interspecies couplings. Turning on self-attraction, we find that the system may phase separate into a macroscopic domain of such chaotic chasing bands coexisting with a dilute gas. We show that the chaotic dynamics of bands at the interfaces of this phase-separated phase results in anomalously slow coarsening.

Inverted Sedimentation of Active Particles in Unbiased ac Fields

Gaining control over the motion of active particles is crucial for applications ranging from targeted cargo delivery to nanomedicine. While much progress has been made recently to control active motion based on external forces, flows, or gradients in concentration or light intensity, which all have a well-defined direction or bias, little is known about how to steer active particles in situations where no permanent bias can be realized. Here, we show that ac fields with a vanishing time average provide an alternative route to steering active particles. We exemplify this route for inertial active particles in a gravitational field, observing that a substantial fraction of them persistently travels in the upward direction upon switching on the ac field, resulting in an inverted sedimentation profile at the top wall of a confining container. Our results offer a generic control principle that could be used in the future to steer active motion, direct collective behaviors, and purify mixtures.

Unidirectional rotation of micromotors on water powered by pH-controlled disassembly of chiral molecular crystals

Biological and synthetic molecular motors, fueled by various physical and chemical means, can perform asymmetric linear and rotary motions that are inherently related to their asymmetric shapes. Here, we describe silver-organic micro-complexes of random shapes that exhibit macroscopic unidirectional rotation on water surface through the asymmetric release of cinchonine or cinchonidine chiral molecules from their crystallites asymmetrically adsorbed on the complex surfaces. Computational modeling indicates that the motor rotation is driven by a pH-controlled asymmetric jet-like Coulombic ejection of chiral molecules upon their protonation in water. The motor is capable of towing very large cargo, and its rotation can be accelerated by adding reducing agents to the water.

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

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

Critical behavior of quorum-sensing active particles

It is still a debated issue whether all critical active particles belong to the same universality class. Here we numerically study the critical behavior of quorum sensing active particles that represents the archetypal model for interpreting motility-induced phase separation. Mean-field theory predicts that this model should undergo a full phase separation if particles slow-down enough when sensing the presence of their neighbors and that the coexistence line terminates in a critical point. By performing large-scale numerical simulations, we confirm this scenario, locate the critical point and use finite-size scaling analysis to show that the static and dynamic critical exponents of this active system substantially agree with those of the Ising universality class.

Anomalous Cooling and Overcooling of Active Colloids

The phenomenon that a system at a hot temperature cools faster than at a warm temperature, referred to as the Mpemba effect, has recently been realized for trapped colloids. Here, we investigate the cooling and heating process of a self-propelled active colloid using numerical simulations and theoretical calculations with a model that can be directly tested in experiments. Upon cooling, activity induces a Mpemba effect and the active particle transiently escapes an effective temperature description. At the end of the cooling process the notion of temperature is recovered and the system can exhibit even smaller temperatures than its final temperature, a surprising phenomenon which we refer to as activity-induced overcooling.

Force Generation in Confined Active Fluids: The Role of Microstructure

We experimentally determine the force exerted by a bath of active particles onto a passive probe as a function of its distance to a wall and compare it to the measured averaged density distribution of active particles around the probe. Within the framework of an active stress, we demonstrate that both quantities are-up to a factor-directly related to each other. Our results are in excellent agreement with a minimal numerical model and confirm a general and system-independent relationship between the microstructure of active particles and transmitted forces.

Breaking action-reaction with active apolar colloids: emergent transport and velocity inversion

Artificial active particles are autonomous agents able to convert energy from the environment into net propulsion, breaking detailed balance and the action-reaction law, clear signatures of their out-of-equilibrium nature. Here we investigate the emergence of directed motion in clusters composed of passive and catalytically active apolar colloids. We use a light-induced chemophoretic flow to rapidly assemble hybrid self-propelling clusters composed of hematite particles and passive silica spheres. By increasing the size of the passive cargo, we observe a reversal in the transport direction of the pair. We explain this complex yet rich phenomenon using a theoretical model which accounts for the generated chemical field and its coupling with the surrounding medium. We exploit further our technique to build up more complex, chemically driven, architectures capable of carrying several passive or active species, that quickly assemble and disassemble under light control.

Active colloid with externally induced periodic bipolar motility and its cooperative motion

Active matter physics has been developed with various types of self-propelled particles, including those with polar and bipolar motility and beyond. However, the bipolar motions experimentally realized so far have been either random along the axis or periodic at intrinsic frequencies. Here we report another kind of bipolar active particles, whose periodic bipolar self-propulsion is set externally at a controllable frequency. We used Quincke rollers-dielectric particles suspended in a conducting liquid driven by an electric field-under an AC electric field instead of the usually used DC field. Reciprocating motion of a single particle at the external frequency was observed experimentally and characterized theoretically as stable periodic motion. Experimentally, we observed not only the reciprocating motion but also non-trivial active Brownian particle (ABP)-like persistent motion in a long time scale. This resulted in a Lorentzian spectrum around zero frequency, which is not accounted for by a simple extension of the conventional model of Quincke rollers to the AC field. It was found that ABP-like motion can be reproduced by considering the top-bottom asymmetry in the experimental system. Moreover, we found a rotational diffusion coefficient much larger than the thermal one, as also reported in previous experiments, which may have resulted from roughness of the electrode surface. We also found self-organized formation of small clusters, such as doublets and triplets, and characterized cooperative motion of particles therein. The AC Quincke rollers reported here may serve as a model experimental system of bipolar active matter, which appears to deserve further investigations.

Role of cohesion in the flow of active particles through bottlenecks

We experimentally and numerically study the flow of programmable active particles (APs) with tunable cohesion strength through geometric constrictions. Similar to purely repulsive granular systems, we observe an exponential distribution of burst sizes and power-law-distributed clogging durations. Upon increasing cohesion between APs, we find a rather abrupt transition from an arch-dominated clogging regime to a cohesion-dominated regime where droplets form at the aperture of the bottleneck. In the arch-dominated regime the flow-rate only weakly depends on the cohesion strength. This suggests that cohesion must not necessarily decrease the group's efficiency passing through geometric constrictions or pores. Such behavior is explained by "slippery" particle bonds which avoids the formation of a rigid particle network and thus prevents clogging. Overall, our results confirm the general applicability of the statistical framework of intermittent flow through bottlenecks developed for granular materials also in case of active microswimmers whose behavior is more complex than that of Brownian particles but which mimic the behavior of living systems.

Aging or DEAD: Origin of the non-monotonic response to weak self-propulsion in active glasses

Among amorphous states, glass is defined by relaxation times longer than the observation time. This nonergodic nature makes the understanding of glassy systems an involved topic, with complex aging effects or responses to further out-of-equilibrium external drivings. In this respect, active glasses made of self-propelled particles have recently emerged as a stimulating systems, which broadens and challenges our current understanding of glasses by considering novel internal out-of-equilibrium degrees of freedom. In previous experimental studies we have shown that in the ergodicity broken phase, the dynamics of dense passive particles first slows down as particles are made slightly active, before speeding up at larger activity. Here, we show that this nonmonotonic behavior also emerges in simulations of soft active Brownian particles and explore its cause. We refute that the deadlock by emergence of active directionality model we proposed earlier describes our data. However, we demonstrate that the nonmonotonic response is due to activity enhanced aging and thus confirm the link with ergodicity breaking. Beyond self-propelled systems, our results suggest that aging in active glasses is not fully understood.

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.

Efficiency of isothermal active matter engines: Strong driving beats weak driving

We study microscopic engines that use a single active particle as their "working medium." Part of the energy required to drive the directed motion of the particle can be recovered as work, even at a constant temperature. A wide class of synthetic active particles can be captured by schematically accounting for the chemical degrees of freedom that power the directed motion without having to resolve the exact microscopic mechanism. We derive analytical results for the quasistatic thermodynamic efficiency, i.e., the fraction of available chemical energy that can be recovered as mechanical work. While this efficiency is vanishingly small for colloidal particles, it increases as the dissipation is increased beyond the linear-response regime and goes through a maximum at large propulsion speeds. Our results demonstrate that driving beyond the linear-response regime has nontrivial consequences for the efficiency of active engines.

Relaxation to steady states of a binary liquid mixture around an optically heated colloid

We study the relaxation dynamics of a binary liquid mixture near a light-absorbing Janus particle after switching on and off illumination using experiments and theoretical models. The dynamics is controlled by the temperature gradient formed around the heated particle. Our results show that the relaxation is asymmetric: The approach to a nonequilibrium steady state is much slower than the return to thermal equilibrium. Approaching a nonequilibrium steady state after a sudden temperature change is a two-step process that overshoots the response of spatial variance of the concentration field. The initial growth of concentration fluctuations after switching on illumination follows a power law in agreement with the hydrodynamic and purely diffusive model. The energy outflow from the system after switching off illumination is well described by a stretched exponential function of time with characteristic time proportional to the ratio of the energy stored in the steady state to the total energy flux in this state.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

Mode-coupling theory for tagged-particle motion of active Brownian particles

We derive a mode-coupling theory (MCT) to describe the dynamics of a tracer particle that is embedded in a dense system of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian motion and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density-correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a single active particle in a glass-forming passive host suspensions, that of a passive colloidal particle in a suspension of ABP, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We confirm in the simulations a peculiar feature of the transient and stationary dynamical density-correlation functions regarding their lack of symmetry under time reversal, demonstrating the nonequilibrium nature of the system and how it manifests itself in the theory.

Spontaneous chiralization of polar active particles

Polar active particles constitute a wide class of active matter that is able to propel along a preferential direction, given by their polar axis. Here, we demonstrate a generic active mechanism that leads to their spontaneous chiralization through a symmetry-breaking instability. We find that the transition of an active particle from a polar to a chiral symmetry is characterized by the emergence of active rotation and of circular trajectories. The instability is driven by the advection of a solute that interacts differently with the two portions of the particle surface and it occurs through a supercritical pitchfork bifurcation.

Work fluctuation relation of an active Brownian particle in a viscoelastic fluid

We experimentally investigate the work fluctuations of an active Brownian particle (ABP) during its self-propelled motion in a viscoelastic medium. Under such conditions, ABPs display a persistent circular motion which allows the determination of the orientational work fluctuations along its trajectory. Due to the nonlinear coupling to the non-Markovian bath, we find strong deviations from the work fluctuation theorem (WFT) due to observed increased rotational ABP dynamics. Taking this enhanced rotational diffusion into account, the orientational work distributions can be recasted to be in accordance with the WFT by considering an effective temperature of about two orders of magnitude larger than k_{B}T. This approach is confirmed by the good agreement of the torque exerted by the viscoelastic bath on the ABP obtained from the WFT with the value obtained from the mean angular velocity and the friction coefficient of the ABP.

Thermotaxis of Janus particles

The interactions of autonomous microswimmers play an important role for the formation of collective states of motile active matter. We study them in detail for the common microswimmer-design of two-faced Janus spheres with hemispheres made from different materials. Their chemical and physical surface properties may be tailored to fine-tune their mutual attractive, repulsive or aligning behavior. To investigate these effects systematically, we monitor the dynamics of a single gold-capped Janus particle in the external temperature field created by an optically heated metal nanoparticle. We quantify the orientation-dependent repulsion and alignment of the Janus particle and explain it in terms of a simple theoretical model for the induced thermoosmotic surface fluxes. The model reveals that the particle's angular velocity is solely determined by the temperature profile on the equator between the Janus particle's hemispheres and their phoretic mobility contrast. The distortion of the external temperature field by their heterogeneous heat conductivity is moreover shown to break the apparent symmetry of the problem.

Transport coefficients in dense active Brownian particle systems: mode-coupling theory and simulation results

We discuss recent advances in developing a mode-coupling theory of the glass transition (MCT) of two-dimensional systems of active Brownian particles (ABPs). The theory describes the structural relaxation close to the active glass in terms of transient dynamical density correlation functions. We summarize the equations of motion that have been derived for the collective density-fluctuation dynamics and those for the tagged-particle motion. The latter allow to study the dynamics of both passive and active tracers in both passive and active host systems. In the limit of small wave numbers, they give rise to equations of motion describing the mean-squared displacements (MSDs) of these tracers and hence the long-time diffusion coefficients as a transport coefficient quantifying long-range tracer motion. We specifically discuss the case of a single ABP tracer in a glass-forming passive host suspension, a case that has recently been studied in experiments on colloidal Janus particles. We employ event-driven Brownian dynamics (ED-BD) computer simulations to test the ABP-MCT and find good agreement between the two for the MSD, provided that known errors in MCT already for the passive system (i.e., an overestimation of the glassiness of the system) are accounted for by an empirical mapping of packing fractions and host-system self-propulsion forces. The ED-BD simulation results also compare well to experimental data, although a peculiar non-monotonic mapping of self-propulsion velocities is required. The ABP-MCT predicts a specific self-propulsion dependence of the Stokes-Einstein relation between the long-time diffusion coefficient and the host-system viscosity that matches well the results from simulation. An application of ABP-MCT within the integration-through transients framework to calculate the density-renormalized effective swim velocity of the interacting ABP agrees qualitatively with the ED-BD simulation data at densities close to the glass transition and quantitatively for the full density range only after the mapping of packing fractions employed for the passive system.

Active colloids under geometrical constraints in viscoelastic media

We study the behavior of active particles (APs) moving in a viscoelastic fluid in the presence of geometrical confinements. Upon approaching a flat wall, we find that APs slow down due to compression of the enclosed viscoelastic fluid. In addition, they receive a viscoelastic torque leading to sudden orientational changes and departure from walls. Based on these observations, we develop a numerical model which can also be applied to other geometries and yields good agreement with experimental data. Our results demonstrate, that APs are able to move through complex geometrical structures more effectively when suspended in a viscoelastic compared to a Newtonian fluid.

Self-Motility of an Active Particle Induced by Correlations in the Surrounding Solution

Current models of phoretic transport rely on molecular forces creating a "diffuse" particle-fluid interface. We investigate theoretically an alternative mechanism, in which a diffuse interface emerges solely due to a nonvanishing correlation length of the surrounding solution. This mechanism can drive self-motility of a chemically active particle. Numerical estimates indicate that the velocity can reach micrometers per second. The predicted phenomenology includes a bilinear dependence of the velocity on the activity and a possible double velocity reversal upon varying the correlation length.

Autonomously Probing Viscoelasticity in Disordered Suspensions

Recent experiments show a strong rotational diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions.

Unravelling the role of phoretic and hydrodynamic interactions in active colloidal suspensions

Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external force. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically the suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamically resolved solute-mediated phoretic interactions and solvent-mediated hydrodynamic interactions. Our results show that the system displays different scenarios at changing the colloid-solute affinity and it develops a cluster phase in the chemoattractive case. We study the statistics of cluster sizes and cluster morphologies for different magnitudes of colloidal activity. Finally, we provide evidences that hydrodynamics plays a relevant role in the aggregation kinetics and cluster morphology, significantly hindering cluster growth.

Effective interactions mediated between two permeable disks in an active fluid

We study steady-state properties of a bath of active Brownian particles (ABPs) in two dimensions in the presence of two fixed, permeable (hollow) disklike inclusions, whose interior and exterior regions can exhibit mismatching motility (self-propulsion) strengths for the ABPs. We show that such a discontinuous motility field strongly affects spatial distribution of ABPs and thus also the effective interaction mediated between the inclusions through the active bath. Such net interactions arise from soft interfacial repulsions between ABPs that sterically interact with and/or pass through permeable membranes assumed to enclose the inclusions. Both regimes of repulsion and attractive (albeit with different mechanisms) are reported and summarized in overall phase diagrams.

Transient coarsening and the motility of optically heated Janus colloids in a binary liquid mixture

A gold-capped Janus particle suspended in a near-critical binary liquid mixture can self-propel under illumination. We have immobilized such a particle in a narrow channel and carried out a combined experimental and theoretical study of the non-equilibrium dynamics of a binary solvent around it - lasting from the very moment of switching illumination on until the steady state is reached. In the theoretical study we use both a purely diffusive and a hydrodynamic model, which we solve numerically. Our results demonstrate a remarkable complexity of the time evolution of the concentration field around the colloid. This evolution is governed by the combined effects of the temperature gradient and the wettability, and crucially depends on whether the colloid is free to move or is trapped. For the trapped colloid, all approaches indicate that the early time dynamics is purely diffusive and characterized by composition layers travelling with constant speed from the surface of the colloid into the bulk of the solvent. Subsequently, hydrodynamic effects set in. Anomalously large nonequilibrium fluctuations, which result from the temperature gradient and the vicinity of the critical point of the binary liquid mixture, give rise to strong concentration fluctuations in the solvent and to permanently changing coarsening patterns not observed for a mobile particle. The early time dynamics around initially still Janus colloids produces a force which is able to set the Janus colloid into motion. The propulsion due to this transient dynamics is in the direction opposite to that observed after the steady state is attained.

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)'.

Microscale Marangoni Surfers

We apply laser light to induce the asymmetric heating of Janus colloids adsorbed at water-oil interfaces and realize active micrometric "Marangoni surfers." The coupling of temperature and surfactant concentration gradients generates Marangoni stresses leading to self-propulsion. Particle velocities span 4 orders of magnitude, from microns/s to cm/s, depending on laser power and surfactant concentration. Experiments are rationalized by finite elements simulations, defining different propulsion regimes relative to the magnitude of the thermal and solutal Marangoni stress components.

Information and motility exchange in collectives of active particles

We examine the interplay of motility and information exchange in a model of run-and-tumble active particles where the particle's motility is encoded as a bit of information that can be exchanged upon contact according to the rules of AND and OR logic gates in a circuit. Motile AND particles become non-motile upon contact with a non-motile particle. Conversely, motile OR particles remain motile upon collision with their non-motile counterparts. AND particles that have become non-motile additionally "reawaken", i.e., recover their motility, at a fixed rate μ, as in the SIS (susceptible, infected, susceptible) model of epidemic spreading, where an infected agent can become healthy again, but keeps no memory of the recent infection, hence it is susceptible to a renewed infection. For μ = 0, both AND and OR particles relax irreversibly to absorbing states of all non-motile or all motile particles, respectively. The relaxation kinetics is, however, faster for OR particles that remain active throughout the process. At finite μ, the AND dynamics is controlled by the interplay between reawakening and collision rates. The system evolves to a state of all motile particles (an absorbing state in the language of absorbing phase transitions) for μ > μc and to a mixed state with coexisting motile and non-motile particles (an active state in the language of absorbing phase transitions) for μ < μc. The final state exhibits a rich structure controlled by motility-induced aggregation. Our work can be relevant to biochemical signaling in motile bacteria, the spreading of epidemics and of social consensus, as well as light-controlled organization of active colloids.

Light-switchable propulsion of active particles with reversible interactions

Active systems such as microorganisms and self-propelled particles show a plethora of collective phenomena, including swarming, clustering, and phase separation. Control over the propulsion direction and switchability of the interactions between the individual self-propelled units may open new avenues in designing of materials from within. Here, we present a self-propelled particle system, consisting of half-gold-coated titania (TiO2) particles, in which we can quickly and on-demand reverse the propulsion direction, by exploiting the different photocatalytic activities on both sides. We demonstrate that the reversal in propulsion direction changes the nature of the hydrodynamic interaction from attractive to repulsive and can drive the particle assemblies to undergo both fusion and fission transitions. Moreover, we show these active colloids can act as nucleation sites, and switch rapidly the interactions between active and passive particles, leading to reconfigurable assembly and disassembly. Our experiments are qualitatively described by a minimal hydrodynamic model.

A simple microswimmer model inspired by the general equation for nonequilibrium reversible-irreversible coupling

A simple mean-field microswimmer model is presented. The model is inspired by the nonequilibrium thermodynamics of multi-component fluids that undergo chemical reactions. These thermodynamics can be rigorously described in the context of the GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) framework. More specifically, this approach was recently applied to non-ideal polymer solutions [T. Indei and J. D. Schieber, J. Chem. Phys. 146, 184902 (2017)]. One of the species of the solution is an unreactive polymer chain represented by the bead-spring model. Using this detailed description as inspiration, we then make several simplifying assumptions to obtain a mean-field model for a Janus microswimmer. The swimmer model considered here consists of a polymer dumbbell in a sea of reactants. One of the beads of the dumbbell is allowed to act as a catalyst for a chemical reaction between the reactants. We show that the mean-squared displacement (MSD) of the center of mass of this Janus dumbbell exhibits ballistic behavior at time scales at which the concentration of the reactant is large. The time scales at which the ballistic behavior is observed in the MSD coincide with the time scales at which the cross-correlation between the swimmer's orientation and the direction of its displacement exhibits a maximum. Since the swimmer model was inspired by the GENERIC framework, it is possible to ensure that the entropy generation is always positive, and therefore, the second law of thermodynamics is obeyed.

Formation of stable and responsive collective states in suspensions of active colloids

Many animal species organise into disordered swarms, polarised flocks or swirls to protect from predators or optimise foraging. Previous studies suggest that such collective states are related to a critical point, which could explain their balance between robustness to noise and high responsiveness regarding external perturbations. Here we provide experimental evidence for this idea by investigating the stability of swirls formed by light-responsive active colloids which adjust their individual motion to positions and orientations of neighbours. Because their behaviour can be precisely tuned, controlled changes between different collective states can be achieved. During the transition between stable swirls and swarms we observe a maximum of the group's susceptibility indicating the vicinity of a critical point. Our results support the idea of system-independent organisation principles of collective states and provide useful strategies for the realisation of responsive yet stable ensembles in microrobotic systems.

Direct-imaging of light-driven colloidal Janus particles in weightlessness

We describe a highly integrated automated experiment module that allows us to investigate the active Brownian motion of light-driven colloidal Janus-particle suspensions. The module RAMSES (RAndom Motion of SElf-propelled particles in Space) is designed for the sounding rocket platform MAPHEUS (MAterialPHysikalische Experimente Unter Schwerelosigkeit). It allows us to perform experiments under weightlessness conditions in order to avoid sedimentation of the Janus particles and thus to study the spatially three-dimensional dynamics in the suspension. The module implements a newly developed strong homogeneous light source to excite self-propulsion in the Janus particles. The light source is realized through an array of high-power light-emitting diodes and replaces the conventional laser source, thus reducing heat dissipation and spatial extension of the experiment setup. The rocket module contains ten independent sample cells in order to ease the systematic study of the effect of control parameters such as light intensity or particle concentration and size in a single sounding-rocket flight. For each sample cell, transmitted light intensities are stored for postflight analysis in terms of differential dynamical microscopy.

Active particles sense micromechanical properties of glasses

Understanding the mechanical properties of glasses is a great scientific challenge. A powerful technique to study the material response on a microscopic scale is microrheology, in which one analyses the translational dynamics of an externally driven probe particle. Here we show that the translational and rotational dynamics of a self-propelled probe particle with an unconstrained orientational motion can be used to gather information about the mechanical properties of a colloidal glassy system. We find that its rotational diffusion coefficient continuously increases towards the glass transition and drops down in the glassy state. Such unexpected behaviour demonstrates a strong coupling mechanism between the orientation of the active probe particle and the glassy structure, which can be well described by a simple rheological model. Our results suggest that active probe particles may be useful for the micromechanical characterization of complex materials.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Generalized Ornstein-Uhlenbeck model for active motion

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E 90, 012111 (2014)10.1103/PhysRevE.90.012111]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.

Illumination-induced motion of a Janus nanoparticle in binary solvents

Using a fluid particle dynamics method we numerically investigate the motion of a spherical Janus particle suspended in a binary liquid mixture, which emerges under heating of one-half of a colloid surface. The method treats simultaneously the flow of the solvent and the motion of the particle, hence, the velocity of the particle can be computed directly. Our approach accounts for a phenomenon of critical adsorption, therefore, a particle that is adsorptionwise nonneutral is always completely covered by an adsorption layer (droplet). In order to establish the mechanism of self-propulsion, we study systematically various combinations of adsorption preference on both hemispheres of the Janus colloid as function of the heating power for symmetric and nonsymmetric binary solvents and for various particle sizes in three spatial dimensions. Only for a particle for which the heated hemisphere is neutral whereas the other hemisphere prefers one of the two components of the mixture does the reversal of the direction of motion occur. The particle self-propels much faster in nonsymmetric binary solvents. Self-propulsion originates from a gradient of mechanical stress, in a way similar to the Marangoni effect. This stress is not localized at the edge but distributed within the whole droplet. We compare our findings with the experimental observations and other theoretical results.

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.

Group formation and cohesion of active particles with visual perception-dependent motility

Group formation in living systems typically results from a delicate balance of repulsive, aligning, and attractive interactions. We found that a mere motility change of the individuals in response to the visual perception of their peers induces group formation and cohesion. We tested this principle in a real system of active particles whose motilities are controlled by an external feedback loop. For narrow fields of view, individuals gathered into cohesive nonpolarized groups without requiring active reorientations. For wider fields of view, cohesion could be achieved by lowering the response threshold. We expect this motility-induced cohesion mechanism to be relevant not only for the self-organization of living systems, but also for the design of robust and scalable autonomous systems.

Diffusing wave paradox of phototactic particles in traveling light pulses

Cells navigate through complex surroundings by following cues from their environment. A prominent example is Dictyostelium, which is directed by chemotaxis towards regions with higher concentrations. In the presence of traveling chemical waves, however, amoebae migrate counter to the running wave. Such behavior, referred to as diffusing wave paradox, suggests the existence of adaptation and directional memory. Here we experimentally investigate the response of phototactic self-propelled microparticles to traveling light-pulses. Despite their entirely memory-less (i.e., strictly local) response to the environment, we observe the same phenomenological behavior, i.e., particle motion counter to the pulse direction. Our findings are supported by a minimal model which considers active particle reorientations within local light gradients. The complex and robust behavior of synthetic active particles to spatially and temporally varying stimuli enables new strategies for achieving collective behavior and can be used for the design of micro-robotic systems with limited signal-processing capabilities.

Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast

We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity, and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one species is localized close to the minimum and the other one is centered around in an outer shell. For a very strong aligning torque, there is an exact mapping onto an equilibrium system in an effective external potential that is minimal at the intensity minima. This external potential is similar to (height-dependent) gravity such that one can define effective "heaviness" of the self-propelled particles. In analogy to shaken granular matter in gravity, we define a "colloidal Brazil nut effect" if the heavier particles are floating on top of the lighter ones. Using extensive Brownian dynamics simulations, we identify system parameters for the active colloidal Brazil nut effect to occur and explain it based on a generalized Archimedes' principle within the effective equilibrium model: heavy particles are levitated in a dense fluid of lighter particles if their effective mass density is lower than that of the surrounding fluid. We also perform real-space experiments on light-activated self-propelled colloidal mixtures which confirm the theoretical predictions.

Which interactions dominate in active colloids?

Despite mounting evidence that the same gradients, which active colloids use for swimming, induce important cross-interactions (phoretic interactions), they are still ignored in most many-body descriptions, perhaps to avoid complexity and a zoo of unknown parameters. Here we derive a simple model, which reduces phoretic far-field interactions to a pair-interaction whose strength is mainly controlled by one genuine parameter (swimming speed). The model suggests that phoretic interactions are generically important for autophoretic colloids (unless effective screening of the phoretic fields is strong) and should dominate over hydrodynamic interactions for the typical case of half-coating and moderately nonuniform surface mobilities. Unlike standard minimal models, but in accordance with canonical experiments, our model generically predicts dynamic clustering in active colloids at a low density. This suggests that dynamic clustering can emerge from the interplay of screened phoretic attractions and active diffusion.