Purely hydrodynamic ordering of rotating disks at a finite Reynolds number

Tunable colloidal spinners: Active chirality and hydrodynamic interactions governed by rotating external electric fields

The rotational dynamics of microparticles in liquids have a wide range of applications, including chemical microreactors, biotechnologies, microfluidic devices, tunable heat and mass transfer, and fundamental understanding of chiral active soft matter which refers to systems composed of particles that exhibit a handedness in their rotation, breaking mirror symmetry at the microscopic level. Here, we report on the study of two effects in colloids in rotating electric fields: (i) the rotation of individual colloidal particles in rotating electric field and related to that (ii) precession of pairs of particles. We show that the mechanism responsible for the rotation of individual particles is related to the time lag between the external field applied to the particle and the particle polarization. Using numerical simulations and experiments with silica particles in a water-based solvent, we prove that the observed rotation of particle pairs and triplets is governed by the tunable rotation of individual particles and can be explained and described by the action of hydrodynamic forces. Our findings demonstrate that colloidal suspensions in rotating electric fields, under some conditions, represent a novel class of chiral soft active matter-tunable colloidal spinners. The experiments and the corresponding theoretical framework we developed open novel prospects for future studies of these systems and for their potential applications.

Collective Hall current in chiral active fluids: Coupling of phase and mass transport through traveling bands

Active fluids composed of constituents that are constantly driven away from thermal equilibrium can support spontaneous currents and can be engineered to have unconventional transport properties. Here, we report the emergence of (meta)stable traveling bands in computer simulations of aligning circle swimmers. These bands are different from polar flocks and, through coupling phase with mass transport, induce a bulk particle current with a component perpendicular to the propagation direction, thus giving rise to a collective Hall (or Magnus) effect. Traveling bands require sufficiently small orbits and undergo a discontinuous transition into a synchronized state with transient polar clusters for large orbital radii. Within a minimal hydrodynamic theory, we show that the bands can be understood as nondispersive soliton solutions fully accounting for the numerically observed properties.

Shaping active matter from crystalline solids to active turbulence

Active matter drives its constituent agents to move autonomously by harnessing free energy, leading to diverse emergent states with relevance to both biological processes and inanimate functionalities. Achieving maximum reconfigurability of active materials with minimal control remains a desirable yet challenging goal. Here, we employ large-scale, agent-resolved simulations to demonstrate that modulating the activity of a wet phoretic medium alone can govern its solid-liquid-gas phase transitions and, subsequently, laminar-turbulent transitions in fluid phases, thereby shaping its emergent pattern. These two progressively emerging transitions, hitherto unreported, bring us closer to perceiving the parallels between active matter and traditional matter. Our work reproduces and reconciles seemingly conflicting experimental observations on chemically active systems, presenting a unified landscape of phoretic collective dynamics. These findings enhance the understanding of long-range, many-body interactions among phoretic agents, offer new insights into their non-equilibrium collective behaviors, and provide potential guidelines for designing reconfigurable materials.

Acoustically Powered Nano- and Microswimmers: From Individual to Collective Behavior

Micro- and nanoscopic particles that swim autonomously and self-assemble under the influence of chemical fuels and external fields show promise for realizing systems capable of carrying out large-scale, predetermined tasks. Different behaviors can be realized by tuning swimmer interactions at the individual level in a manner analogous to the emergent collective behavior of bacteria and mammalian cells. However, the limited toolbox of weak forces with which to drive these systems has made it difficult to achieve useful collective functions. Here, we review recent research on driving swimming and particle self-organization using acoustic fields, which offers capabilities complementary to those of the other methods used to power microswimmers. With either chemical or acoustic propulsion (or a combination of the two), understanding individual swimming mechanisms and the forces that arise between individual particles is a prerequisite to harnessing their interactions to realize collective phenomena and macroscopic functionality. We discuss here the ingredients necessary to drive the motion of microscopic particles using ultrasound, the theory that describes that behavior, and the gaps in our understanding. We then cover the combination of acoustically powered systems with other cross-compatible driving forces and the use of ultrasound in generating collective behavior. Finally, we highlight the demonstrated applications of acoustically powered microswimmers, and we offer a perspective on the state of the field, open questions, and opportunities. We hope that this review will serve as a guide to students beginning their work in this area and motivate others to consider research in microswimmers and acoustic fields.

Extreme Spontaneous Deformations of Active Crystals

We demonstrate that two-dimensional crystals made of active particles can experience extremely large spontaneous deformations without melting. Using particles mostly interacting via pairwise repulsive forces, we show that such active crystals maintain long-range bond order and algebraically decaying positional order, but with an exponent η not limited by the 1/3 bound given by the (equilibrium) KTHNY theory. We rationalize our findings using linear elastic theory and show the existence of two well-defined effective temperatures quantifying respectively large-scale deformations and bond-order fluctuations. The root of these phenomena lies in the sole time-persistence of the intrinsic axes of particles, and they should thus be observed in many different situations.

Hydrodynamic spin-orbit coupling in asynchronous optically driven micro-rotors

Vortical flows of rotating particles describe interactions ranging from molecular machines to atmospheric dynamics. Yet to date, direct observation of the hydrodynamic coupling between artificial micro-rotors has been restricted by the details of the chosen drive, either through synchronization (using external magnetic fields) or confinement (using optical tweezers). Here we present a new active system that illuminates the interplay of rotation and translation in free rotors. We develop a non-tweezing circularly polarized beam that simultaneously rotates hundreds of silica-coated birefringent colloids. The particles rotate asynchronously in the optical torque field while freely diffusing in the plane. We observe that neighboring particles orbit each other with an angular velocity that depends on their spins. We derive an analytical model in the Stokes limit for pairs of spheres that quantitatively explains the observed dynamics. We then find that the geometrical nature of the low Reynolds fluid flow results in a universal hydrodynamic spin-orbit coupling. Our findings are of significance for the understanding and development of far-from-equilibrium materials.

Collective Flows Drive Cavitation in Spinner Monolayers

Hydrodynamic interactions can give rise to a collective motion of rotating particles. This, in turn, can lead to coherent fluid flows. Using large scale hydrodynamic simulations, we study the coupling between these two in spinner monolayers at weakly inertial regime. We observe an instability, where the initially uniform particle layer separates into particle void and particle rich areas. The particle void region corresponds to a fluid vortex, and it is driven by a surrounding spinner edge current. We show that the instability originates from a hydrodynamic lift force between the particle and fluid flows. The cavitation can be tuned by the strength of the collective flows. It is suppressed when the spinners are confined by a no-slip surface, and multiple cavity and oscillating cavity states are observed when the particle concentration is reduced.

Three-Dimensionally Complex Phase Behavior and Collective Phenomena in Mixtures of Acoustically Powered Chiral Microspinners

The process of dynamic self-organization of small building blocks is fundamental to the emergent function of living systems and is characteristic of their out-of-equilibrium homeostasis. The ability to control the interactions of synthetic particles in large groups could lead to the realization of analogous macroscopic robotic systems with microscopic complexity. Rotationally induced self-organization has been observed in biological systems and modeled theoretically, but studies of fast, autonomously moving synthetic rotors remain rare. Here, we report switchable, out-of-equilibrium hydrodynamic assembly and phase separation in suspensions of acoustically powered chiral microspinners. Semiquantitative modeling suggests that three-dimensionally (3D) complex spinners interact through viscous and weakly inertial (streaming) flows. The interactions between spinners were studied over a range of densities to construct a phase diagram, which included gaseous dimer pairing at low density, collective rotation and multiphase separation at intermediate densities, and ultimately jamming at high density. The 3D chirality of the spinners leads to self-organization in parallel planes, forming a three-dimensionally hierarchical system that goes beyond the 2D systems that have so far been modeled computationally. Dense mixtures of spinners and passive tracer particles also show active-passive phase separation. These observations are consistent with recent theoretical predictions of the hydrodynamic coupling between rotlets generated by autonomous spinners and provide an exciting experimental window to the study of colloidal active matter and microrobotic systems.

Tunable collective dynamics of ellipsoidal Quincke particles

Collective behaviors in active systems become dramatically complicated in the presence of chirality. In this study, we show that ellipsoidal Quincke particles driven by an electric field exhibit flexible and tunable chirality because of the tilting of the spinning axis. As the tilting torque decreases with the increase of angular speed, the motion of individual particles transforms from localized circle motion to global rolling. However, because of the anisotropic shape and the resulting anisotropic polar interactions, it is dynamically easier for ellipsoids to bind and form rotating structures rather than to align their velocities. In dense systems, the suppression of velocity aligning produces transient dense clusters which produce dynamic heterogeneity. The formation and dissociation of dense clusters prohibit the emergence of large-scale collective motions and limit the amplitude of density fluctuations. These findings demonstrate that collective dynamics and thus the scale of density fluctuations in active systems with tunable chirality can be well controlled. This has potential applications in exploring disordered hyperuniform states.

Probing Fast Transformation of Magnetic Colloidal Microswarms in Complex Fluids

The rapidly transformed morphology of natural swarms enables fast response to environmental changes. Artificial microswarms can reconfigure their swarm patterns like natural swarms, which have drawn extensive attention due to their active adaptability in complex environments. However, as a prerequisite for biomedical applications of microswarms in confined environments, achieving on-demand control of pattern transformation rates remains a challenge. In this work, we report a strategy for optimizing pattern transformation rates of colloidal microswarms by coordinating the inner interactions. The influences of magnetic field parameters on pattern transformation rates are theoretically and experimentally studied, which elucidates the mechanism for optimal transformation rate control. The feasibility of the strategy is then validated in viscous Newtonian fluids and non-Newtonian biofluids. Moreover, the strategy is further validated in dynamic flow environments, exhibiting a promising future for practical applications in targeted delivery tasks with an optimal pattern transformation manner.

Hydrodynamic synchronization and clustering in ratcheting colloidal matter

Ratchet transport systems are widespread in physics and biology; however, the effect of the dispersing medium in the collective dynamics of these out-of-equilibrium systems has been often overlooked. We show that, in a traveling wave magnetic ratchet, long-range hydrodynamic interactions (HIs) produce a series of remarkable phenomena on the transport and assembly of interacting Brownian particles. We demonstrate that HIs induce the resynchronization with the traveling wave that emerges as a "speed-up" effect, characterized by a net raise of the translational speed, which doubles that of single particles. When competing with dipolar forces and the underlying substrate symmetry, HIs promote the formation of clusters that grow perpendicular to the driving direction. We support our findings both with Langevin dynamics and with a theoretical model that accounts for the fluid-mediated interactions. Our work illustrates the role of the dispersing medium on the dynamics of driven colloidal matter and unveils the growing process and cluster morphologies above a periodic substrate.

Spontaneously rotating clusters of active droplets

We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while spinning around the plane normal. This effect exists for symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming an ordered cluster, the droplets cooperatively suppress their chaotic dynamics and turn the transient instability into a steady rotational state. We analyse the collective rotational dynamics as a function of droplet activity and cluster size and further propose that the stable collective rotation in the cluster is caused by a cooperative coupling between the rotational modes of individual droplets in the cluster.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Hyperuniformity and phase enrichment in vortex and rotor assemblies

Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such rotors are found in the natural world spanning vastly disparate length scales — from the rotor proteins in cellular membranes to models of atmospheric dynamics. Here we show that an initially random distribution of either driven rotors in a viscous membrane, or ideal vortices with minute perturbations, spontaneously self assemble into a distinct arrangement. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in prominent structural states. We find that the rotationally invariant interactions isotropically suppress long-wavelength fluctuations — a hallmark of a disordered hyperuniform material. With increasing area fraction, the system orders into a hexagonal lattice. In mixtures of two co-rotating populations, the stronger population will gain order from the other and both will become phase enriched. Finally, we show that classical 2D point vortex systems arise as exact limits of the experimentally accessible microscopic membrane rotors, yielding a new system through which to study topological defects.

Rotor-like dynamics is observed in many natural systems, from the rotor proteins in cellular membranes to atmospheric models. Here, the authors uncover geometrical conservation laws that limit distribution of driven rotors in a membrane or a soap film and allow to predict their structural states.

Order and information in the patterns of spinning magnetic micro-disks at the air-water interface

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules hampers the ability of these systems to serve as model systems for further exploring the links between information and structures. Here, we use, as a model experimental system, hundreds of spinning magnetic micro-disks self-organizing at the air-water interface to generate various spatiotemporal patterns with varying degrees of order. Using the neighbor distance as the information-bearing variable, we demonstrate the links among information, structure, and interactions. We establish a direct link between information and structure without using explicit knowledge of interactions. Last, we show that the Shannon entropy by neighbor distances is a powerful observable in characterizing structural changes. Our findings are relevant for analyzing natural self-organizing systems and for designing collective robots.

Chiral Active Hexatics: Giant Number Fluctuations, Waves, and Destruction of Order

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

Two-Phase Crystallization in a Carpet of Inertial Spinners

We study the dynamics of torque driven spherical spinners settled on a surface, and demonstrate that hydrodynamic interactions at finite Reynolds numbers can lead to a concentration dependent and nonuniform crystallization. At semidilute concentrations, we observe a rapid formation of a uniform hexagonal structure in the spinner monolayer. We attribute this to repulsive hydrodynamic interactions created by the secondary flow of the spinning particles. Increasing the surface coverage leads to a state with two coexisting spinner densities. The uniform hexagonal structure deviates into a high density crystalline structure surrounded by a continuous lower density hexatically ordered state. We show that this phase separation occurs due to a nonmonotonic hydrodynamic repulsion, arising from a concentration dependent spinning frequency.

Reconfigurable emergent patterns in active chiral fluids

Active fluids comprised of autonomous spinning units injecting energy and angular momentum at the microscopic level represent a promising platform for active materials design. The complexity of the accessible dynamic states is expected to dramatically increase in the case of chiral active units. Here, we use shape anisotropy of colloidal particles to introduce chiral rollers with activity-controlled curvatures of their trajectories and spontaneous handedness of their motion. By controlling activity through variations of the energizing electric field, we reveal emergent dynamic phases, ranging from a gas of spinners to aster-like vortices and rotating flocks, with either polar or nematic alignment of the particles. We demonstrate control and reversibility of these dynamic states by activity. Our findings provide insights into the onset of spatial and temporal coherence in a broad class of active chiral systems, both living and synthetic, and hint at design pathways for active materials based on self-organization and reconfigurability.

Reconfigurable structure and tunable transport in synchronized active spinner materials

Ensembles of actuated colloids are excellent model systems to explore emergent out-of-equilibrium structures, complex collective dynamics, and design rules for the next generation materials. Here, we demonstrate that ferromagnetic microparticles suspended at an air-water interface and energized by an external rotating magnetic field spontaneously form dynamic ensembles of synchronized spinners in a certain range of the excitation field parameters. Each spinner generates strong hydrodynamic flows, and collective interactions of the multiple spinners promote a formation of dynamic lattices. On the basis of experiments and simulations, we reveal structural transitions from liquid to nearly crystalline states in this novel active spinner material and demonstrate that dynamic spinner lattices are reconfigurable, capable of self-healing behavior and that the transport of embedded inert cargo particles can be remotely tuned by the parameters of the external excitation field. Our findings provide insights into the behavior of active spinner materials with reconfigurable structural order and tunable functionalities.

Robust boundary flow in chiral active fluid

We perform experiments on an active chiral fluid system of self-spinning rotors in a confining boundary. Along the boundary, actively rotating rotors collectively drive a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. Flow strength initially increases then decreases with rotor density (quantified by area fraction ϕ); peak strength appears around a density ϕ=0.65. Boundary curvature plays an important role: flow near a concave boundary is stronger than that near a flat or convex boundary in the same confinements. Our experimental results in all cases can be reproduced by a continuum theory with single free fitting parameter, which describes the frictional property of the boundary. Our results support the idea that boundary flow in active chiral fluid is topologically protected; such robust flow can be used to develop materials with novel functions.

Rotating Membrane Inclusions Crystallize Through Hydrodynamic and Steric Interactions

We show that rotating membrane inclusions can crystallize due to combined hydrodynamic and steric interactions. Alone, steric repulsion of unconfined particles, even with thermal fluctuations, does not lead to crystallization, nor do rotational hydrodynamic interactions which allow only a marginally stable lattice. Hydrodynamic interactions enable particles to explore states inaccessible to a nonrotational system, yet, unlike Brownian motion, Hamiltonian conservation confines the ensemble which, when combined with steric interactions, anneals into a stable crystal state.

Physics driven behavioural clustering of free-falling paper shapes

Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour.

Disordering, clustering, and laning transitions in particle systems with dispersion in the Magnus term

We numerically examine a two-dimensional system of repulsively interacting particles with dynamics that are governed by both a damping term and a Magnus term. The magnitude of the Magnus term has one value for half of the particles and a different value for the other half of the particles. In the absence of a driving force, the particles form a triangular lattice, while when a driving force is applied, we find that there is a critical drive above which a Magnus-induced disordering transition can occur even if the difference in the Magnus term between the two particle species is as small as one percent. The transition arises due to the different Hall angles of the two species, which causes their motion to decouple at the critical drive. At higher drives, the disordered state can undergo both species and density phase separation into a density-modulated stripe that is oriented perpendicular to the driving direction. We observe several additional phases that occur as a function of drive and Magnus force disparity, including a variety of density-modulated diagonal-laned phases. In general, we find a much richer variety of states compared to systems of oppositely driven overdamped Yukawa particles. We discuss the implications of our work for skyrmion systems, where we predict that even for small skyrmion dispersities, a drive-induced disordering transition can occur along with clustering phases and pattern-forming states.

Cargo carrying bacteria at interfaces

The displacements of ensembles of colloids at the interface between oil and suspensions of the bacterium Pseudomonas aeruginosa PA14ΔpelA indicate enhanced colloid mobilities and apparently diffusive motion driven by interactions with the bacteria. However, inspection of individual trajectories of ∼500 particles reveals prolonged, directed displacements inconsistent with purely hydrodynamic interactions between swimming bacteria and colloids. Analysis of the properties of colloid paths indicates trajectories can be sorted into four distinct categories, including diffusive, persistent, curly, and mixed trajectory types. Non-diffusive trajectories are the norm, comprising 2/3 of the observed trajectories. Imaging of colloids in the interface reveals anisotropic assemblies formed by colloids decorated with one or more adhered bacteria that drive the colloids along these paths. The trajectories and enhanced transport result from individual colloids being moved as cargo by these adhered bacteria. The implications of these structures and open questions for interfacial transport are discussed and related to the active colloid literature.

Blood Crystal: Emergent Order of Red Blood Cells Under Wall-Confined Shear Flow

Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report numerical simulations and an analytical model revealing that deformable particles and, in particular, red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The pattern wavelength concurs well with our experimental observations. The order is of a pure hydrodynamic and inertialess origin, and it emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls that drives deformable cells towards the channel midplane and (ii) intercellular hydrodynamic interactions that can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on the RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order.

Physical foundation of the fluid particle dynamics method for colloid dynamics simulation

Colloid dynamics is significantly influenced by many-body hydrodynamic interactions mediated by a suspending fluid. However, theoretical and numerical treatments of such interactions are extremely difficult. To overcome this situation, we developed a fluid particle dynamics (FPD) method [H. Tanaka and T. Araki, Phys. Rev. Lett., 2000, 35, 3523], which is based on two key approximations: (i) a colloidal particle is treated as a highly viscous particle and (ii) the viscosity profile is described by a smooth interfacial profile function. Approximation (i) makes our method free from the solid-fluid boundary condition, significantly simplifying the treatment of many-body hydrodynamic interactions while satisfying the incompressible condition without the Stokes approximation. Approximation (ii) allows us to incorporate an extra degree of freedom in a fluid, e.g., orientational order and concentration, as an additional field variable. Here, we consider two fundamental problems associated with these approximations. One is the introduction of thermal noise and the other is the incorporation of coupling of the colloid surface with an order parameter introduced into a fluid component, which is crucial when considering colloidal particles suspended in a complex fluid. Here, we show that our FPD method makes it possible to simulate colloid dynamics properly while including full hydrodynamic interactions, inertia effects, incompressibility, thermal noise, and additional degrees of freedom of a fluid, which may be relevant for wide applications in colloidal and soft matter science.

Advances in colloidal manipulation and transport via hydrodynamic interactions

In this review article, we highlight many recent advances in the field of micromanipulation of colloidal particles using hydrodynamic interactions (HIs), namely solvent mediated long-range interactions. At the micrsocale, the hydrodynamic laws are time reversible and the flow becomes laminar, features that allow precise manipulation and control of colloidal matter. We focus on different strategies where externally operated microstructures generate local flow fields that induce the advection and motion of the surrounding components. In addition, we review cases where the induced flow gives rise to hydrodynamic bound states that may synchronize during the process, a phenomenon essential in different systems such as those that exhibit self-assembly and swarming.

Emergent hydrodynamic bound states between magnetically powered micropropellers

Hydrodynamic interactions (HIs), namely, solvent-mediated long-range interactions between dispersed particles, play a crucial role in the assembly and dynamics of many active systems, from swimming bacteria to swarms of propelling microrobots. We experimentally demonstrate the emergence of long-living hydrodynamic bound states between model microswimmers at low Reynolds numbers. A rotating magnetic field forces colloidal hematite microparticles to translate at a constant and frequency-tunable speed close to a bounding plane in a viscous fluid. At high driving frequency, HIs dominate over magnetic dipolar ones, and close propelling particles couple into bound states by adjusting their translational speed to optimize the transport of the pair. The physical system is described by considering the HIs with the boundary surface and the effect of gravity, providing an excellent agreement with the experimental data for all the range of parameters explored. Moreover, we show that in dense suspensions, these bound states can be extended to one-dimensional arrays of particles assembled by the sole HIs. Our results manifest the importance of the boundary surface in the interaction and dynamics of confined propelling microswimmers.

Active turbulence in a gas of self-assembled spinners

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air-liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generated advection flows. The same-chirality spinners (clockwise or counterclockwise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. Our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale.

Nonequilibrium fluctuations of lipid membranes by the rotating motor protein F1F0-ATP synthase

The shape of biological membranes is constantly remodeled and maintained out of equilibrium by active proteins. The functional capacity of membrane deformation is mainly determined by the mechanical interplay between protein activity and bending elasticity. In our experiments, we find that ATP synthase, a rotating membrane protein that synthesizes the biochemical energy in cells through proton-pumping activity across the membrane, promotes localized nonequilibrium membrane fluctuations when reconstituted in giant lipid vesicles. The large membrane deformations emerge from the pumping action of rotating proteins clustered at specific emplacements in the membrane. Our results pave the way to new experimental realizations to explore the collective effects of rotating ATP synthases and their possible biological implications for biomembrane organization and protein functionality.

ATP synthase is a rotating membrane protein that synthesizes ATP through proton-pumping activity across the membrane. To unveil the mechanical impact of this molecular active pump on the bending properties of its lipid environment, we have functionally reconstituted the ATP synthase in giant unilamellar vesicles and tracked the membrane fluctuations by means of flickering spectroscopy. We find that ATP synthase rotates at a frequency of about 20 Hz, promoting large nonequilibrium deformations at discrete hot spots in lipid vesicles and thus inducing an overall membrane softening. The enhanced nonequilibrium fluctuations are compatible with an accumulation of active proteins at highly curved membrane sites through a curvature−protein coupling mechanism that supports the emergence of collective effects of rotating ATP synthases in lipid membranes.

Dynamic and programmable self-assembly of micro-rafts at the air-water interface

Dynamic self-assembled material systems constantly consume energy to maintain their spatiotemporal structures and functions. Programmable self-assembly translates information from individual parts to the collective whole. Combining dynamic and programmable self-assembly in a single platform opens up the possibilities to investigate both types of self-assembly simultaneously and to explore their synergy. This task is challenging because of the difficulty in finding suitable interactions that are both dissipative and programmable. We present a dynamic and programmable self-assembling material system consisting of spinning at the air-water interface circular magnetic micro-rafts of radius 50 μm and with cosinusoidal edge-height profiles. The cosinusoidal edge-height profiles not only create a net dissipative capillary repulsion that is sustained by continuous torque input but also enable directional assembly of micro-rafts. We uncover the layered arrangement of micro-rafts in the patterns formed by dynamic self-assembly and offer mechanistic insights through a physical model and geometric analysis. Furthermore, we demonstrate programmable self-assembly and show that a 4-fold rotational symmetry encoded in individual micro-rafts translates into 90° bending angles and square-based tiling in the assembled structures of micro-rafts. We anticipate that our dynamic and programmable material system will serve as a model system for studying nonequilibrium dynamics and statistical mechanics in the future.

Emergence of collective dynamical chirality for achiral active particles

Emergence of collective dynamical chirality (CDC) at mesoscopic scales plays a key role in many formation processes of chiral structures in nature, which may also provide possible routines for people to fabricate complex chiral architectures. So far, most of the reported CDCs have been found in systems of active objects with individual structure chirality or/and dynamical chirality, and whether CDC can arise from simple and achiral units is still an attractive mystery. Here, we report a spontaneous formation of CDC in a system of both dynamically and structurally achiral particles motivated by active motion of cells adhered onto a substrate. Active motion, confinement and hydrodynamic interaction are found to be the three key factors. Detailed analysis shows that the system can support abundant collective dynamical behaviors, including rotating droplets, rotating bubbles, CDC oscillations, arrays of collective rotations, and interesting transitions such as chirality transition, structure transition and state reentrance.

Fission and fusion scenarios for magnetic microswimmer clusters

Fission and fusion processes of particle clusters occur in many areas of physics and chemistry from subnuclear to astronomic length scales. Here we study fission and fusion of magnetic microswimmer clusters as governed by their hydrodynamic and dipolar interactions. Rich scenarios are found that depend crucially on whether the swimmer is a pusher or a puller. In particular a linear magnetic chain of pullers is stable while a pusher chain shows a cascade of fission (or disassembly) processes as the self-propulsion velocity is increased. Contrarily, magnetic ring clusters show fission for any type of swimmer. Moreover, we find a plethora of possible fusion (or assembly) scenarios if a single swimmer collides with a ringlike cluster and two rings spontaneously collide. Our predictions are obtained by computer simulations and verifiable in experiments on active colloidal Janus particles and magnetotactic bacteria.

Spatiotemporal order and emergent edge currents in active spinner materials

Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion (i.e., spinning without walking) remains less explored. Here, we numerically and theoretically investigate the behavior of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-assemble into a triangular lattice with their orientations phase-locked into spatially periodic phases. The phase-locked patterns form dynamical analogs of the ground states of various spin models, transitioning from the three-state Potts antiferromagnet at low densities to the striped herringbone phase of planar quadrupoles at higher densities. As the density is raised further, the competition between active rotations and interactions leads to melting of the active spinner crystal. Emergent edge currents, whose direction is set by the chirality of the active spinning, arise as a nonequilibrium signature of the transition to the active spinner liquid and vanish when the system eventually undergoes kinetic arrest at very high densities. Our findings may be realized in systems ranging from liquid crystal and colloidal experiments to tabletop realizations using macroscopic chiral grains.

Dynamics of inert spheres in active suspensions of micro-rotors

Inert particles suspended in active fluids of self-propelled particles are known to often exhibit enhanced diffusion and novel coherent structures. Here we numerically investigate the dynamical behavior and self-organization in a system consisting of passive and actively rotating spheres of the same size. The particles interact through direct collisions and the fluid flows generated as they move. In the absence of passive particles, three states emerge in a binary mixture of spinning spheres depending on particle fraction: a dilute gas-like state where the rotors move chaotically, a phase-separated state where like-rotors move in lanes or vortices, and a jammed state where crystals continuously assemble, melt and move (K. Yeo, E. Lushi, and P. M. Vlahovska, Phys. Rev. Lett., 2015, 114, 188301). Passive particles added to the rotor suspension modify the system dynamics and pattern formation: while states identified in the pure active suspension still emerge, they occur at different densities and mixture proportions. The dynamical behavior of the inert particles is also non-trivially dependent on the system composition.

Elasticity-induced force reversal between active spinning particles in dense passive media

The self-organization of active particles is governed by their dynamic effective interactions. Such interactions are controlled by the medium in which such active agents reside. Here we study the interactions between active agents in a dense non-active medium. Our system consists of actuated, spinning, active particles embedded in a dense monolayer of passive, or non-active, particles. We demonstrate that the presence of the passive monolayer alters markedly the properties of the system and results in a reversal of the forces between active spinning particles from repulsive to attractive. The origin of such reversal is due to the coupling between the active stresses and elasticity of the system. This discovery provides a mechanism for the interaction between active agents in complex and structured media, opening up opportunities to tune the interaction range and directionality via the mechanical properties of the medium.

Physics out-of-equilibrium is necessary to understand a variety of interactions, for example in biological systems. Here, the authors show that the interactions between non-Brownian active spinning particles can change from repulsive to attractive depending on the properties of the surrounding passive medium.

Coarsening dynamics of binary liquids with active rotation

Active matter comprised of many self-driven units can exhibit emergent collective behaviors such as pattern formation and phase separation in both biological (e.g., mussel beds) and synthetic (e.g., colloidal swimmers) systems. While these behaviors are increasingly well understood for ensembles of linearly self-propelled "particles", less is known about the collective behaviors of active rotating particles where energy input at the particle level gives rise to rotational particle motion. A recent simulation study revealed that active rotation can induce phase separation in mixtures of counter-rotating particles in 2D. In contrast to that of linearly self-propelled particles, the phase separation of counter-rotating fluids is accompanied by steady convective flows that originate at the fluid-fluid interface. Here, we investigate the influence of these flows on the coarsening dynamics of actively rotating binary liquids using a phenomenological, hydrodynamic model that combines a Cahn-Hilliard equation for the fluid composition with a Navier-Stokes equation for the fluid velocity. The effect of active rotation is introduced though an additional force within the Navier-Stokes equations that arises due to gradients in the concentrations of clockwise and counter-clockwise rotating particles. Depending on the strength of active rotation and that of frictional interactions with the stationary surroundings, we observe and explain new dynamical behaviors such as "active coarsening" via self-generated flows as well as the emergence of self-propelled "vortex doublets". We confirm that many of the qualitative behaviors identified by the continuum model can also be found in discrete, particle-based simulations of actively rotating liquids. Our results highlight further opportunities for achieving complex dissipative structures in active materials subject to distributed actuation.

Effects of hydrodynamic interactions on the crystallization of passive and active colloidal systems

Effects of hydrodynamic interactions (HI) on the crystallization of a two-dimensional suspension of colloidal particles have been investigated, by applying a multiscale simulation method combining multiparticle collision dynamics for solvent particles with standard molecular dynamics for the colloids. For a passive system, we find that HI slightly shifts the freezing point to a smaller density, while the equilibrium structure remains nearly unchanged for a given global order parameter. For an active system, however, HI can significantly shift the freezing density to a higher value and the freezing transition becomes more continuous compared to its passive counterpart. This HI-induced shift becomes more remarkable with increasing propelling force. In addition, HI may also enhance the structural heterogeneities in an active system. For both passive and active systems, it is shown that HI can accelerate the relaxation process to their final steady state.

Collective dynamics in a binary mixture of hydrodynamically coupled microrotors

We study, numerically, the collective dynamics of self-rotating nonaligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence of large-scale dynamical patterns compared to those observed in dry systems. In dilute suspensions, the flow stirred by the rotors induces clustering of opposite-spin rotors, while at higher densities same-spin rotors phase separate. Above a critical rotor density, dynamic hexagonal crystals form. Our findings underscore the importance of inclusion of the many-body, long-range hydrodynamic interactions in predicting the phase behavior of active particles.