Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we identify how alignment between the neighboring particles is responsible for the interruption of the full phase separation. This experimental study, which provides the first large scale observation of the phase separation kinetics in active colloids, combined with single particle analysis of the local mechanisms, points towards the new physics observed when both alignment and short-range repulsions are present.
Designing microscopic and nanoscopic self-propelled particles and characterising their motion has become a major scientific challenge over the past decades. To this purpose, phoretic effects, namely propulsion mechanisms relying on local field gradients, have been the focus of many theoretical and experimental studies. In this review, we adopt a tutorial approach to present the basic physical mechanisms at stake in phoretic motion, and describe the different experimental works that lead to the fabrication of active particles based on this principle. We also present the collective effects obser…
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 spe…
Microorganisms are able to overcome the thermal randomness of their surroundings by harvesting energy to navigate in viscous fluid environments. In a similar manner, synthetic colloidal microswimmers are capable of mimicking complex biolocomotion by means of simple self-propulsion mechanisms. Although experimentally the speed of active particles can be controlled by e.g. self-generated chemical and thermal gradients, an in-situ change of swimming direction remains a challenge. In this work, we study self-propulsion of half-coated spherical colloids in critical binary mixtures and show that the…
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 studied the nonequilibrium dynamics of a binary solvent around it, using experiment and numerical simulations. For the latter we consider both a purely diffusive and a hydrodynamic model. All approaches indicate that the early time dynamics is purely diffusive and characterized by composition layers traveling with a constant speed from the surface of the colloid into the bulk. Subsequently, hydrodynamic effects set in an…
Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. In this article, the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved simulations. First, the interplay between activity and shear in the solid to the liquid transition of the suspension is analysed. While both self-propulsion and shear destroy order and melt the system b…
Thermal ratchets can extract useful work from random fluctuations. This is common in the molecular scale, such as motor proteins, and has also been used to achieve directional transport in microfluidic devices. In this work, we use the ratchet principle to induce net motility in an externally powered magnetic colloid, which otherwise shows reciprocal (back and forth) motion. The experimental system is based on ferromagnetic micro helices driven by oscillating magnetic fields, where the reciprocal symmetry is broken through asymmetric actuation timescales. The swimmers show net motility with an…
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 a pulsating transport whose strength and direction c…
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 f…
Combining model experiments and theory, we investigate the dense phases of polar active matter beyond the conventional flocking picture. We show that above a critical density flocks assembled from self-propelled colloids arrest their collective motion, lose their orientational order and form solids that actively rearrange their local structure while continuously melting and freezing at their boundaries. We establish that active solidification is a first-order dynamical transition: active solids nucleate, grow, and slowly coarsen until complete phase separation with the polar liquids they coexi…
We present the Brownian dynamics simulation of active colloidal suspension in two dimensions, where the self-propulsion speed of a colloid is regulated according to the local density sensed by it. The role of concentration-dependent motility on the phase-separation of colloids and their dynamics is investigated in detail. Interestingly, the system phase separates at a very low packing fraction ($Φ\approx 0.125$) at higher self-propulsion speeds ($\text{Pe}$), which coexists with a homogeneous phase and attains long-range crystalline order beyond a transition point. The transition point is quan…
Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.
The creation of synthetic systems that emulate the defining properties of living matter, such as motility, gradient-sensing, signalling and replication, is a grand challenge of biomimetics. Such imitations of life crucially contain active components that transform chemical energy into directed motion. These artificial realizations of motility point in the direction of a new paradigm in en- gineering, through the design of emergent behavior by manipulating properties at the scale of the individual components. Catalytic colloidal swimmers are a particularly promising example of such systems. Her…
We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions between the active rods, reminiscent of an artificial, semi-permeable membrane. This "active membrane" engulfes rods which are locally trapped in low-motility regions and thereby further enhances the trapping efficiency by self-organization, an effect which we call "self-encapsulation". Our results are gained by computer simulations of self-propelled rod mod…
Because of consuming energy to drive their motion, systems of active colloids are intrinsically out of equilibrium. In the past decade, a variety of intriguing dynamic patterns have been observed in systems of active colloids, and they offer a new platform for studying non-equilibrium physics, in which computer simulation and analytical theory have played an important role. Here we review the recent progress in understanding the dynamic assembly of active colloids by using numerical and analytical tools. We review the progress in understanding the motility induced phase separation in the past …
We have developed a lab work module where we teach undergraduate students how to quantify the dynamics of a suspension of microscopic particles, measuring and analyzing the motion of those particles at the individual level or as a group. Differential Dynamic Microscopy (DDM) is a relatively recent technique that precisely does that and constitutes an alternative method to more classical techniques such as dynamics light scattering (DLS) or video particle tracking (VPT). DDM consists in imaging a particle dispersion with a standard light microscope and a camera. The image analysis requires the …
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends explicitly on the particle orientation. In this case, the active particle moves faster when oriented along one direction and slower when oriented along another, leading to an anisotropic translational dynamics which is coupled to the particle's rotational diffusion. We propose a basic model of active Brownian motion for orientation-dependent motility. Based on this m…
We numerically investigate the competition between phase separation and dynamical arrest in a colloidal system interacting via a short ranged attractive potential. Equilibrium fluid configurations are quenched at two different temperatures below the critical temperature and followed during their time evolution. At the lowest studied $T$, the phase separation process is interrupted by the formation of an attractive glass in the dense phase. At the higher $T$, no arrest is observed and the phase separation process proceeds endless in the simulated time window. The final structure of the glass re…
Minimal models of active Brownian colloids consisting of self-propelled spherical particles with purely repulsive interactions have recently been identified as excellent quantitative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation. These systems do not exhibit aligned or flocking states, but do have a rich phase diagram, forming active gases, liquids and solids with novel mechanical properties. This article reviews recent advances in the understanding of such models, including the description of the active gas and its …
We study the dynamical steady-states of a monolayer of chemically active self-phoretic colloids as a function of packing fraction and self-propulsion speed by means of Brownian dynamics simulations. We focus on the case that a chemical field induces competing attractive positional and repulsive orientational interactions. Analyzing the distribution of cluster size and local density as well as the hexatic order parameter, we distinguish four distinct dynamical states which include collapsed, active gas, dynamical clustering, and motility-induced phase-separated states. The long-range chemical f…
Chemically active colloids move by creating gradients in the composition of the surrounding solution and by exploiting the differences in their interactions with the various molecular species in solution. If such particles move near boundaries, e.g., the walls of the container confining the suspension, gradients in the composition of the solution are also created along the wall. This give rise to chemi-osmosis (via the interactions of the wall with the molecular species forming the solution), which drives flows coupling back to the colloid and thus influences its motility. Employing an approxi…
Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles, and their motility induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separa…
Active colloids constitute a novel class of materials composed of colloidal-scale particles locally converting chemical energy into motility, mimicking micro-organisms. Evolving far from equilibrium, these systems display structural organizations and dynamical properties distinct from thermalized colloidal assemblies. Harvesting the potential of this new class of systems requires the development of a conceptual framework to describe these intrinsically nonequilibrium systems. We use sedimentation experiments to probe the nonequilibrium equation of state of a bidimensional assembly of active Ja…
We present a simple chemical strategy for the formation of a self-propelling cluster via the process of capture and assembly of passive colloids on the surface of a chemically active colloid. The two species of colloids that are isotropic and Brownian otherwise interact to form propelling cluster. With the help of coarse-grained numerical simulations, we show that a chemically active colloid can induce diffusiophoretic motility to nearby chemically inert colloids towards itself. This propulsion and then self-assembly can then lead to the formation of active cluster. We observe the formation of…
Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications - such as nanoantennas, plasmonic sensors, and nanocircuits - pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find…
We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial dimensions. By a stability analysis of the field theory, we obtain equations for the spinodal that describes the onset of a motility-induced instability leading to cluster formation in such mixtures. The prediction for the spinodal is found to be in good agreement with particle-resolved computer simulations. Furthermore, we show that in active-passive mixtures the spi…
Run-and-tumble (RNT) motion is a prominent locomotion strategy employed by many living microorganisms. It is characterized by straight swimming intervals (runs), which are interrupted by sudden reorientation events (tumbles). In contrast, directional changes of synthetic microswimmers (active particles, APs) are caused by rotational diffusion, which is superimposed with their translational motion and thus leads to rather continuous and slow particle reorientations. Here we demonstrate that active particles can also perform a swimming motion where translational and orientational changes are dis…
We create controllable active particles in the form of metal-dielectric Janus colloids which acquire motility through a nematic liquid crystal film by transducing the energy of an imposed perpendicular AC electric field. We achieve complete command over trajectories by varying field amplitude and frequency, piloting the colloids at will in the plane spanned by the axes of the particle and the nematic. The underlying mechanism exploits the sensitivity of electro-osmotic flow to the asymmetries of the particle surface and the liquid-crystal defect structure. We present a calculation of the dipol…
Non-aligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods and analytic theory to examine the kinetics of formation of the dense phase. Despite the intrinsically nonequilibrium nature of the phase transition, we show that the kinetics can be described using an approach analogous to equilibrium classical nucleation theory, governed by an effective free energy of cluster formation with identifiable bulk and surface term…
The flagellated bacterium Escherichia coli is increasingly used experimentally as a self-propelled swimmer. To obtain meaningful, quantitative results that are comparable between different laboratories, reproducible protocols are needed to control, `tune' and monitor the swimming behaviour of these motile cells. We critically review the knowledge needed to do so, explain methods for characterising the colloidal and motile properties of E.coli, cells, and propose a protocol for keeping them swimming at constant speed at finite bulk concentrations. In the process of establishing this protocol, w…
Active particles such as swimming bacteria or self-propelled colloids are known to spontaneously organize into fascinating large-scale dynamic structures. The emergence of these collective states from the motility pattern of the individual particles, typically a random walk, is yet to be probed in a well-defined synthetic system. Here, we report the experimental realization of intermittent colloidal motion that reproduces the run-and-tumble and Levy trajectories common to many swimming and swarming bacteria. Our strategy enables to tailor the sequence of repeated "runs" (nearly constant-speed …
Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: the steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density, for either biochemical or steric reasons. This creates positive feedback which can lead to motility-induced phase separation (MIPS) between dense and dilute f…
We study numerically the role of hydrodynamics in the liquid-hexatic transition of active colloids at intermediate activity, where motility induced phase separation (MIPS) does not occur. We show that in the case of active Brownian particles (ABP), the critical density of the transition decreases upon increasing the particle's mass, enhancing ordering, while self-propulsion has the opposite effect in the activity regime considered. Active hydrodynamic particles (AHP), instead, undergo the liquid-hexatic transition at higher values of packing fraction $ϕ$ than the corresponding ABP, suggesting …
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. …
One of the most intriguing phenomena in active matter has been the gas-liquid like motility induced phase separation (MIPS) observed in repulsive active particles. However, experimentally no particle can be a perfect sphere, and the asymmetric shape, mass distribution or catalysis coating can induce an active torque on the particle, which makes it a chiral active particle. Here using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles (cABPs) in two dimensions generates a dynamical clustering state interrupting the…
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, Infect…
A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective equilibrium system [Farage et al., Phys. Rev. E, 91 (2015) 042310]. In addition to the known accumulation at surfaces, we predict wetting and drying transitions at a flat repulsive wall and capillary condensation and evaporation in a slit pore. These new phenomena are closely related to the motility-induced phase separation (MIPS) in the bulk.
In many biological systems, the curvature of the surfaces cells live on influence their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) that curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, whic…
An active colloid is a suspension of particles that transduce free energy from their environment and use the energy to engage in intrinsically non-equilibrium activities such as growth, replication and self-propelled motility. An obvious example of active colloids is a suspension of bacteria such as Escherichia coli, their physical dimensions being almost invariably in the colloidal range. Synthetic self-propelled particles have also become available recently, such as two-faced, or Janus, particles propelled by differential chemical reactions on their surfaces driving a self-phoretic motion. I…
Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large-scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed experimental studies revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested b…
Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) -- as employed in many experimental studies -- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers [S. Michelin and E. Lauga, J. Fluid Mech. \textbf{747}, 572 (2014)]. Accordingly, intuitively appealing analogies …
Active colloids belong to a class of non-equilibrium systems where energy uptake, conversion and dissipation occurs at the level of individual colloidal particles, which can lead to particles self-propelled motion and surprising collective behavior. Examples include coexistence of vapor and liquid-like steady states for active particles with repulsive interactions only, phenomena known as motility induced phase transition. Similarly to motile unicellular organisms, active colloids tend to accumulate at confining surfaces forming dense adsorbed films. In this work, we study the structure and dy…
Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase…
Many active particles, both of biological and synthetic origin, can have a light controllable propulsion speed, a property that in biology is commonly referred to as photokinesis. Here we investigate directed transport of photokinetic particles by traveling light patterns. We find general expressions for the current in the cases where the motility wave, induced by light, shifts very slow or very fast. These asymptotic formulas are independent on the shape of the wave and are valid for a wide class of active particle models. Moreover we derive an exact solution for the one-dimensional "run and …
Active matter exhibits striking behaviour reminiscent of living matter and molecular fluids, and has promising applications in drug delivery or mixing at the micron scale. Active colloidal systems provide important models with simple and controllable interactions amenable to theory and computer simulation. Experimental work is dominated by (quasi) two--dimensional (2d) systems at relatively low concentration, and rather less is known of the 3d case at concentrations pertinent to motility induced phase separation or to mimic morphogenesis. Here we investigate a 3d experimental system of active …
We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, w…
