Cooperative behavior and pattern formation in mixtures of driven and nondriven colloidal assemblies

Competition between lanes and transient jammed clusters in driven binary mixtures

We consider mixtures of oppositely driven particles, showing that their nonequilibrium steady states form lanes parallel to the drive, which coexist with transient jammed clusters where particles are temporarily immobilized. We analyze the interplay between these two types of nonequilibrium pattern formation, including their implications for macroscopic demixing perpendicular to the drive. Finite-size scaling analysis indicates that there is no critical driving force associated with demixing, which appears as a crossover in finite systems. We attribute this effect to the disruption of long-ranged order by the transient jammed clusters.

Unjamming and emergent nonreciprocity in active ploughing through a compressible viscoelastic fluid

A dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, forms a natural setting to study the emergence of nonreciprocity during a dynamical phase transition. At these densities, the transport of active particles is strongly influenced by the passive medium and shows a dynamical jamming transition as a function of activity and medium density. In the process, the compressible medium is actively churned up - for low activity, the active particle gets self-trapped in a cavity of its own making, while for large activity, the active particle ploughs through the medium, either accompanied by a moving anisotropic wake, or leaving a porous trail. A hydrodynamic approach makes it evident that the active particle generates a long-range density wake which breaks fore-aft symmetry, consistent with the simulations. Accounting for the back-reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical non-reciprocal attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time. We emphasize that these nonreciprocal effects appear only when the active particles are moving and so manifest in the vicinity of the jamming-unjamming transition.

Perpendicular and parallel phase separation in two-species driven diffusive lattice gases

We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving field. In all cases, the perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbor attractive or repulsive interaction between particles of the same or opposite species. We discuss the connections between these results and the behavior found in off-lattice systems, including laning and freezing by heating.

Premelting controlled active matter in ice

Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called thermal regelation. When the host material is ice and the embedded particle is a biological entity, one has a particularly different form of active matter, which addresses interplay between a wide range of problems, from extremophiles of both terrestrial and exobiological relevance to ecological dynamics in Earth's cryosphere. Of basic importance in all such settings is the combined influence of biological activity and thermal regelation in controlling the redistribution of bioparticles. Therefore, we recast this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics and make predictions relevant to this and related problems of interest in biological and geophysical problems. We examine how thermal regelation compromises paleoclimate studies in the context of ice core dating and we find that the activity influences particle dynamics during thermal regelation by enhancing the effective diffusion coefficient. Therefore, accurate dating relies on a quantitative treatment of both effects.

Field-driven tracer diffusion through curved bottlenecks: fine structure of first passage events

Using scaling arguments and extensive numerical simulations, we study the dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary.

Tracer diffusion in crowded narrow channels

We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.

Laning and clustering transitions in driven binary active matter systems

It is well known that a binary system of nonactive disks that experience driving in opposite directions exhibits jammed, phase separated, disordered, and laning states. In active matter systems, such as a crowd of pedestrians, driving in opposite directions is common and relevant, especially in conditions which are characterized by high pedestrian density and emergency. In such cases, the transition from laning to disordered states may be associated with the onset of a panic state. We simulate a laning system containing active disks that obey run-and-tumble dynamics, and we measure the drift mobility and structure as a function of run length, disk density, and drift force. The activity of each disk can be quantified based on the correlation timescale of the velocity vector. We find that in some cases, increasing the activity can increase the system mobility by breaking up jammed configurations; however, an activity level that is too high can reduce the mobility by increasing the probability of disk-disk collisions. In the laning state, the increase of activity induces a sharp transition to a disordered strongly fluctuating state with reduced mobility. We identify a novel drive-induced clustered laning state that remains stable even at densities below the activity-induced clustering transition of the undriven system. We map out the dynamic phase diagrams highlighting transitions between the different phases as a function of activity, drive, and density.

Velocity force curves, laning, and jamming for oppositely driven disk systems

Using simulations we examine a two-dimensional disk system in which two disk species are driven in opposite directions. We measure the average velocity of one of the species versus the applied driving force and identify four phases as function of drive and disk density: a jammed state, a completely phase separated state, a continuously mixing phase, and a laning phase. The transitions between these phases are correlated with jumps in the velocity-force curves that are similar to the behavior observed at dynamical phase transitions in driven particle systems with quenched disorder such as vortices in type-II superconductors. In some cases the transitions between phases are associated with negative differential mobility in which the average absolute velocity of either species decreases with increasing drive. We also consider the situation where the drive is applied to only one species as well as systems in which both species are driven in the same direction with different drive amplitudes. We show that the phases are robust against the addition of thermal fluctuations. Finally, we discuss how the transitions we observe could be related to absorbing phase transitions where a system in a phase separated or laning regime organizes to a state in which contacts between the disks no longer occur and dynamical fluctuations are lost.

Cooperative behavior of biased probes in crowded interacting systems

We study, via extensive numerical simulations, dynamics of a crowded mixture of mutually interacting (with a short-range repulsive potential) colloidal particles immersed in a suspending solvent, acting as a heat bath. The mixture consists of a majority component - neutrally buoyant colloids subject to internal stimuli only, and a minority component - biased probes (BPs) also subject to a constant force. In such a system each of the BPs alters the distribution of the colloidal particles in its vicinity, driving their spatial distribution out of equilibrium. This induces effective long-range interactions and multi-tag correlations between the BPs, mediated by an out-of-equilibrium majority component, and prompts the BPs to move collectively assembling in clusters. We analyse the size-distribution of the self-assembling clusters in the steady-state, their specific force-velocity relations and also properties of the effective interactions emerging between the BPs.

Transport and selective chaining of bidisperse particles in a travelling wave potential

We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe-patterned magnetic garnet film. The substrate generates a one-dimensional periodic energy landscape above its surface. The application of an elliptically polarized rotating magnetic field causes the landscape to translate, inducing direct transport of paramagnetic particles placed above the film. The ellipticity of the applied field can be used to control and tune the interparticle interactions, from net repulsive to net attractive. When considering particles of two distinct sizes, we find that, depending on their elevation above the surface of the magnetic substrate, the particles feel effectively different potentials, resulting in different mobilities. We exploit this feature to induce selective chaining for certain values of the applied field parameters. In particular, when driving two types of particles, we force only one type to condense into travelling parallel chains. These chains confine the movement of the other non-chaining particles within narrow colloidal channels. This phenomenon is explained by considering the balance of pairwise magnetic forces between the particles and their individual coupling with the travelling landscape.

Driven binary colloidal mixture in a 2D narrow channel with hard walls

We have investigated the properties of a driven equi-molar binary colloidal mixture confined to a two-dimensional narrow channel. The walls are hard and periodic boundary condition is applied along the channel. Colloidal particles perform Brownian motion in a solvent having a fixed temperature and interact with each other via a Debye-Hückel Coulombic interaction (Yukawa potential). A constant external force drives the colloids along the channel. Two species move oppositely to each other. Hydrodynamic interactions are neglected and the dynamics is assumed to be over-damped. The flow increases nonlinearly with the external force but does not exhibit a notable dependence on channel width. Above a critical driving force the system undergoes a homogeneous-to-laning transition. It is shown that the mean lane width as well as the laning order parameter increases with the channel width. The reentrance effect is observed in the narrow channel geometry.

Understanding the nonlinear dynamics of driven particles in supercooled liquids in terms of an effective temperature

In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.

Microscopic dynamics of synchronization in driven colloids

Synchronization of coupled oscillators has been scrutinized for over three centuries, from Huygens' pendulum clocks to physiological rhythms. One such synchronization phenomenon, dynamic mode locking, occurs when naturally oscillating processes are driven by an externally imposed modulation. Typically only averaged or integrated properties are accessible, leaving underlying mechanisms unseen. Here, we visualize the microscopic dynamics underlying mode locking in a colloidal model system, by using particle trajectories to produce phase portraits. Furthermore, we use this approach to examine the enhancement of mode locking in a flexible chain of magnetically coupled particles, which we ascribe to breathing modes caused by mode-locked density waves. Finally, we demonstrate that an emergent density wave in a static colloidal chain mode locks as a quasi-particle, with microscopic dynamics analogous to those seen for a single particle. Our results indicate that understanding the intricate link between emergent behaviour and microscopic dynamics is key to controlling synchronization.

Synchronization may occur when naturally oscillating systems are driven by an external modulation, for example, in charge density waves. Here, Juniper et al. visualize the locked modes of synchronization at a microscopic level using a colloidal system.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential

We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.

Nonlinear response and crowding effects in microrheology

The mobility of tagged particles in a microrheological setup has been investigated via molecular dynamics simulations of a three-dimensional Lennard-Jones binary mixture. After coupling a small number of particles to a constant external driving force, the drift velocity and other observables of the dragged probe particles are reported in the linear and nonlinear response regime. In the nonlinear regime significant crowding effects are observed, thereby creating stringlike structures. Formation of the strings further enhances the nonlinear effects. A systematic study of these effects' dependence on temperature and total number of driven probe atoms is presented.

The nature of the laning transition in two dimensions

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures ('lanes') characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262,144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Depinning and collective dynamics of magnetically driven colloidal monolayers

We study the collective dynamics of interacting paramagnetic colloids transported via a magnetic ratchet effect above a modulated periodic potential. Upon increasing the modulation frequency, the particles undergo a series of dynamic transitions, from a continuous smectic flow to a disorder flow, and later enter into a two phase flow regime, ending in a complete pinned state. In the disordered phase, the system organizes into density waves due to traffic jams, as in granular systems, while the two phase flow regime shows strong similarities with plastic flow in vortex matter. Finally, it is shown that induced attractive interactions between the moving colloids lead to enhancement of the particle current due to formation of condensed chains traveling along the modulated landscape.

Dynamics of lane formation in driven binary complex plasmas

The dynamical onset of lane formation is studied in experiments with binary complex plasmas under microgravity conditions. Small microparticles are driven and penetrate into a cloud of big particles, revealing a strong tendency towards lane formation. The observed time-resolved lane-formation process is in good agreement with computer simulations of a binary Yukawa model with Langevin dynamics. The laning is quantified in terms of the anisotropic scaling index, leading to a universal order parameter for driven systems.

Negative differential mobility of weakly driven particles in models of glass formers

We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be nonmonotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Other significant nonlinear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these results can be explained analytically by a continuous-time random walk approximation where there is decoupling between persistence and exchange times for local displacements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle displacements. We discuss the relevance of our results to experiments.

Lane formation in oppositely charged colloids driven by an electric field: chaining and two-dimensional crystallization

A binary mixture of oppositely charged colloids which is driven by an external electric field is studied by extensive Brownian dynamics computer simulations, ignoring hydrodynamic interactions. The particle interaction is modeled via a screened Coulomb potential together with a steric repulsion. A strong electric field leads to lane formation of oppositely driven lanes. Each lane comprises particles of the same charge. A nonequilibrium "phase diagram" classifying different steady states is obtained as a function of the colloidal volume fraction and the Coulomb coupling. Different steady states are characterized by structural correlations perpendicular and parallel to the applied field. We find a variety of different phases involving lane chains at small volume fraction and low screening, and lanes with two-dimensional crystalline order perpendicular to the field at high volume fraction. The lateral crystalline order can be a square, triangular, or rhombic lattice. In between there is a lateral network structure. These predictions can be verified in real-space experiments on oppositely charged colloids.