Clogging and depinning of ballistic active matter systems in disordered media

Clogging transition and anomalous transport in driven suspensions in a disordered medium

We study computationally the dynamics of forced, Brownian particles through a disordered system. As the concentration of mobile particles and/or fixed obstacles increase, we characterize the different regimes of flow and address how clogging develops. We show that clogging is preceded by a wide region of anomalous transport, characterized by a power law decay of intermittent bursts. We analyze the velocity distribution of the moving particles and show that this abnormal flow region is characterized by a coexistence between mobile and arrested particles, and their relative populations change smoothly as clogging is approached. The comparison of the regimes of anomalous transport and clogging with the corresponding scenarios of particles pushed through a single bottleneck show qualitatively the same trends highlighting the generality of the transport regimes leading to clogging.

Morphologies and dynamics of free surfaces of crystals composed of active particles

Active matter exhibits various collective motions and nonequilibrium phases, such as crystals; however, their surface properties have been poorly explored. Here, we use Brownian dynamics simulations to investigate the surface morphology and dynamics of two-dimensional active crystals during and after growth. For crystal growth on a substrate, the position and roughness of the crystal surface reach steady states at different times. In the steady state, the surface exhibits superdiffusive behaviour at the short time, and the roughness is insensitive to the roughening process and particle activity. We observe two-stage and three-stage surface roughening at different Péclet numbers. The result of dynamic scaling analysis shows that the surface is similar to anomalous roughening, which is distinct from the normal roughening typically found in conventional passive systems. Capillary wave theory for a thermal equilibrium system can describe the active surface fluctuations only in the long-wavelength regime, indicating that active particles mainly drive the surface out of equilibrium locally. These similarities and differences between the active and passive crystal surfaces are essential for understanding active crystals and interfaces.

Activity-driven phase separation and ordering kinetics of passive particles

The steady state and phase ordering kinetics in a pure active Brownian particle system are studied in recent years. In binary mixture of active and passive Brownian particles passive particles are used as probe to understand the properties of active medium. In our present study, we study the mixture of passive and active Brownian particles. Here, we aim to understand the steady state and kinetics of small passive particles in the mixture. In our system, the passive particles are small in size and large in number, whereas ABPs are large in size and small in number. The system is studied on a two-dimensional substrate using overdamped Langevin dynamic simulation. The steady state and kinetics of passive particles are studied for various size and activity of active particles. Passive particles are purely athermal in nature and have dynamics only due to bigger ABPs. For small size ratio and activity, the passive particles remain homogeneous in the system, whereas on increasing size ratio and activity they form periodic hexagonal close pack (HCP) spanning clusters in the system. We have also studied the kinetics of growing passive particle clusters. The mass of the largest cluster shows a much slower growth kinetics in contrast to conserved growth kinetics in ABP system. Our study provides an understanding of steady state and kinetics of passive particles in the presence of bigger active particles. The mixture can be thought of as effect of big microorganism moving in passive medium.

Transport and phase separation of active Brownian particles in fluctuating environments

In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing diffusivity model where the equation of motion of the active particle involves a time-dependent motility and diffusivities. Within our model, those fluctuations are coupled to each other. Using analytical methods, we obtain the probability distribution function of particle displacement and its moments for a single particle. We then investigate the impact of the environmental fluctuations on the collective behavior of the active Brownian particles by means of extensive numerical simulations. Our results show that the fluctuations hinder the motility-induced phase separation, accompanied by a significant change of the density dependence of particle velocities. These effects are interpreted using our analytical results for the dynamics of a single particle.

The dynamics of chemically propelled dimer motor on a pinning substrate

The dynamics of self-propelled micro-motors, in a thin fluid film containing an attractive substrate, is investigated by means of a particle-based simulation. A chemically powered sphere dimer, consisting of a...

Susceptibility of Orientationally Ordered Active Matter to Chirality Disorder

We investigate the susceptibility of long-range ordered phases of two-dimensional dry aligning active matter to population disorder, taken in the form of a distribution of intrinsic individual chiralities. Using a combination of particle-level models and hydrodynamic theories derived from them, we show that while in finite systems all ordered phases resist a finite amount of such chirality disorder, the homogeneous ones (polar flocks and active nematics) are unstable to any amount of disorder in the infinite-size limit. On the other hand, we find that the inhomogeneous solutions of the coexistence phase (bands) may resist a finite amount of chirality disorder even asymptotically.

Active matter shepherding and clustering in inhomogeneous environments

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

Absorption of self-propelled particles into a dense porous medium

We study the absorption of self-propelled particles into a finite-size dense porous medium, which is mimicked by an obstacle array. We find that, depending on the competition of the propelling strength versus the repulsive barrier formed by obstacles and the contrast between the characteristic time scales of permeation and propelling persistence, the absorption process exhibits three distinct types of behavior. In Type I and II behavior, the propelling strength is not large enough to surmount the barrier, and hence particles transport in the medium by barrier-hopping dynamics. The initial permeation of particles toward the medium center is phenomenologically similar to a normal slow diffusion process. But, surprisingly, after the initial permeation process, a concentrated nucleus of particle aggregates forms and grows at the medium center in Type I, due to the long propelling persistence. Such an abnormal "nucleation" phenomenon does not appear in Type II, in which the propelling persistence is low. When the propelling strength is very high (Type III), particles transport smoothly in the medium, hence the initial slow diffusion process disappears and small particle clusters form and merge randomly in the medium. Our results provide a foundation for applications of active objects in a complex environment and also suggest the possible usage of a porous medium, for example, in the selection or sorting of active matter.

Clogging, dynamics, and reentrant fluid for active matter on periodic substrates

We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity, while at higher activity, the density becomes increasingly heterogeneous and an active clogged state emerges in which the mobility is strongly reduced. For driving along nonsymmetry or incommensurate directions, there are two different clogging behaviors consisting of a drive-dependent clogged state in the low activity thermal limit and a drive-independent clogged state at high activity. These regimes are separated by a uniform flowing liquid at intermediate activity. There is a critical activity level above which the thermal clogged state does not occur, as well as an optimal activity level that maximizes the disk mobility. Thermal clogged states are dependent on the driving direction while active clogged states are not. In the low activity regime, diluting the obstacles produces a monotonic increase in the mobility; however, for large activities, the mobility is more robust against obstacle dilution. We also examine the velocity-force curves for driving along nonsymmetry directions and find that they are linear when the activity is low or intermediate but become nonlinear at high activity and show behavior similar to that found for the plastic depinning of solids. At higher drives, the active clustering is lost. For low activity, we also find a reentrant fluid phase, where the system transitions from a high mobility fluid at low drives to a clogged state at higher drives and then back into another fluid phase at very high drives. We map the regions in which the thermally clogged, partially clogged, active uniform fluid, clustered fluid, active clogged, and directionally locked states occur as a function of disk density, drift force, and activity.

Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder

We show that spatial quenched disorder affects polar active matter in ways more complex and far reaching than heretofore believed. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.

Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays

We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.

Disorder-Induced Long-Ranged Correlations in Scalar Active Matter

We study the impact of quenched random potentials and torques on scalar active matter. Microscopic simulations reveal that motility-induced phase separation is replaced in two dimensions by an asymptotically homogeneous phase with anomalous long-ranged correlations and nonvanishing steady-state currents. Using a combination of phenomenological models and a field-theoretical treatment, we show the existence of a lower-critical dimension d_{c}=4, below which phase separation is only observed for systems smaller than an Imry-Ma length scale. We identify a weak-disorder regime in which the structure factor scales as S(q)∼1/q^{2}, which accounts for our numerics. In d=2, we predict that, at larger scales, the behavior should cross over to a strong-disorder regime. In d>2, these two regimes exist separately, depending on the strength of the potential.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

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 behavior 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. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α=3 and α=4. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environments.

Directional locking effects for active matter particles coupled to a periodic substrate

Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45^{∘} directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ=arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

Crowding-Enhanced Diffusion: An Exact Theory for Highly Entangled Self-Propelled Stiff Filaments

We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counterintuitive "crowded is faster" behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled, crowded, passive to active systems. We predict a scaling theory for the effective diffusivity as a function of the Péclet number and the filament number density. Subsequently, we show that an exact expression derived for a single self-propelled filament with motility parameters as input can predict the nontrivial spatiotemporal dynamics over the entire range of length and timescales. In particular, our theory captures short-time diffusion, directed swimming motion at intermediate times, and the transition to complete orientational relaxation at long times.

Transport of self-propelled particles across a porous medium: trapping, clogging, and the Matthew effect

We study the transport of self-propelled particles from one free chamber to another across two stripe-like areas of dense porous medium. The medium is mimicked by arrays of obstacles. We find that active motion could greatly speed up the transport of particles. However, more and more particles become trapped in the obstacle arrays with the enhancement of activity. At high persistence (low rotational diffusion rate) and moderate particle concentration, we observe the Matthew effect in the aggregation of particles in the two obstacle arrays. This effect is weakened by introduction of randomness or deformability into the obstacle arrays. Moreover, the dependence on deformability shows the characteristics of first-order phase transition. In rare situations, the system could be stuck in a dynamic unstable state, e.g. the particles alternatively gather more in one of the two obstacle arrays, exhibiting oscillation of particle number between the arrays. Our results reveal new features in the transport of active objects in a complex medium and have implications for manipulating their collective assembly.

Vortex formation of spherical self-propelled particles around a circular obstacle

A vortex is a common ratchet phenomenon in active systems. The spatial symmetry is usually broken by introducing asymmetric shapes or spontaneously by collective motion in the presence of hydrodynamic interactions or other alignment effects. Unexpectedly, we observe, by simulations, the formation of a vortex in the simplest model of a circular obstacle immersed in a bath of spherical self-propelled particles. No symmetry-breaking factors mentioned above are included in this model. The vortex forms only when the particle activity is high, i.e. large persistence. The obstacle size is also a key factor and the vortex only forms in a limited range of obstacle sizes. The sustainment of the vortex originates from the bias of the rotating particle cluster around the obstacle in accepting the incoming particles based on their propelling directions. Our results provide new understanding of and insights into the spontaneous symmetry-breaking and ratchet phenomena in active matter.

Diffusion properties of self-propelled particles in cellular flows

We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the particle as a function of persistence time and free-diffusion coefficient, revealing non-monotonic behaviors, with the occurrence of a minimum and a steep growth in the regime of large persistence time. In the latter limit, we obtain an analytical prediction for the scaling of the diffusion coefficient with the parameters of the active force. Our study sheds light on the effect of a flow-field on the diffusion of active particles, such as living microorganisms and motile phytoplankton in fluids.

Motile dissenters disrupt the flocking of active granular matter

We report flocking in the dry active granular matter of millimeter-sized two-step-tapered rods without an intervening medium. The system undergoes the flocking phase transition at a threshold area fraction of ∼0.12 having high orientational correlations between the particles. However, the one-step-tapered rods do not flock and are used as the motile dissenters in the flock-forming granular matter. At the critical fraction of dissenters of ∼0.3, the flocking order of the system gets completely destroyed. The variance of the system's order parameter shows a maximum near the dissenter fraction f∼0.05, suggesting a finite-size crossover between the ordered and disordered phases. Our experiments bring out the disruption of the cooperative behavior in heterogeneous active systems with possible implications in real-life examples.

Collective forces in scalar active matter

Large-scale collective behavior in suspensions of active particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.

From scalar to polar active matter: Connecting simulations with mean-field theory

We study numerically the phase behavior of self-propelled elliptical particles interacting through the "hard" repulsive Gay-Berne potential at infinite Péclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obtain a complete and consistent picture, unifying the paradigms of scalar and polar active matter.

Enhanced dynamics of active Brownian particles in periodic obstacle arrays and corrugated channels

We study the motion of an active Brownian particle (ABP) using the overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the ABP exhibits a super-diffusive dynamics in the corrugated channel. The transport property is independent of the shape of the channel; rather it depends on the packing fraction of the obstacles in the system. However, the ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel with flat boundary.

Flow and clogging of particles in shaking random obstacles

Transport of three types of particles (passive particles, active particles, and polar particles) is investigated in a random obstacle array in the presence of a dc drift force. The obstacles are static or synchronously shake along the given direction. When the obstacles are static, the average velocity is a peaked function of the dc drift force (negative differential mobility) for low particle density, while the average velocity monotonically increases with the dc drift force (positive differential mobility) for high particle density. Under the same conditions, passive particles are most likely to pass through the obstacles, while polar particles are easily trapped by the obstacles. The polar alignment can strongly reduce the overall mobility of particles. When the obstacles shake along the given direction, the optimal shaking frequency or amplitude can maximize the average velocity. It is more effective to reduce clogging for the transverse shaking than that for the longitudinal shaking.

Diffusion of active particles in a complex environment: Role of surface scattering

Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on run-and-tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations for pusherlike collisions. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how nonclassical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

Nutrient Transport Driven by Microbial Active Carpets

We demonstrate that active carpets of bacteria or self-propelled colloids generate coherent flows towards the substrate, and propose that these currents provide efficient pathways to replenish nutrients that feed back into activity. A full theory is developed in terms of gradients in the active matter density and velocity, and applied to bacterial turbulence, topological defects and clustering. Currents with complex spatiotemporal patterns are obtained, which are tunable through confinement. Our findings show that diversity in carpet architecture is essential to maintain biofunctionality.

Transport of particles driven by the traveling obstacle arrays

Transport of three types of particles (passive particles, active particles without polar interaction, and active particles with polar interaction) is numerically investigated in the presence of traveling obstacle arrays. The transport behaviors are different for different types of particles. For passive particles, there exists an optimal traveling speed (or the translational diffusion) at which the average velocity of particles takes its maximum value. For active particles without polar interaction, the average velocity of particles is a peaked function of the obstacle traveling speed. The average velocity decreases monotonically with increase of the rotational diffusion for large driving speed, while it is a peaked function of the rotational diffusion for small driving speed. For active particles with polar interaction, interestingly, within particular parameter regimes, active particles can move in the opposite direction to the obstacles. The average velocity of particles can change its direction by changing the system parameters (the obstacles driving speed, the polar interaction strength, and the rotational diffusion).