Self-propelled particle transport in regular arrays of rigid asymmetric obstacles

Dispersion of run-and-tumble microswimmers through disordered media

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function f(ϕ,Pe) of the obstacle area fraction ϕ and Péclet number Pe, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media (Peϕ≪1), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

Brownian motors powered by nonreciprocal interactions

Traditional models for molecular (Brownian) motors predominantly depend on nonequilibrium driving, while particle interactions rigorously adhere to Newton's third law. However, numerous living and natural systems at various scales seem to defy this well-established law. In this study, we investigated the transport of mixed Brownian particles in a two-dimensional ratchet potential with nonreciprocal interactions. Our findings reveal that these nonreciprocal interactions can introduce a zero-mean nonequilibrium driving force. This force is capable of disrupting the thermodynamic equilibrium and inducing directed motion. The direction of this motion is determined by the asymmetry of the potential. Interestingly, the average velocity is a peaked function of the degree of nonreciprocity, while the effective diffusion consistently increases with the increase of nonreciprocity. There exists an optimal temperature or packing fraction at which the average velocity reaches its maximum value. We share a mechanism for particle rectification, devoid of particle-autonomous nonequilibrium drive, with potential usage in systems characterized by nonreciprocal interactions.

Mixtures of self-propelled particles interacting with asymmetric obstacles

In the presence of an obstacle, active particles condensate into a surface "wetting" layer due to persistent motion. If the obstacle is asymmetric, a rectification current arises in addition to wetting. Asymmetric geometries are therefore commonly used to concentrate microorganisms like bacteria and sperms. However, most studies neglect the fact that biological active matter is diverse, composed of individuals with distinct self-propulsions. Using simulations, we study a mixture of "fast" and "slow" active Brownian disks in two dimensions interacting with large half-disk obstacles. With this prototypical obstacle geometry, we analyze how the stationary collective behavior depends on the degree of self-propulsion "diversity," defined as proportional to the difference between the self-propulsion speeds, while keeping the average self-propulsion speed fixed. A wetting layer rich in fast particles arises. The rectification current is amplified by speed diversity due to a superlinear dependence of rectification on self-propulsion speed, which arises from cooperative effects. Thus, the total rectification current cannot be obtained from an effective one-component active fluid with the same average self-propulsion speed, highlighting the importance of considering diversity in active matter.

Inertial active ratchet: Simulation versus theory

We present the inertial active dynamics of an Ornstein-Uhlenbeck particle in a piecewise sawtooth ratchet potential. Using the Langevin simulation and matrix continued fraction method (MCFM), the particle transport, steady-state diffusion, and coherence in transport are investigated in different parameter regimes of the model. Spatial asymmetry is found to be a key criterion for the possibility of directed transport in the ratchet. The MCFM results for net particle current of overdamped dynamics of the particle agree well with the simulation results. The simulated particle trajectories for the inertial dynamics and the corresponding position and velocity distribution functions reveal that the system passes through an activity-induced transition in the transport from the running phase to the locked phase of the dynamics. This is further corroborated by the mean square displacement (MSD) calculations, where the MSD gets suppressed with increase in the persistent duration of activity or self-propulsion in the medium and finally approaches zero for a very large value of self propulsion time. The nonmonotonic behavior of the particle current and Péclet number with self-propulsion time confirms that the particle transport and its coherence can be enhanced or reduced by fine tuning the persistent duration of activity. Moreover, for intermediate ranges of self-propulsion time as well as mass of the particle, even though the particle current shows a pronounced unusual maximum with mass, there is no enhancement in the Péclet number, instead the Péclet number decreases with mass, confirming the degradation of coherence in transport.

Rotation and separation of chiral active particles in a ring-shaped channel

Transport of chiral active particles is numerically investigated in a two-dimensional ring-shaped channel. The ring-shaped channel is transversal asymmetric and can induce the directed transport (rotation) of chiral active particles. For the particles with small chirality, they slide along the outer boundary of the channel. For the particles with large chirality, the particles move along some small local circular orbits and can also exhibit directed rotation. Moreover, the rotation effect can be strongly enhanced by modifying the inner boundary geometry. Based on the study of particle rotation, we further study the separation of active particles with different chiralities. It is found that the particles with different chiralities may be distributed in different regions of the ring-shaped channel. Interestingly, these particles can be completely separated by shifting the channel's inner boundary or adding a blocking plate in the channel. Our results may be useful for understanding relevant experimental phenomena and provide a scheme for the separation of binary mixtures.

A framework to quantify flow through coral reefs of varying coral cover and morphology

Flow velocities within coral reefs are greatly reduced relative to those at the water surface. The in-reef flow controls key processes that flush heat, cycle nutrients and transport sediment from the reef to adjacent beaches, all key considerations in assessments of reef resilience and restoration interventions. An analytical framework is proposed and tested with a suite of high-resolution numerical experiments. We demonstrate a single parameter that describes the total coral frontal area explains variation of horizontally averaged velocity within a reef canopy across morphologies, densities, and flow depths. With the integration of existing data of coral cover and geometry, this framework is a practical step towards the prediction of near-bed flows in diverse reef environments.

Obstacle-induced giant jammed aggregation of active semiflexible filaments

Filaments driven by bound motor proteins and chains of self-propelled colloidal particles are a typical example of active polymers (APs). Due to deformability, APs exhibit very rich dynamic behaviors and collective assembling structures. Here, we are concerned with a basic question: how APs behave near a single obstacle? We find that, in the presence of a big single obstacle, the assembly of APs becomes a two-state system, i.e. APs either gather nearly completely together into a giant jammed aggregate (GJA) on the surface of the obstacle or distribute freely in space. No partial aggregation is observed. Such a complete aggregation/collection is unexpected since it happens on a smooth convex surface instead of, e.g., a concave wedge. We find that the formation of a GJA experiences a process of nucleation and the curves of the transition between the GJA and the non-aggregate state form hysteresis-like loops. Statistical analysis of massive data on the growing time, chirality and angular velocity of both the GJAs and the corresponding nuclei shows the strong random nature of the phenomenon. Our results provide new insights into the behavior of APs in contact with porous media and also a reference for the design and application of polymeric active materials.

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.

Rotation reversal of a ratchet gear powered by active particles

Rotation of a gear powered by active particles is numerically investigated in a circular chamber. Due to the nonequilibrium properties of active particles, net gear rotation is achieved in a bath composed of self-propelling particles. Our setup can convert the random motion of active particles into the directional rotation of the ratchet gear. The direction of rotation is determined by the asymmetry of the gear and the persistence length (the ratio of the self-propulsion speed to the rotation diffusion coefficient) of active particles. Remarkably, the direction of rotation for large persistence length is opposite to the direction of rotation for small persistence length. Therefore, for a given asymmetric gear, we can observe the rotation reversal when tuning the system parameters (e.g., the self-propulsion speed, the rotation diffusion coefficient, and the packing fraction of active particles). Our findings are relevant to the experimental pursuit of rectifying random motion to directional motion in active matter.

An attraction-repulsion transition of force on two asymmetric wedges induced by active particles

Effective interaction between two asymmetric wedges immersed in a two-dimensional active bath is investigated by computer simulations. The attraction–repulsion transition of effective force between two asymmetric wedges is subjected to the relative position of two wedges, the wedge-to-wedge distance, the active particle density, as well as the apex angle of two wedges. By exchanging the position of the two asymmetric wedges in an active bath, firstly a simple attraction–repulsion transition of effective force occurs, completely different from passive Brownian particles. Secondly the transition of effective force is symmetric for the long-range distance between two asymmetric wedges, while it is asymmetric for the short-range case. Our investigations may provide new possibilities to govern the motion and assembly of microscopic objects by taking advantage of the self-driven behaviour of active particles.

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.

Controlling the transport of active matter in disordered lattices of asymmetrical obstacles

We investigate the transport of active matter in the presence of a disordered square lattice of asymmetric obstacles, which is built by removing a fraction of them from the initial full lattice. We obtain a spontaneous inversion of the net particle current, compared to the usual sense of such a current as a function of the fraction of removed obstacles and particle density. We observed that the negative current regime is the consequence of trapping of particles among the obstacles which favors that more particles move in the negative current direction. The same reasoning applies to the positive current regime as well. We show a calculation that partially reproduces our numerical results, based on the argument that the mean current is given by the product of the mean speed and the mean number of travelers in each direction; the breakdown of this assumption is responsible for the failure of our calculation to reproduce the initial negative current regime.

Transport of active particles induced by wedge-shaped barriers in straight channels with hard and soft walls

The transport of active particles in straight channels is numerically investigated. The periodic wedge-shaped barriers can produce the asymmetry of the system and induce the directed transport of the active particles. The direction of the transport is determined by the apex angle of the wedge-shaped barriers. By confining the particles in channels with hard and soft walls, the transport exhibits similar behaviors. The average velocity is a peaked function of the translational diffusion, while it decreases monotonously with the increase of the rotational diffusion. Moreover, the simulation results show that the transport is sensitive to the parameters of the confined structures, such as the pore width, the intensity of potential, and the channel period.

Current reversals of active particles in time-oscillating potentials

Rectification of interacting active particles is numerically investigated in a two-dimensional time-oscillating potential. It is found that the oscillation of the potential and the self-propulsion of active particles are two different types of nonequilibrium driving, which can induce net currents with opposite directions. For a given asymmetry of the potential, the direction of the transport is determined by the competition of the self-propulsion and the oscillation of the potential. There exists an optimal oscillating angular frequency (or self-propulsion speed) at which the average velocity takes its maximal positive or negative value. Remarkably, when the oscillation of the potential competes with the self-propulsion, the average velocity can change direction several times due to the change in the oscillating frequency. Especially, particles with different self-propulsion velocities will move in opposite directions and can be separated. Our results provide a novel and convenient method for controlling and manipulating the transport (or separation) of active particles.

Transport of alignment active particles in funnel structures

We study the transport of alignment active particles in complex confined structures (an array of asymmetric funnels). It is found that due to the existence of the multiple pathways, the alignment interaction can enrich the transport behavior of active particles. In an array of asymmetric funnels, the purely nematic alignment always suppresses the rectification. However, the polar alignment does not always promote the rectification, the rectification is suppressed for large self-propulsion speed. In addition, we also found the existence of optimal parameters (the self-propulsion speed and the rotational diffusion coefficient) at which the directed velocity takes its maximal value.

Transport of underdamped active particles in ratchet potentials

We study the rectified transport of underdamped active noninteracting particles in an asymmetric periodic potential. It is found that the ratchet effect of active noninteracting particles occurs in a single direction (along the easy direction of the substrate asymmetry) in the overdamped limit. However, when the inertia is considered, it is possible to observe reversals of the ratchet effect, where the motion is along the hard direction of the substrate asymmetry. By changing the friction coefficient or the self-propulsion force, the average velocity can change its direction several times. Therefore, by suitably tailoring the parameters, underdamped active particles with different self-propulsion forces can move in different directions and can be separated.

Effects of hydrodynamic interactions on rectified transport of self-propelled particles

Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well.

Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are only partially coupled to the substrate and form a phase-separated cluster state. This transition is associated with a drop in the net disk flux, and it can occur as a function of the substrate speed, maximum substrate force, disk run time, and disk density. Since variation of the disk activity parameters produces different disk drift rates for a fixed traveling-wave speed on the substrate, the system we consider could be used as an efficient method for active matter species separation. Within the cluster phase, we find that in some regimes the motion of the cluster center of mass is in the opposite direction to that of the traveling wave, while when the maximum substrate force is increased, the cluster drifts in the direction of the traveling wave. This suggests that swarming or clustering motion can serve as a method by which an active system can collectively move against an external drift.

The effect of changing topography on the coordinated marching of locust nymphs

Collective motion has traditionally been studied in the lab in homogeneous, obstacle-free environments, with little work having been conducted with changing landscapes or topography. Here, the impact of spatial heterogeneity on the collective motion exhibited by marching desert locust nymphs was studied under controlled lab conditions. Our experimental circular arenas, incorporating a funnel-like narrowing followed by re-widening, did not constitute a major barrier to the locusts but, rather, mimicked a changing topography in the natural environment. We examined its effects on macroscopic features of the locust collective behavior, as well as the any changes in their marching kinematics. A major finding was that of the limited extent to which the changing topography affected system-level features of the marching locust group, such as the order parameter and the fraction of walking individuals, despite increased crowding at the funnel. Overall, marching kinematics was also very little affected, suggesting that locust marching bands adjust to the environment, with little effect on the overall dynamics of the group. These findings are in contrast to recent theoretical results predicting that environmental heterogeneities qualitatively alter the dynamics of collectively moving particles; and highlight the crucial role of rapid individual plasticity and adaptability in the dynamics of flocks and swarms. Our study has revealed other important features of the marching behavior of the desert locust in addition to its robustness: the locusts demonstrated both, clear thigmotaxis and a tendency to spread-out and fill the available space.

Depletion forces on circular and elliptical obstacles induced by active matter

Depletion forces exerted by self-propelled particles on circular and elliptical passive objects are studied using numerical simulations. We show that a bath of active particles can induce repulsive and attractive forces which are sensitive to the shape and orientation of the passive objects (either horizontal or vertical ellipses). The resultant force on the passive objects due to the active particles is studied as a function of the shape and orientation of the passive objects, magnitude of the angular noise, and distance between the passive objects. By increasing the distance between obstacles the magnitude of the repulsive depletion force increases, as long as such a distance is less than one active particle diameter. For longer distances, the magnitude of the force always decreases with increasing distance. We also found that attractive forces may arise for vertical ellipses at high enough area fraction.

Collective ratchet effects and reversals for active matter particles on quasi-one-dimensional asymmetric substrates

Using computer simulations, we study a two-dimensional system of sterically interacting self-mobile run-and-tumble disk-shaped particles with an underlying periodic quasi-one-dimensional asymmetric substrate, and show that a rich variety of collective active ratchet behaviors arise as a function of particle density, activity, substrate period, and the maximum force exerted by the substrate. The net dc drift, or ratchet transport flux, is nonmonotonic since it increases with increased activity but is diminished by the onset of self-clustering of the active particles. Increasing the particle density decreases the ratchet transport flux for shallow substrates but increases the ratchet transport flux for deep substrates due to collective hopping events. At the highest particle densities, the ratchet motion is destroyed by a self-jamming effect. We show that it is possible to realize reversals of the direction of the net dc drift in the deep substrate limit when multiple rows of active particles can be confined in each substrate minimum, permitting emergent particle-like excitations to appear that experience an inverted effective substrate potential. We map out a phase diagram of the forward and reverse ratchet effects as a function of the particle density, activity, and substrate properties.

Ratchet transport powered by chiral active particles

We numerically investigate the ratchet transport of mixtures of active and passive particles in a transversal asymmetric channel. A big passive particle is immersed in a ‘sea’ of active particles. Due to the chirality of active particles, the longitudinal directed transport is induced by the transversal asymmetry. For the active particles, the chirality completely determines the direction of the ratchet transport, the counterclockwise and clockwise particles move to the opposite directions and can be separated. However, for the passive particle, the transport behavior becomes complicated, the direction is determined by competitions among the chirality, the self-propulsion speed, and the packing fraction. Interestingly, within certain parameters, the passive particle moves to the left, while active particles move to the right. In addition, there exist optimal parameters (the chirality, the height of the barrier, the self-propulsion speed and the packing fraction) at which the rectified efficiency takes its maximal value. Our findings could be used for the experimental pursuit of the ratchet transport powered by chiral active particles.

Chirality separation of mixed chiral microswimmers in a periodic channel

Dynamics and separation of mixed chiral microswimmers are numerically investigated in a channel with regular arrays of rigid half-circle obstacles. For zero shear flow, transport behaviors are the same for different chiral particles: the average velocity decreases with increase of the rotational diffusion coefficient, the direction of the transport can be reversed by tuning the angular velocity, and there exists an optimal value of the packing fraction at which the average velocity takes its maximal value. However, when the shear flow is considered, different chiral particles show different behaviors. By suitably tailoring parameters, particles with different chiralities can move in different directions and can be separated. In addition, we also proposed a space separation method by introducing a constant load, where counterclockwise and clockwise particles stay in different regions of the channel.