Constraint Dependence of Active Depletion Forces on Passive Particles

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Active osmoticlike pressure on permeable inclusions

We use a standard minimal active Brownian model to investigate the osmotic-like effective pressure generated by active fluids on fixed hollow inclusions. These inclusions are enclosed by a permeable (albeit nonflexible) membrane, and the interior and exterior regions of the inclusions have different particle motility strengths. We consider both rectangular and disklike inclusions and analyze the effects of various system parameters, such as excluded volume interaction between active particles, hardness of membrane, and active particle density, on the effective pressure produced on the enclosing membrane. We focus on the range of intermediate to high motility strengths and analyze the effective pressure in the steady state. Our findings for the active pressure produced in the interior and exterior regions of the inclusion indicate that the pressure is higher in the region with lower motility due to the relatively stronger accumulation of active particles.

On particle motion in a confined square domain filled with active fluids

The motion of passive particles in a confined square domain filled with active fluids has been numerically simulated using a direct-fictitious domain method. The ratio of particle diameter to the side length of the square domain (dp/L) is adopted to classify the degree of confinement (i.e., strong or weak confinement). The translational mean-squared displacement (MSDT) of weakly-confined particles scales well with the reported theoretical and experimental results in a short time and eventually reaches a plateau because of the confined environment. Additionally, the radial probability densities of the particle positions gradually increase with increasing distance from the center of the square domain at relatively high activity levels, displaying an apparent rise near the boundary and maximize near the corner. Conversely, the strongly confined particles migrate toward the center of the square domain or approach the corner with continuous rotation. In addition, the localized minima of the angular velocity of the particles show a periodic behavior, with the vortices periodically becoming more organized. Moreover, with increasing activity, two distinct linearly correlated regimes emerge in the relationship between the particle's rotational velocity and the activity. A comprehensive analysis of the collective dynamics reveals that the cutoff length is Rc ≈ 0.19(2.375dp), pointing to the distance at which the velocities of two particles are uncorrelated. Moreover, the spatial correlation function (Ip) shows a small peak at Rr ≈ 0.12(1.5dp), suggesting a relatively strong correlation between a given particle and another particle located at a distance Rr from it. Interestingly, both Rc and Rr are smaller than those observed in an unbounded flow, which indicates that boundary confinement significantly influences the ability of the particles to form coherent structures.

Kinetic temperature and pressure of an active Tonks gas

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.

Interplay of cell motility and self-secreted extracellular polymeric substance induced depletion effects on spatial patterning in a growing microbial colony

Reproducing bacteria self-organize to develop patterned biofilms in various conditions. Various factors contribute to the shaping of a multicellular bacterial organization. Here we investigate how motility force and self-secreted extracellular polymeric substances (EPS) influence bacterial cell aggregation, leading to phase-separated colonies using a particle-based/individual-based model. Our findings highlight the critical role of the interplay between motility force and depletion effects in regulating phase separation within a growing colony under far-from-equilibrium conditions. We observe that increased motility force hinders depletion-induced cell aggregation and phase segregation, necessitating a higher depletion effect for highly motile bacteria to undergo phase separation within a growing biofilm. We present a phase diagram illustrating the systematic variation of motility force and repulsive mechanical force, shedding light on the combined contributions of these two factors: self-propulsive motion and aggregation due to the depletion effect, resulting in the presence of small to large bacterial aggregates. Furthermore, our study reveals the dynamic nature of clustering, marked by changes in cluster size over time. Additionally, our findings suggest that differential dispersion among the components can lead to the localization of EPS at the periphery of a growing colony. Our study enhances the understanding of the collective dynamics of motile bacterial cells within a growing colony, particularly in the presence of a self-secreted polymer-driven depletion effect.

Hydrodynamics-Induced Long-Range Attraction between Plates in Bacterial Suspensions

We perform optical-tweezers experiments and mesoscale fluid simulations to study the effective interactions between two parallel plates immersed in bacterial suspensions. The plates are found to experience a long-range attraction, which increases linearly with bacterial density and decreases with plate separation. The higher bacterial density and orientation order between plates observed in the experiments imply that the long-range effective attraction mainly arises from the bacterial flow field, instead of the direct bacterium-plate collisions, which is confirmed by the simulations. Furthermore, the hydrodynamic contribution is inversely proportional to the squared interplate separation in the far field. Our findings highlight the importance of hydrodynamics on the effective forces between passive objects in active baths, providing new possibilities to control activity-directed assembly.

Hydrodynamic Anisotropy of Depletion in Nonequilibrium

Active colloids in a bath of inert particles of smaller size cause anisotropic depletion. The active hydrodynamics of this nonequilibrium phenomenon, which is fundamentally different from its equilibrium counterpart and passive particles in an active bath, remains scarcely understood. Here we combine mesoscale hydrodynamic simulation as well as theoretical analysis to examine the physical origin for the active depletion around a self-propelled noninteractive colloid. Our results elucidate that the variable hydrodynamic effect critically governs the microstructure of the depletion zone. Three characteristic states of anisotropic depletion are identified, depending on the strength and stress of activity. This yields a state diagram of depletion in the two-parameter space, captured by developing a theoretical model with the continuum kinetic theory and leading to a mechanistic interpretation of the hydrodynamic anisotropy of depletion. Furthermore, we demonstrate that such depletion in nonequilibrium results in various clusters with ordered organization of squirmers, which follows a distinct principle contrary to that of the entropy scenario of depletion in equilibrium. The findings might be of immediate interest to tune the hydrodynamics-mediated anisotropic interactions and active nonequilibrium organizations in the self-propulsion systems.

Phase separation of passive particles in active liquids

The transport properties of colloidal particles in active liquids have been studied extensively. It has led to a deeper understanding of the interactions between passive and active particles. However, the phase behavior of colloidal particles in active media has received little attention. Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles. Our study reveals dynamic clustering of colloids in active media due to an interplay of activity and attractive effective potential between the colloids. The strength of the effective potential is set by the size ratio of passive particles to the active ones. As the relative size of the passive particles increases, the effective potential becomes stronger and the average size of the clusters grows. The simulations reveal a macroscopic phase separation at sufficiently large size ratios. We will discuss the effect of density fluctuations of active particles on the nature of effective interactions between passive ones.

Spontaneous symmetry-breaking of the active cluster drives the directed movement and self-sustained oscillation of symmetric rod-like passive particles

Active particles without detailed balance can rectify their random motions to drive the directed movement or rotation of asymmetric passive obstacles. However, whether they can drive the directed movement of symmetric passive obstacles is still unclear. Here, we show that a rod-like passive particle which is fixed to move along the x-axis in an active bath can keep long-lived directed movement at nearly constant speed due to the spontaneous symmetry breaking of the neighboring active particle cluster. If the passive particle is further confined by a harmonic potential, it may undergo self-sustained periodic oscillation for an appropriate length of the passive particle and self-propelled velocity of active particles. The restoring force from the harmonic potential will trigger the velocity jump-off and thus lead to self-sustained periodic oscillation. Remarkably, the relationship between the velocity of the passive particle and the external force shows that the effective viscosity of the active bath may become negative in some regime. Finally, we develop a minimum 1D theoretical model to further probe the mechanism underlying the directed movement and self-sustained oscillation of the passive particle. Our findings reveal the effect of the moving boundary on the active bath and demonstrate a novel method to extract practical mechanical work from the active bath to propel microdevices.

Force Generation in Confined Active Fluids: The Role of Microstructure

We experimentally determine the force exerted by a bath of active particles onto a passive probe as a function of its distance to a wall and compare it to the measured averaged density distribution of active particles around the probe. Within the framework of an active stress, we demonstrate that both quantities are-up to a factor-directly related to each other. Our results are in excellent agreement with a minimal numerical model and confirm a general and system-independent relationship between the microstructure of active particles and transmitted forces.

Active depletion torque between two passive rods

The active depletion torque experienced by two anisotropic objects in an active bath is a conceptional generalization of the equilibrium entropic torque. Using Brownian dynamics simulations, we compute the active depletion torque suffered by two passive rods immersed in an ensemble of active Brownian particles. Our results demonstrate that the active depletion torque is qualitatively different from its passive counterpart. Interestingly, we find that the active depletion torque can be greatly affected by the external constraint applied on the rotational degree of freedom of the rods, and even the direction may be changed with the orientational constraint, which is in contrast to the equilibrium depletion torque. The main reason for the remarkable features of the active depletion torque is that the active particles can significantly accumulate in the vicinity of the rods due to persistent self-propulsion, which is sensitively dependent on the constraint strength and the rod configurations. Our findings could be relevant for understanding the self-assembly and dynamics of anisotropic macromolecules in living environments.

Effective single component description of steady state structures of passive particles in an active bath

We model a binary mixture of passive and active Brownian particles in two dimensions using the effective interaction between passive particles in the active bath. The activity of active particles and the size ratio of two types of particles are the two control parameters in the system. The effective interaction is calculated from the average force on two particles generated by the active particles. The effective interaction can be attractive or repulsive, depending on the system parameters. The passive particles form four distinct structural orders for different system parameters, viz., homogeneous structures, disordered cluster, ordered cluster, and crystalline structure. The change in structure is dictated by the change in nature of the effective interaction. We further confirm the four structures using a full microscopic simulation of active and passive mixture. Our study is useful to understand the different collective behavior in non-equilibrium systems.

Small Obstacle in a Large Polar Flock

We show that arbitrarily large polar flocks are susceptible to the presence of a single small obstacle. In a wide region of parameter space, the obstacle triggers counterpropagating dense bands leading to reversals of the flow. In very large systems, these bands interact, yielding a never-ending chaotic dynamics that constitutes a new disordered phase of the system. While most of these results were obtained using simulations of aligning self-propelled particles, we find similar phenomena at the continuous level, not when considering the basic Toner-Tu hydrodynamic theory, but in simulations of truncations of the relevant Boltzmann equation.

Dynamic clustering of passive colloids in dense suspensions of motile bacteria

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.

Migration of an active colloidal cell in inhomogeneous environments

Living cells on a substrate with mechanical inhomogeneities often migrate along or against the mechanical gradient, i.e., mechanotaxis, which inspires us to ask how biomimetic cells without biochemical signaling processes respond to environmental inhomogeneity. Here, we perform computer simulations to study the migration of a 2D active colloidal cell (ACC), which consists of active particles enclosed by a passive vesicle, in a heterogeneous environment composed of two adjoining uniform regions with different attributes (influencing the persistent length of the active particle). We find that the ACC can migrate unidirectionally across the interface separating the heterogeneous region and behave tactically. Interestingly, the tactic motion of the ACC is qualitatively different from that of the constituent active particles themselves. In addition, the ACC may also experience a directed drift along the interface of the heterogeneous environment. The tactic behavior of the ACC can be explained by analyzing the pressure distribution on the cell membrane exerted by the enclosed active particles. The findings provide insights into understanding the taxis of biological cells and designing biomimetic cells with environment-sensitive capabilities.

Experimental investigation of active noise on a rotor in an active granular bath

In an active bath, besides thermal noise, immersed passive objects also persistently experience collisions from active particles, which are often coarse-grained into a colored active noise with an assumed exponential time correlation. The exponentially correlated active noise extremely simplifies the theoretical description of immersed passive objects but so far lacks direct experimental verification. Here, we experimentally investigate the active noise subjected by a passive rotor confined in an active granular bath. On the basis of Langevin dynamics, we extract the characteristic of the active noise by analyzing the power spectrum of the rotor trajectory. Our experimental results find that the active noise experienced by the granular rotor does show an exponential time correlation to a good extent, even though due to the small experimental system and low collision frequency, the profile of the active noise in our system is non-Gaussian. Our findings give direct experimental evidence, which supports the widely-used active Ornstein-Uhlenbeck particle model in our dry active system.

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.

Dimeric colloidal inclusion in a chiral active bath: Effective interactions and chirality-induced torque

Colloidal inclusions suspended in a bath of smaller particles experience an effective bath-mediated attraction at small intersurface separations, which is known as the depletion interaction. In an active bath of nonchiral self-propelled particles, the effective force changes from attraction to repulsion, an effect that is suppressed when the active bath particles are chiral. Using Brownian dynamics simulations, we study the effects of channel confinement and bath chirality on the effective forces and torques that are mediated between two inclusions that may be fixed within the channel or may be allowed to rotate freely as a rigid dimer around its center of mass. We show that the confinement has a strong effect on the effective interactions, depending on the orientation of the dimer relative to the channel walls. The active particle chirality leads to a force imbalance and, hence, a net torque on the inclusion dimer, which we investigate as a function of the bath chirality strength and the channel height.

Noncentral forces mediated between two inclusions in a bath of active Brownian rods

Using Brownian Dynamics simulations, we study effective interactions mediated between two identical and impermeable disks (inclusions) immersed in a bath of identical, active (self-propelled), Brownian rods in two spatial dimensions, by assuming that the self-propulsion axis of the rods may generally deviate from their longitudinal axis. When the self-propulsion is transverse (perpendicular to the rod axis), the accumulation of active rods around the inclusions is significantly enhanced, causing a more expansive steric layering (ring formation) of the rods around the inclusions, as compared with the reference case of longitudinally self-propelling rods. As a result, the transversally self-propelling rods also mediate a significantly longer ranged effective interaction between the inclusions. The bath-mediated interaction arises due to the overlaps between the active-rod rings formed around the inclusions, as they are brought into small separations. When the self-propulsion axis is tilted relative to the rod axis, we find an asymmetric imbalance of active-rod accumulation around the inclusion dimer. This leads to a noncentral interaction, featuring an anti-parallel pair of transverse force components and, hence, a bath-mediated torque on the dimer.

Dependency of active pressure and equation of state on stiffness of wall

Autonomous motion and motility are hallmarks of active matter. Active agents, such as biological cells and synthetic colloidal particles, consume internal energy or extract energy from the environment to generate self-propulsion and locomotion. These systems are persistently out of equilibrium due to continuous energy consumption. It is known that pressure is not always a state function for generic active matter. Torque interaction between active constituents and confinement renders the pressure of the system a boundary-dependent property. The mechanical pressure of anisotropic active particles depends on their microscopic interactions with a solid wall. Using self-propelled dumbbells confined by solid walls as a model system, we perform numerical simulations to explore how variations in the wall stiffness influence the mechanical pressure of dry active matter. In contrast to previous findings, we find that mechanical pressure can be independent of the interaction of anisotropic active particles with walls, even in the presence of intrinsic torque interaction. Particularly, the dependency of pressure on the wall stiffness vanishes when the stiffness is above a critical level. In such a limit, the dynamics of dumbbells near the walls are randomized due to the large torque experienced by the dumbbells, leading to the recovery of pressure as a state variable of density.

Topologically Protected Transport of Cargo in a Chiral Active Fluid Aided by Odd-Viscosity-Enhanced Depletion Interactions

The discovery of topological edge states that unidirectionally propagate along the boundary of system without backscattering has enabled the development of new design principles for material or information transport. Here, we show that the topological edge flow supported by the chiral active fluid composed of spinners can even robustly transport an immersed intruder with the aid of the spinner-mediated depletion interaction between the intruder and boundary. Importantly, the effective interaction significantly depends on the dissipationless odd viscosity of the chiral active fluid, which originates from the spinning-induced breaking of time-reversal and parity symmetries, rendering the transport controllable. Our findings propose a novel avenue for robust cargo transport and could open a range of new possibilities throughout biological and microfluidic systems.

Tunable depletion force in active and crowded environments

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Effective interactions mediated between two permeable disks in an active fluid

We study steady-state properties of a bath of active Brownian particles (ABPs) in two dimensions in the presence of two fixed, permeable (hollow) disklike inclusions, whose interior and exterior regions can exhibit mismatching motility (self-propulsion) strengths for the ABPs. We show that such a discontinuous motility field strongly affects spatial distribution of ABPs and thus also the effective interaction mediated between the inclusions through the active bath. Such net interactions arise from soft interfacial repulsions between ABPs that sterically interact with and/or pass through permeable membranes assumed to enclose the inclusions. Both regimes of repulsion and attractive (albeit with different mechanisms) are reported and summarized in overall phase diagrams.

Active noise experienced by a passive particle trapped in an active bath

We study the properties of active noise experienced by a passive particle harmonically trapped in an active bath. The active bath is either explicitly simulated by an ensemble of active Brownian particles or abstractly represented by an active colored noise in theory. Assuming the equivalence of the two descriptions of the active bath, the active noise in the simulation system, which is directly extracted by fitting theoretical predictions to simulation measurements, is shown to depend on the constraint suffered by the passive tracer. This scenario is in significant contrast to the case of thermal noise that is independent of external trap potentials. The constraint dependence of active noise arises from the fact that the persistent force on the passive particle from the active bath can be influenced by the particle relaxation dynamics. Moreover, due to the interplay between the active collisions and particle relaxation dynamics, the effective temperature of the passive tracer quantified as the ratio of fluctuation to dissipation increases as the constraint strengthens, while the average potential and kinetic energies of the passive particle both decrease.