Active Bath Research Articles

Passive probe particle in an active bath: can we tell it is out of equilibrium?

We study a passive probe immersed in a fluid of active particles. Despite the system's non-equilibrium nature, the trajectory of the probe does not exhibit non-equilibrium signatures: its velocity distribution remains Gaussian, the second fluctuation dissipation theorem is not fundamentally violated, and the motion does not indicate breaking of time reversal symmetry. To tell that the probe is out of equilibrium requires examination of its behavior in tandem with that of the active fluid: the kinetic temperature of the probe does not equilibrate to that of the surrounding active particles. As a strategy to diagnose non-equilibrium from probe trajectories alone, we propose to examine their response to a small perturbation which reveals a non-equilibrium signature through a violation of the first fluctuation dissipation theorem.

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.

Passive Janus particles are self-propelled in active nematics

While active systems possess notable potential to form the foundation of new classes of autonomous materials (Zhang et al 2021 Nat. Rev. Mater. 6 437), designing systems that can extract functional work from active surroundings has proven challenging. In this work, we extend these efforts to the realm of designed active liquid crystal/colloidal composites. We propose suspending colloidal particles with Janus anchoring conditions in an active nematic medium. These passive Janus particles become effectively self-propelled once immersed into an active nematic bath. The self-propulsion of passive Janus particles arises from the effective +1/2 topological charge their surface enforces on the surrounding active fluid. We analytically study their dynamics and the orientational dependence on the position of a companion −1/2 defect. We predict that at sufficiently small activity, the colloid and companion defect remain bound to each other, with the defect strongly orienting the colloid to propel either parallel or perpendicular to the nematic. At sufficiently high activity, we predict an unbinding of the colloid/defect pair. This work demonstrates how suspending engineered colloids in active liquid crystals may present a path to extracting activity to drive functionality.

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.

Odd Diffusivity of Chiral Random Motion.

Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general characteristic of random motion breaking time-reversal and parity symmetries, as encountered in chiral active matter. In analogy with the odd viscosity appearing in chiral active fluids, we term this component the odd diffusivity. We show how odd diffusivity emerges in a chiral random walk model, and demonstrate the applicability of the Green-Kubo relations through molecular dynamics simulations of a passive tracer particle diffusing in a chiral active bath.

Active bath-induced localization and collapse of passive semiflexible polymers.

The conformational and dynamical properties of a passive polymer embedded in a bath of active Brownian particles (ABPs) are studied by Langevin dynamics simulations. Various activities and ABP concentrations below and above the critical values for motility-induced phase separation (MIPS) are considered. In a homogeneous ABP fluid, the embedded polymer swells with increasing bath activity, with stronger swelling for larger densities. The polymer dynamics is enhanced, with the diffusion coefficient increasing by a power-law with increasing activity, where the exponent depends on the ABP concentration. For ABP concentrations in the MIPS regime, we observe a localization of the polymer in the low-density ABP phase associated with polymer collapse for moderate activities and a reswelling for high activities accompanied by a preferred localization in the high-density ABP phase. Localization and reswelling are independent of the polymer stiffness, with stiff polymers behaving similarly to flexible polymers. The polymer collapse is associated with a slowdown of its dynamics and a significantly smaller center-of-mass diffusion coefficient. In general, the polymer dynamics can only partially be described by an effective (bath) temperature. Moreover, the properties of a polymer embedded in a homogeneous active bath deviate quantitatively from those of a polymer composed of active monomers, i.e., linear chains of ABPs; however, such a polymer exhibits qualitatively similar activity-dependent features.

Simulation study of passive rod diffusion in active bath: Nonmonotonic length dependence and abnormal translation-rotation coupling

Diffusion of tracer particles in active bath has attracted extensive attention in recent years. So far, most studies have considered isotropic spherical tracer particles, while the diffusion of anisotropic particles has rarely been involved. Here we investigate the diffusion dynamics of a rigid rod tracer in a bath of active particles by using Langevin dynamics simulations in a two-dimensional space. Particular attention is paid to how the translation (rotation) diffusion coefficient DT (DR) change with the length of rod L and active strength Fa. In all cases, we find that rod exhibits superdiffusion behavior in a short time scale and returns to normal diffusion in the long time limit. Both DT and DR increase with Fa, but interestingly, a nonmonotonic dependence of DT (DR) on the rod length has been observed. We have also studied the translation-rotation coupling of rod, and interestingly, a negative translation-rotation coupling is observed, indicating that rod diffuses more slowly in the parallel direction compared to that in the perpendicular direction, a counterintuitive phenomenon that would not exist in an equilibrium counterpart system. Moreover, this anomalous (diffusion) behavior is reentrant with the increase of Fa, suggesting two competitive roles played by the active feature of bath particles.

Energetics of critical oscillators in active bacterial baths

We investigate the nonequilibrium energetics near a critical point of a non-linear oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power exerted by a constant non-conservative torque , where D a is the effective diffusivity and τ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an optimal, minimum value for finite τ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below 2k B T eff, with T eff the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context by considering the example of driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.

Work fluctuations in a generalized Gaussian active bath

We theoretically investigate the dynamics and work distribution of a Brownian particle in a Gaussian active bath. By modeling the active noise as a generalized form of Ornstein–Uhlenbeck process (OUP), we show that the dynamics approaches asymptotically to a superdiffusive regime. Two protocols are considered to perform work on the system, and exact expressions for the probability distribution function (PDF) of work are obtained. Further, we show, by employing the large deviation principle (LDP), that the PDF follows an anomalous scaling with time, in contrast to the normal LDP. Then, fluctuation relations (FR) of work are studied to find that the transient FR does not exist, but a non-conventional FR emerges in the long-time limit. Also, the known results for the usual OUP bath are recovered.

λ -like transition in the dynamics of ratchet gears in active bath

To what extent the orientational order of self-propelling particles affects the dynamics of active bath-immersed ratchet devices remains unclear. We report experimental results of an inverse λ-like transition of the angular velocity of two ratchet gears in an active bath of self-propelling granular rods (SPRs) at different gear distances. The transition is caused by the phase transition in the orientational order of those SPRs located in the space between the gears. Brownian dynamics simulation of confined SPRs supports these observations. Thus, conditions for the upper bound efficiency of systems of active ratchet gears were obtained.

Effective Langevin equations for a polar tracer in an active bath

We study the motion of a polar tracer, having a concave surface, immersed in a two-dimensional suspension of active particles. Using Brownian dynamics simulations, we measure the distributions and auto-correlation functions of force and torque exerted by active particles on the tracer. The tracer experiences a finite average force along its polar axis, while all the correlation functions show exponential decay in time. Using these insights we construct the full coarse-grained Langevin description for tracer position and orientation, where the active particles are subsumed into an effective self-propulsion force and exponentially correlated noise for both translations and rotations. The ensuing mesoscopic dynamics can be described in terms of five dimensionless parameters. We perform a thorough parameter study of the mean squared displacement, which illustrates how the different parameters influence the tracer dynamics, which crosses over from a ballistic to diffusive motion. We also demonstrate that the distribution of tracer displacements evolves from a non-Gaussian shape at early stages to a Gaussian behavior for sufficiently long times. Finally, for a given set of microscopic parameters, we establish a procedure to estimate the matching parameters of our effective model, and show that the resulting dynamics is in a very good quantitative agreement with the one obtained in Brownian dynamics simulations.

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.

An attraction\u2013repulsion 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.

Hydrodynamics of polymers in an active bath.

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

Rectification in Nonequilibrium Parity Violating Metamaterials

Uncovering new mechanisms for rectification of stochastic fluctuations has been a longstanding problem in non-equilibrium statistical mechanics. Here, using a model parity violating metamaterial that is allowed to interact with a bath of active energy consuming particles, we uncover new mechanisms for rectification of energy and motion. Our model active metamaterial can generate energy flows through an object in the absence of any temperature gradient. The nonreciprocal microscopic fluctuations responsible for generating the energy flows can further be used to power locomotion in, or exert forces on, a viscous fluid. Taken together, our analytical and numerical results elucidate how the geometry and inter-particle interactions of the parity violating material can couple with the non-equilibrium fluctuations of an active bath and enable rectification of energy and motion.

The inhibition of concentrated active baths.

Passive tracers in the active bath express fascinating behaviors. However, most studies are restricted to dilute active baths. Here, we use 2D simulation of suspensions consisting of active Brownian particles and a passive disk-shaped tracer to investigate tracers' diffusive behaviors in a wide range of volume fractions. Due to the competition between the thermal noise and collisions with active particles, tracers express a first transition from the normal diffusion to the superdiffusion at a short time scale and recur to normal diffusion at a long time scale. At a low volume fraction, infrequent active collisions retard the first transition of smaller tracers. At a high volume fraction, active particles with high activity aggregating around tracers induce a bimodal probability distribution function of tracer displacements during superdiffusion. Considering the enhancement of diffusion, the non-dimensional enhanced diffusivity increases asymptotically with the Peclet number. The asymptotic line gives an upper limit of non-dimensional enhanced diffusivity of tracers. Cases with lower enhanced diffusion have a high volume fraction and a low active velocity that indicates the inhibition of concentrated active baths. With the high negentropic work of these cases, the inhibition is explained as the change of the configuration of active baths for introducing tracers.

Constraint Dependence of Active Depletion Forces on Passive Particles.

Using simulations and experiments, we demonstrate that the effective interaction between passive particles in an active bath substantially depends on an external constraint suffered by the passive particles. Particularly, the effective interaction between two free passive particles, which is directly measured in simulation, is qualitatively different from the one between two fixed particles. Moreover, we find that the friction experienced by the passive particles-a kinematic constraint-similarly influences the effective interaction. These remarkable features are in significant contrast to the equilibrium cases, and mainly arise from the accumulation of the active particles near the concave gap formed by the passive spheres. This constraint dependence not only deepens our understanding of the "active depletion force," but also provides an additional tool to tune the effective interactions in an active bath.

Lorentz forces induce inhomogeneity and flux in active systems

We consider the nonequilibrium dynamics of a charged active Brownian particle in the presence of a space dependent magnetic field. It has recently been shown that the Lorentz force induces a particle flux perpendicular to density gradients, thus preventing a diffusive description of the dynamics. Whereas a passive system will eventually relax to an equilibrium state, unaffected by the magnetic field, an active system subject to a spatially varying Lorentz force settles into a nonequilibrium steady state characterized by an inhomogeneous density and divergence-free bulk fluxes. A macroscopic flux of charged active particles is induced by the gradient of the magnetic field only and does not require additional symmetric breaking such as density or potential gradients. This stands in marked contrast to similar phenomena in condensed matter such as the classical Hall effect. In a confined geometry we observe circulating fluxes, which can be reversed by inverting the direction of the magnetic field. Our theoretical approach, based on coarse-graining of the Fokker-Planck equation, yields analytical results for the density, fluxes, and polarization in the steady state, all of which are validated by direct computer simulation. We demonstrate that passive tracer particles can be used to measure the essential effects of the Lorentz force on the active particle bath, and we discuss under which conditions the effects of the flux could be observed experimentally.

Constraint dependence of average potential energy of a passive particle in an active bath**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874397, 11674365, 11774393, and 11774394).

We quantify the mean potential energy of a passive colloidal particle harmonically confined in a bacterial solution using optical traps. We find that the average potential energy of the passive particle depends on the trap stiffness, in contrast to the equilibrium case where energy partition is independent of the external constraints. The constraint dependence of the mean potential energy originates from the fact that the persistent collisions between the passive particle and the active bacteria are influenced by the particle relaxation dynamics. Our experimental results are consistent with the Brownian dynamics simulations, and confirm the recent theoretical prediction.

Effective temperature scaled dynamics of a flexible polymer in an active bath

Langevin dynamics simulations are employed to study the dynamical properties of a flexible polymer in an active bath. The diffusion of the centre of mass and end-to-end distance fluctuation are particularly analysed. We modulate both active force and active particle size to probe the activity-induced facilitation of polymer dynamics. Results indicate diffusivity and chain relaxation time can be well scaled by the effective temperature of the active bath. In addition, diffusion dynamics demonstrates an anomalous superdiffusive behaviour in short time scales, which becomes more prominent with increasing active particle size. Lastly, we extract the effective viscosity experienced by the probed chain, showing a sharp decrease with increment of effective temperature. The attenuation of effective viscosity due to activity might be responsible for the facilitated polymer dynamics.