Active Brownian particles escaping a channel in single file

Single-file diffusion of active Brownian particles

Single-file diffusion (SFD) is a key mechanism underlying transport phenomena in confined physical and biological systems. In a typical SFD process, microscopic particles are restricted to moving in a narrow channel where they cannot pass one another, resulting in constrained motion and anomalous long-time diffusion. In this study, we use Brownian dynamics simulations and analytical theory to investigate the SFD of athermal active Brownian particles (ABPs)-a minimal model of active colloids. Building on prior work [Schiltz-Rouse et al., Phys. Rev. E 108, 064601 (2023)], where the kinetic temperature, pressure, and compressibility of the single-file ABP system were derived, we develop an accurate analytical expression for the mean square displacement (MSD) of a tagged particle. We find that the MSD exhibits ballistic behavior at short times, governed by the reduced kinetic temperature of the system. At long times, the characteristic subdiffusive scaling of SFD, [⟨(Δx)2⟩∼ t1/2], is preserved. However, self-propulsion introduces significant changes to the 1D-mobility, which we directly relate to the system's compressibility. Furthermore, we demonstrate that the generalized 1D-mobility, originally proposed by Kollmann for equilibrium systems [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)], can be extended to active systems with minimal modification. These findings provide a framework for understanding particle transport in active systems and for tuning transport properties at the microscale, particularly in geometries where motion is highly restricted.

Exit times of totally asymmetric simple exclusion processes

We address the question of the time needed by N particles, initially located on the first sites of a finite one-dimensional lattice of size L, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when N≪L, the mean exit time of the particles is asymptotically given by T_{N}(L)∼L+β_{N}sqrt[L] for large lattices. Building upon exact results obtained for two particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients β_{N}. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of N particles in the regime where N is finite while the lattice size L→∞. This complements previous asymptotic results obtained by Johansson [Commun. Math. Phys. 209, 437 (2000)0010-361610.1007/s002200050027] in the limit where both N and L tend to infinity while keeping the particle density N/L finite.

Phase behaviour and dynamics of three-dimensional active dumbbell systems

We present a comprehensive numerical study of the phase behavior and dynamics of a three-dimensional active dumbbell system with attractive interactions. We demonstrate that attraction is essential for the system to exhibit nontrivial phases. We construct a detailed phase diagram by exploring the effects of the system's activity, density, and attraction strength. We identify several distinct phases, including a disordered, a gel, and a completely phase-separated phase. Additionally, we discover a novel dynamical phase, that we name percolating network, which is characterized by the presence of a spanning network of connected dumbbells. In the phase-separated phase we characterize numerically and describe analytically the helical motion of the dense cluster.

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.

Rescaling invariance and anomalous energy transport in a small vertical column of grains

It is well known that energy dissipation and finite size can deeply affect the dynamics of granular matter, often making usual hydrodynamic approaches problematic. Here we report on the experimental investigation of a small model system, made of ten beads constrained into a 1D geometry by a narrow vertical pipe and shaken at the base by a piston excited by a periodic wave. Recording the beads motion with a high frame rate camera allows to investigate in detail the microscopic dynamics and test hydrodynamic and kinetic models. Varying the energy, we explore different regimes from fully fluidized to the edge of condensation, observing good hydrodynamic behavior down to the edge of fluidization, despite the small system size. Density and temperature fields for different system energies can be collapsed by suitable space and time rescaling, and the expected constitutive equation holds very well when the particle diameter is considered. At the same time, the balance between dissipated and fed energy is not well described by commonly adopted dependence due to the up-down symmetry breaking. Our observations, supported by the measured particle velocity distributions, show a different phenomenological temperature dependence, which yields equation solutions in agreement with experimental results.

Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns

We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.

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.

Correlated escape of active particles across a potential barrier

We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the unified colored noise approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory, which explains the linear dependence of the escape time with the persistence of the active force. In the second part of the work, we consider the escape on two active particles mutually repelling. Interestingly, the subtle interplay of active and repulsive forces may lead to a correlation between particles, favoring the simultaneous jump across the barrier. This mechanism cannot be observed in the escape process of two passive particles. Finally, we find that in the small persistence regime, the repulsion favors the escape, such as in passive systems, in agreement with our theoretical predictions, while for large persistence times, the repulsive and active forces produce an effective attraction, which hinders the barrier crossing.

Diversity of self-propulsion speeds reduces motility-induced clustering in confined active matter

Self-propelled swimmers such as bacteria agglomerate into clusters as a result of their persistent motion. In 1D, those clusters do not coalesce macroscopically and the stationary cluster size distribution (CSD) takes an exponential form. We develop a minimal lattice model for active particles in narrow channels to study how clustering is affected by the interplay between self-propulsion speed diversity and confinement. A mixture of run-and-tumble particles with a distribution of self-propulsion speeds is simulated in 1D. Particles can swap positions at rates proportional to their relative self-propulsion speed. Without swapping, we find that the average cluster size L_c decreases with diversity and follows a non-arithmetic power mean of the single-component L_c's, unlike the case of tumbling-rate diversity previously studied. Effectively, the mixture is thus equivalent to a system of identical particles whose self-propulsion speed is the harmonic mean self-propulsion speed of the mixture. With swapping, particles escape more quickly from clusters. As a consequence, L_c decreases with swapping rates and depends less strongly on diversity. We derive a dynamical equilibrium theory for the CSDs of binary and fully polydisperse systems. Similarly to the clustering behaviour of one-component models, our qualitative results for mixtures are expected to be universal across active matter. Using literature experimental values for the self-propulsion speed diversity of unicellular swimmers known as choanoflagellates, which naturally differentiate into slower and faster cells, we predict that the error in estimating their L_cvia one-component models which use the conventional arithmetic mean self-propulsion speed is around 30%.

Morphologies and dynamics of the interfaces between active and passive phases

Active matters exhibit interesting collective behaviors and novel phases, which provide an important platform for the study of nonequilibrium physics. Mixtures of active and passive particles have been intensively studied in motility-induced phase separation, but the morphology of the active-passive interface has been poorly explored. In this work, we investigate the interface morphology in two-dimensional mixtures of active and passive particles using Brownian dynamics simulations. By systematically changing the Péclet number (Pe) and area fraction (ρ), we obtain the phase diagram of the active-passive interface, including rough sharp, rough invasive and flat interdiffusive interfaces. For a sharp interface, dynamic scaling analysis in the propagation stage shows that the roughness exponent α, the growth exponent β, the time exponent κ, and the dynamic exponent z satisfy z = α/(β - κ). Such anomalous scaling indicates that the roughening behavior does not belong to the conventional universality classes with Family-Vicsek scaling for the growth of passive interfaces. On the other hand, the interface in the middle-wavelength regime during the morphology relaxation stage can be described by capillary wave theory. The mean interface position propagates with time as t^1/2, which is robust at different ρ and Pe values in the propagation stage and exhibits superdiffusion in the morphology relaxation stage. These similarities and differences between the active-inactive interfaces and passive interfaces cast light on the interfacial growth of active matter.

Lattice model for active flows in microchannels

We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.188303] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length L<L^{*} and for high tumbling rates λ>λ^{*}, with threshold values L^{*} and λ^{*} which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs.

Universal scaling in active single-file dynamics

We study the single-file dynamics of three classes of active particles: run-and-tumble particles, active Brownian particles and active Ornstein-Uhlenbeck particles. At high activity values, the particles, interacting via purely repulsive and short-ranged forces, aggregate into several motile and dynamical clusters of comparable size, and do not display bulk phase-segregation. In this dynamical steady-state, we find that the cluster size distribution of these aggregates is a scaled function of the density and activity parameters across the three models of active particles with the same scaling function. The velocity distribution of these motile clusters is non-Gaussian. We show that the effective dynamics of these clusters can explain the observed emergent scaling of the mean-squared displacement of tagged particles for all the three models with identical scaling exponents and functions. Concomitant with the clustering seen at high activities, we observe that the static density correlation function displays rich structures, including multiple peaks that are reminiscent of particle clustering induced by effective attractive interactions, while the dynamical variant shows non-diffusive scaling. Our study reveals a universal scaling behavior in the single-file dynamics of interacting active particles.

Speed-dispersion-induced alignment: A one-dimensional model inspired by swimming droplets experiments

We investigate the collective dynamics of self-propelled droplets, confined in a one-dimensional microfluidic channel. On the one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensate, leaving large regions with very low density. A careful examination of the interactions between two "colliding" droplets demonstrates that local alignment takes place as a result of the interplay between the dispersion of their speeds and the absence of Galilean invariance. Inspired by these observations, we propose a minimalistic 1D model of active particles reproducing such dynamical rules and, combining analytical arguments and numerical evidences, we show that the model exhibits a transition to collective motion in 1D for a large range of values of the control parameters. Condensation takes place as a transient phenomena, which tremendously slows down the dynamics, before the system eventually settles into a homogeneous aligned phase.

Confined 1D Propulsion of Metallodielectric Janus Micromotors on Microelectrodes under Alternating Current Electric Fields

There is mounting interest in synthetic microswimmers ("micromotors") as microrobots as well as a model system for the study of active matters, and spatial navigation is critical for their success. Current navigational technologies mostly rely on magnetic steering or guiding with physical boundaries, yet limitations with these strategies are plenty. Inspired by an earlier work with magnetic domains on a garnet film as predefined tracks, we present an interdigitated microelectrodes (IDE) system where, upon the application of AC electric fields, metallodielectric (e.g., SiO₂-Ti) Janus particles are hydrodynamically confined and electrokinetically propelled in one dimension along the electrode center lines with tunable speeds. In addition, comoving micromotors moved in single files, while those moving in opposite directions primarily reoriented and moved past each other. At high particle densities, turbulence-like aggregates formed as many-body interactions became complicated. Furthermore, a micromotor made U-turns when approaching an electrode closure, while it gradually slowed down at the electrode opening and was collected in large piles. Labyrinth patterns made of serpentine chains of Janus particles emerged by modifying the electrode configuration. Most of these observations can be qualitatively understood by a combination of electroosmotic flows pointing inward to the electrodes, and asymmetric electrical polarization of the Janus particles under an AC electric field. Emerging from these observations is a strategy that not only powers and confines micromotors on prefabricated tracks in a contactless, on-demand manner, but is also capable of concentrating active particles at predefined locations. These features could prove useful for designing tunable tracks that steer synthetic microrobots, as well as to enable the study of single file diffusion, active turbulence, and other collective behaviors of active matters.

Wall accumulation of bacteria with different motility patterns

We systematically investigate the role of different swimming patterns on the concentration distribution of bacterial suspensions confined between two flat walls, by considering wild-type motility Escherichia coli and Pseudomonas aeruginosa, which perform Run and Tumble and Run and Reverse patterns, respectively. The experiments count motile bacteria at different distances from the bottom wall. In agreement with previous studies, an accumulation of motile bacteria close to the walls is observed. Different wall separations, ranging from 100 to 250μm, are tested. The concentration profiles result to be independent on the motility pattern and on the walls' separation. These results are confirmed by numerical simulations, based on a collection of self-propelled dumbbells-like particles interacting only through steric interactions. The good agreement with the simulations suggests that the behavior of the investigated bacterial suspensions is determined mainly by steric collisions and self-propulsion, as well as hydrodynamic interactions.

Coarsening and clustering in run-and-tumble dynamics with short-range exclusion

The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one dimension. The persistent exclusion process, where particles move at directions that change randomly at a low tumble rate α, is extended allowing sites to be occupied by more than one particle, with a maximum n_{max} per site. Three phases are distinguished. For n_{max}=1 a gas of clusters form, with sizes distributed exponentially and no coarsening takes place. For n_{max}≥3 and small values of α, coarsening takes place and few large clusters appear, with a large fraction of the total number of particles in them. In the same range of n_{max} but for larger values of α, a gas phase where a negligible fraction of particles takes part of clusters. Finally, n_{max}=2 corresponds to a crossover phase. The character of the transitions between phases is studied extending the model to allow n_{max} to take real values and jumps to an occupied site are probabilistic. The transition from the gas of clusters to the coarsening phase is continuous and the mass of the large clusters grows continuously when varying the maximum occupancy, and the crossover found corresponds to values close to the transition. The second transition, from the coarsening to the gaseous phase, can be either continuous or discontinuous depending on the parameters, with a critical point separating both cases.

Single-File Escape of Colloidal Particles from Microfluidic Channels

Single-file diffusion is a ubiquitous physical process exploited by living and synthetic systems to exchange molecules with their environment. It is paramount to quantify the escape time needed for single files of particles to exit from constraining synthetic channels and biological pores. This quantity depends on complex cooperative effects, whose predominance can only be established through a strict comparison between theory and experiments. By using colloidal particles, optical manipulation, microfluidics, digital microscopy, and theoretical analysis we uncover the self-similar character of the escape process and provide closed-formula evaluations of the escape time. We find that the escape time scales inversely with the diffusion coefficient of the last particle to leave the channel. Importantly, we find that at the investigated microscale, bias forces as tiny as 10^{-15}  N determine the magnitude of the escape time by drastically reducing interparticle collisions. Our findings provide crucial guidelines to optimize the design of micro- and nanodevices for a variety of applications including drug delivery, particle filtering, and transport in geometrical constrictions.

Self-Sustained Density Oscillations of Swimming Bacteria Confined in Microchambers

We numerically study the dynamics of run-and-tumble particles confined in two chambers connected by thin channels. Two dominant dynamical behaviors emerge: (i) an oscillatory pumping state, in which particles periodically fill the two vessels, and (ii) a circulating flow state, dynamically maintaining a near constant population level in the containers when connected by two channels. We demonstrate that the oscillatory behavior arises from the combination of a narrow channel, preventing bacteria reorientation, and a density-dependent motility inside the chambers.