Clogging and jamming transitions in periodic obstacle arrays

Flow and clogging of capillary droplets

Capillary droplets form due to surface tension when two immiscible fluids are mixed. We describe the motion of gravity-driven capillary droplets flowing through narrow constrictions and obstacle arrays in both simulations and experiments. Our new capillary deformable particle model recapitulates the shape and velocity of single oil droplets in water as they pass through narrow constrictions in microfluidic chambers. Using this experimentally validated model, we simulate the flow and clogging of single capillary droplets in narrow channels and obstacle arrays and find several important results. First, the capillary droplet speed profile is nonmonotonic as the droplet exits the narrow orifice, and we can tune the droplet properties so that the speed overshoots the terminal speed far from the constriction. Second, in obstacle arrays, we find that extremely deformable droplets can wrap around obstacles, which leads to decreased average droplet speed in the continuous flow regime and increased probability for clogging in the regime where permanent clogs form. Third, the wrapping mechanism causes the clogging probability in obstacle arrays to become nonmonotonic with surface tension Γ. At large Γ, the droplets are nearly rigid and the clogging probability is large since the droplets can not squeeze through the gaps between obstacles. With decreasing Γ, the clogging probability decreases as the droplets become more deformable. However, in the small-Γ limit, the clogging probability increases since the droplets are extremely deformable and wrap around the obstacles. The results from these studies are important for developing a predictive understanding of capillary droplet flows through complex and confined geometries.

Reversible, irreversible, and mixed regimes for periodically driven disks in random obstacle arrays

We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and drives, the system rapidly forms a reversible state where the disks return to their exact positions at the end of each cycle. In contrast, at high amplitudes or high densities, the system enters an irreversible state where the disks exhibit normal diffusion. Between these two regimes, there can be an intermediate irreversible state where most of the system is reversible, but localized irreversible regions are present that are prevented from spreading through the system due to a screening effect from the obstacles. We also find states that we term "combinatorial reversible states" in which the disks return to their original positions after multiple driving cycles. In these states, individual disks exchange positions but form the same configurations during the subcycles of the larger reversible cycle.

Chiral active particles are sensitive reporters to environmental geometry

Chiral active particles (CAPs) are self-propelling particles that break time-reversal symmetry by orbiting or spinning, leading to intriguing behaviors. Here, we examined the dynamics of CAPs moving in 2D lattices of disk obstacles through active Brownian dynamics simulations and granular experiments with grass seeds. We find that the effective diffusivity of the CAPs is sensitive to the structure of the obstacle lattice, a feature absent in achiral active particles. We further studied the transport of CAPs in obstacle arrays under an external field and found a reentrant directional locking effect, which can be used to sort CAPs with different activities. Finally, we demonstrated that parallelogram lattices of obstacles without mirror symmetry can separate clockwise and counter-clockwise CAPs. The mechanisms of the above three novel phenomena are qualitatively explained. As such, our work provides a basis for designing chirality-based tools for single-cell diagnosis and separation, and active particle-based environmental sensors.

Reversible to Irreversible Transitions for Cyclically Driven Particles on Periodic Obstacle Arrays

We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density we find that system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ=0{degree sign} and θ=45{degree sign} and the lowest critical densities falling at θ=arctan(0.618), the inverse of the golden ratio, where the flow is the most frustrated. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν=1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.

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

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

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

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

Active matter commensuration and frustration effects on periodic substrates

We show that self-driven particles coupled to a periodic obstacle array exhibit active matter commensuration effects that are absent in the Brownian limit. As the obstacle size is varied for sufficiently large activity, a series of commensuration effects appear in which the motility induced phase separation produces commensurate crystalline states, while for other obstacle sizes we find frustrated or amorphous states. The commensuration effects are associated with peaks in the amount of sixfold ordering and the maximum cluster size. When a drift force is added to the system, the mobility contains peaks and dips similar to those found in transport studies for commensuration effects in superconducting vortices and colloidal particles.

Particle size effect on sorting with optical lattice

Transport of mesoscale particles due to driving flow fields or external forces on a periodic surface appears in many areas. Geometrical and physical characteristics of particles affect the velocities of the particles in these periodic landscapes. In this paper, we present a numerical simulation based on solving the Langevin equation for the meso-size particles subjected to the thermal fluctuations in a periodic array of optical traps. We consider the real-size particles which cause the partial trapping of particles in the optical traps. The particles are sorted for the size-dependency of particles' trajectories. Our results are in good agreement with experiments.

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

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

Collective effects and pattern formation for directional locking of disks moving through obstacle arrays

We examine directional locking effects in an assembly of disks driven through a square array of obstacles as the angle of drive rotates from 0^{∘} to 90^{∘}. For increasing disk densities, the system exhibits a series of different dynamic patterns along certain locking directions, including one-dimensional or multiple-row chain phases and density-modulated phases. For nonlocking driving directions, the disks form disordered patterns or clusters. When the obstacles are small or far apart, a large number of locking phases appear; however, as the number of disks increases, the number of possible locking phases drops due to the increasing frequency of collisions between the disks and obstacles. For dense arrays or large obstacles, we find an increased clogging effect in which immobile and moving disks coexist.

Jamming, fragility and pinning phenomena in superconducting vortex systems

We examine driven superconducting vortices interacting with quenched disorder under a sequence of perpendicular drive pulses. As a function of disorder strength, we find four types of behavior distinguished by the presence or absence of memory effects. The fragile and jammed states exhibit memory, while the elastic and pinning dominated regimes do not. In the fragile regime, the system organizes into a pinned state during the first pulse, flows during the second perpendicular pulse, and then returns to a pinned state during the third pulse which is parallel to the first pulse. This behavior is the hallmark of the fragility proposed for jamming in particulate matter. For stronger disorder, we observe a robust jamming state with memory where the system reaches a pinned or reduced flow state during the perpendicular drive pulse, similar to the shear jamming of granular systems. We show signatures of the different states in the spatial vortex configurations, and find that memory effects arise from coexisting elastic and pinned components of the vortex assembly. The sequential perpendicular driving protocol we propose for distinguishing fragile, jammed, and pinned phases should be general to the broader class of driven interacting particles in the presence of quenched disorder.

Clogging-jamming connection in narrow vertical pipes

We report experimental evidence of clogging due to the spontaneous development of hanging arches when a granular sample composed of spherical particles flows down a narrow vertical pipe. These arches, akin to the ones responsible for silo clogging, can only be possible due to the role of frictional forces; otherwise they will be unstable. We find that, contrary to the silo case, the probability of clogging in vertical narrow tubes does not decrease monotonically with the ratio of the pipe-to-particle diameters. This behavior is related to the clogging prevention caused by the spontaneous ordering of particles apparent in certain aspect ratios. More importantly, by means of numerical simulations, we discover that the interparticle normal force distributions broaden in systems with higher probability of clogging. This feature, which has been proposed before as a distinctive feature of jamming in sheared granular samples, suggests that clogging and jamming are connected in pipe flow.

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.

Structured randomness: jamming of soft discs and pins

Simulations are used to find the zero temperature jamming threshold, φj, for soft, bidisperse disks in the presence of small fixed particles, or "pins", arranged in a lattice. The presence of pins leads, as one expects, to a decrease in φj. Structural properties of the system near the jamming threshold are calculated as a function of the pin density. While the correlation length exponent remains ν = 1/2 at low pin densities, the system is mechanically stable with more bonds, yet fewer contacts than the Maxwell criterion implies in the absence of pins. In addition, as pin density increases, novel bond orientational order and long-range spatial order appear, which are correlated with the square symmetry of the pin lattice.

Flow and clogging of particles in shaking random obstacles

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

Transport of particles driven by the traveling obstacle arrays

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

Decoupling Geometrical and Kinematic Contributions to the Silo Clogging Process

Based on the implementation of a novel silo discharge procedure, we are able to control the grains velocities regardless of the outlet size. This allows isolating the geometrical and kinematic contributions to the clogging process. We find that, for a given outlet size, reducing the grains velocities to extremely low values leads to a clogging probability increment of almost two orders of magnitude, hence revealing the importance of particle kinematics in the silo clogging process. Then, we explore the contribution of both variables, outlet size and grains velocity, and we find that our results agree with an already known exponential expression that relates clogging probability with outlet size. We propose a modification of such expression revealing that only two parameters are necessary to fit all the data: one is related with the geometry of the problem, and the other with the grains kinematics.

Controlled Fluidization, Mobility, and Clogging in Obstacle Arrays Using Periodic Perturbations

We show that the clogging susceptibility and flow of particles moving through a random obstacle array can be controlled with a transverse or longitudinal ac drive. The flow rate can vary over several orders of magnitude, and we find both an optimal frequency and an optimal amplitude of driving that maximizes the flow. For dense arrays, at low ac frequencies, a heterogeneous creeping clogged phase appears in which rearrangements between different clogged configurations occur. At intermediate frequencies, a high-mobility fluidized state forms, and, at high frequencies, the system reenters a heterogeneous frozen clogged state. These results provide a technique for optimizing flow through heterogeneous media that could also serve as the basis for a particle separation method.

Crossover from Jamming to Clogging Behaviours in Heterogeneous Environments

Jamming describes a transition from a flowing or liquid state to a solid or rigid state in a loose assembly of particles such as grains or bubbles. In contrast, clogging describes the ceasing of the flow of particulate matter through a bottleneck. It is not clear how to distinguish jamming from clogging, nor is it known whether they are distinct phenomena or fundamentally the same. We examine an assembly of disks moving through a random obstacle array and identify a transition from clogging to jamming behavior as the disk density increases. The clogging transition has characteristics of an absorbing phase transition, with the disks evolving into a heterogeneous phase-separated clogged state after a critical diverging transient time. In contrast, jamming is a rapid process in which the disks form a homogeneous motionless packing, with a rigidity length scale that diverges as the jamming density is approached.

Clogging and transport of driven particles in asymmetric funnel arrays

We numerically examine the flow and clogging of particles driven through asymmetric funnel arrays when the commensurability ratio of the number of particles per plaquette is varied. The particle-particle interactions are modeled with a soft repulsive potential that could represent vortex flow in type-II superconductors or driven charged colloids. The velocity-force curves for driving in the easy flow direction of the funnels exhibit a single depinning threshold; however, for driving in the hard flow direction, we find that there can be both negative mobility where the velocity decreases with increasing driving force as well as a reentrant pinning effect in which the particles flow at low drives but become pinned at intermediate drives. This reentrant pinning is associated with a transition from smooth 1D flow at low drives to a clogged state at higher drives that occurs when the particles cluster in a small number of plaquettes and block the flow. When the drive is further increased, particle rearrangements occur that cause the clog to break apart. We map out the regimes in which the pinned, flowing, and clogged states appear as a function of plaquette filling and drive. The clogged states remain robust at finite temperatures but develop intermittent bursts of flow in which a clog temporarily breaks apart but quickly reforms.

Active particles with desired orientation flowing through a bottleneck

We report extensive numerical simulations of the flow of anisotropic self-propelled particles through a constriction. In particular, we explore the role of the particles’ desired orientation with respect to the moving direction on the system flowability. We observe that when particles propel along the direction of their long axis (longitudinal orientation) the flow-rate notably reduces compared with the case of propulsion along the short axis (transversal orientation). And this is so even when the effective section (measured as the number of particles that are necessary to span the whole outlet) is larger for the case of longitudinal propulsion. This counterintuitive result is explained in terms of the formation of clogging structures at the outlet, which are revealed to have higher stability when the particles align along the long axis. This generic result might be applied to many different systems flowing through bottlenecks such as microbial populations or different kind of cells. Indeed, it has already a straightforward connection with recent results of pedestrian (which self-propel transversally oriented) and mice or sheep (which self-propel longitudinally oriented).

Negative differential mobility and trapping in active matter systems

Using simulations, we examine the average velocity as a function of applied drift force for active matter particles moving through a random obstacle array. We find that for low drift force, there is an initial flow regime where the mobility increases linearly with drive, while for higher drift forces a regime of negative differential mobility appears in which the velocity decreases with increasing drive due to the trapping of active particles behind obstacles. A fully clogged regime exists at very high drift forces when all the particles are permanently trapped behind obstacles. We find for increasing activity that the overall mobility is nonmonotonic, with an enhancement of the mobility for small levels of activity and a decrease in mobility for large activity levels. We show how these effects evolve as a function of disk and obstacle density, active run length, drift force, and motor force.

Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions

The "faster-is-slower" (FIS) effect was first predicted by computer simulations of the egress of pedestrians through a narrow exit [D. Helbing, I. J. Farkas, and T. Vicsek, Nature (London) 407, 487 (2000)]. FIS refers to the finding that, under certain conditions, an excess of the individuals' vigor in the attempt to exit causes a decrease in the flow rate. In general, this effect is identified by the appearance of a minimum when plotting the total evacuation time of a crowd as a function of the pedestrian desired velocity. Here, we experimentally show that the FIS effect indeed occurs in three different systems of discrete particles flowing through a constriction: (a) humans evacuating a room, (b) a herd of sheep entering a barn, and (c) grains flowing out a 2D hopper over a vibrated incline. This finding suggests that FIS is a universal phenomenon for active matter passing through a narrowing.