Fluctuations, jamming, and yielding for a driven probe particle in disordered disk assemblies

Universal features of the stick-slip dynamics of an intruder moving through a confined granular medium

Experiments and simulations of an intruder dragged by a spring through a two-dimensional annulus of granular material exhibit robust force fluctuations. At low packing fractions (ϕ<ϕ_{0}), the intruder clears an open channel. Above ϕ_{0}, stick-slip dynamics develop, with an average energy release that is independent of the particle-particle and particle-base friction coefficients but does depend on the width W of the annulus and the diameter D of the intruder. A simple model predicts the dependence of ϕ_{0} on W and D, allowing for a data collapse for the average energy release as a function of ϕ/ϕ_{0}. These results pose challenges for theories of mechanical failure in amorphous materials.

Stress propagation in locally loaded packings of disks and pentagons

The mechanical strength and flow of granular materials can depend strongly on the shapes of individual grains. We report quantitative results obtained from photoelasticimetry experiments on locally loaded, quasi-two-dimensional granular packings of either disks or pentagons exhibiting stick-slip dynamics. Packings of pentagons resist the intruder at significantly lower packing fractions than packings of disks, transmitting stresses from the intruder to the boundaries over a smaller spatial extent. Moreover, packings of pentagons feature significantly fewer back-bending force chains than packings of disks. Data obtained on the forward spatial extent of stresses and back-bending force chains collapse when the packing fraction is rescaled according to the packing fraction of steady state open channel formation, though data on intruder forces and dynamics do not collapse. We comment on the influence of system size on these findings and highlight connections with the dynamics of the disks and pentagons during slip events.

Particle dynamics in two-dimensional point-loaded granular media composed of circular or pentagonal grains

Granular packings exhibit significant changes in rheological and structural properties when the rotational symmetry of spherical or circular particles is broken. Here, we report on experiments exploring the differences in dynamics of a grain-scale intruder driven through a packing of either disks or pentagons, where the presence of edges and vertices on grains introduces the possibility of rotational constraints at edge-edge contacts. We observe that the intruder’s stick-slip dynamics are comparable between the disk packing near the frictional jamming fraction and the pentagonal packing at significantly lower packing fractions. We connect this stark contrast in packing fraction with the average speed and rotation fields of grains during slip events, finding that rotation of pentagons is limited and the flow of pentagonal grains is largely confined in front of the intruder, whereas disks rotate more on average and circulate around the intruder to fill the open channel behind it. Our results indicate that grain-scale rotation constraints significantly modify collective motion of grains on mesoscopic scales and correspondingly enhance resistance to penetration of a local intruder.

Intruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics

We present simulation results for an intruder pulled through a two-dimensional granular system by a spring using a model designed to mimic the experiments described by Kozlowski et al. [Phys. Rev. E 100, 032905 (2019)2470-004510.1103/PhysRevE.100.032905]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. We then use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider both static and dynamic basal friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick-slip behavior when the coefficient is decreased below 0.1, while static friction plays only a marginal role.

Dynamics of a grain-scale intruder in a two-dimensional granular medium with and without basal friction

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a two-dimensional granular material composed of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: A frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: Intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.

Active microrheology, Hall effect, and jamming in chiral fluids

We examine the motion of a probe particle driven through a chiral fluid composed of circularly swimming disks. We find that the probe particle travels in both the longitudinal direction, parallel to the driving force, and in the transverse direction, perpendicular to the driving force, giving rise to a Hall angle. Under constant driving force, we show that the probe particle velocity in both the longitudinal and transverse directions exhibits nonmonotonic behavior as a function of the activity of the circle swimmers. The Hall angle is maximized when a resonance occurs between the frequency of the chiral disks and the motion of the probe particle. As the density of the chiral fluid increases, the Hall angle gradually decreases before reaching zero when the system enters a jammed state. We show that the onset of jamming depends on the chiral particle swimming frequency, with a fluid state appearing at low frequencies and a jammed solid occurring at high frequencies.

Observation of Strongly Heterogeneous Dynamics at the Depinning Transition in a Colloidal Glass

We study experimentally the origin of heterogeneous dynamics in strongly driven glass-forming systems. Thereto, we apply a well-defined force with a laser line trap on individual colloidal polystyrene probe particles seeded in an emulsion glass composed of droplets of the same size. Fluid and glass states can be probed. We monitor the trajectories of the probe and measure displacements and their distributions. Our experiments reveal intermittent dynamics around a depinning transition at a threshold force. For smaller forces, linear response connects mean displacement, and quiescent mean squared displacement. Mode coupling theory calculations rationalize the observations.

The physics of jamming for granular materials: a review

Granular materials consist of macroscopic grains, interacting via contact forces, and unaffected by thermal fluctuations. They are one of a class systems that undergo jamming, i.e. a transition between fluid-like and disordered solid-like states. Roughly twenty years ago, proposals by Cates et al for the shear response of colloidal systems and by Liu and Nagel, for a universal jamming diagram in a parameter space of packing fraction, ϕ, shear stress, τ, and temperature, T raised key questions. Contemporaneously, experiments by Howell et al and numerical simulations by Radjai et al and by Luding et al helped provide a starting point to explore key insights into jamming for dry, cohesionless, granular materials. A recent experimental observation by Bi et al is that frictional granular materials have a a re-entrant region in their jamming diagram. In a range of ϕ, applying shear strain, γ, from an initially force/stress free state leads to fragile (in the sense of Cates et al), then anisotropic shear jammed states. Shear jamming at fixed ϕ is presumably conjugate to Reynolds dilatancy, involving dilation under shear against deformable boundaries. Numerical studies by Radjai and Roux showed that Reynolds dilatancy does not occur for frictionless systems. Recent numerical studies by several groups show that shear jamming occurs for finite, but not infinite, systems of frictionless grains. Shear jamming does not lead to known ordering in position space, but Sarkar et al showed that ordering occurs in a space of force tiles. Experimental studies seeking to understand random loose and random close packings (rlp and rcp) and dating back to Bernal have probed granular packings and their response to shear and intruder motion. These studies suggest that rlp's are anisotropic and shear-jammed-like, whereas rcp's are likely isotropically jammed states. Jammed states are inherently static, but the jamming diagram may provide a context for understanding rheology, i.e. dynamic shear in a variety of systems that include granular materials and suspensions.

Casimir effect between pinned particles in two-dimensional jammed systems

The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.

Fluctuations in flows near jamming

Bubbles, droplets or particles in flowing complex media such as foams, emulsions or suspensions follow highly complex paths, with the relative motion of the constituents setting the energy dissipation rate. What is their dynamics, and how is this connected to the global rheology? To address these questions, we probe the statistics and spatio-temporal organization of the local particle motion and energy dissipation in a model for sheared disordered materials. We find that the fluctuations in the local dissipation vary from nearly Gaussian and homogeneous at low densities and fast flows, to strongly intermittent for large densities and slow flows. The higher order moments of the relative particle velocities reveal strong evidence for a qualitative difference between two distinct regimes which are nevertheless connected by a smooth crossover. In the critical regime, the higher order moments are related by novel multiscaling relations. In the plastic regime the relations between these moments take on a different form, with higher moments diverging rapidly when the flow rate vanishes. As these velocity differences govern the energy dissipation, we can distinguish two qualitatively different types of flow: an intermediate density, critical regime related to jamming, and a large density, plastic regime.

Active microrheology in active matter systems: Mobility, intermittency, and avalanches

We examine the mobility and velocity fluctuations of a driven particle moving through an active matter bath of self-mobile disks for varied density or area coverage and varied activity. We show that the driven particle mobility can exhibit nonmonotonic behavior that is correlated with distinct changes in the spatiotemporal structures that arise in the active media. We demonstrate that the probe particle velocity distributions exhibit specific features in the different dynamic regimes and identify an activity-induced uniform crystallization that occurs for moderate activity levels and is distinct from the previously observed higher activity cluster phase. The velocity distribution in the cluster phase has telegraph noise characteristics produced when the probe particle moves alternately through high-mobility areas that are in the gas state and low-mobility areas that are in the dense phase. For higher densities and large activities, the system enters what we characterize as an active jamming regime. Here the probe particle moves in intermittent jumps or avalanches that have power-law-distributed sizes that are similar to the avalanche distributions observed for nonactive disk systems near the jamming transition.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Aspects of jamming in two-dimensional athermal frictionless systems

In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range repulsive interactions, where the onset of jamming occurs at a critical packing density and where certain quantities show a divergence indicative of critical behavior. We describe how aspects of the dynamics change as the jamming density is approached and how these dynamics can be explored using externally driven probes. Different particle shapes can produce jamming densities much lower than those observed for disk-shaped particles, and we show how jamming exhibits fragility for some shapes while for other shapes this is absent. Next we describe the effects of long range interactions and jamming behavior in systems such as charged colloids, vortices in type-II superconductors, and dislocations. We consider the effect of adding obstacles to frictionless jamming systems and discuss connections between this type of jamming and systems that exhibit depinning transitions. Finally, we discuss open questions such as whether the jamming transition in all these different systems can be described by the same or a small subset of universal behaviors, as well as future directions for studies of jamming transitions in two dimensional systems, such as jamming in self-driven or active matter systems.

Colloidal lattice shearing and rupturing with a driven line of particles

We examine the dynamics of two-dimensional colloidal systems using numerical simulations of a system with a drive applied to a thin region in the middle of the sample to produce a local shear. For a monodisperse colloidal assembly, we find a well-defined decoupling transition separating a regime of elastic motion from a plastic phase where the driven particles break away or decouple from the bulk particles and produce a shear band. For a bidisperse assembly, the onset of a bulk disordering transition coincides with the broadening of the shear band. We identify several distinct dynamical regimes that are correlated with features in the velocity-force curves. As a function of bidispersity, the decoupling force shows a nonmonotonic behavior associated with features in the noise fluctuations, power spectra, and bulk velocity profiles. When pinning is added in the bulk, we find that the shear band regions can become more localized, causing a decoupling of the driven particles from the bulk particles. For a system with thermal noise and no pinning, the shear band region becomes more extended and the average velocity of the driven particles drops at the thermal disordering transition of the bulk system.

Nonlinear response and crowding effects in microrheology

The mobility of tagged particles in a microrheological setup has been investigated via molecular dynamics simulations of a three-dimensional Lennard-Jones binary mixture. After coupling a small number of particles to a constant external driving force, the drift velocity and other observables of the dragged probe particles are reported in the linear and nonlinear response regime. In the nonlinear regime significant crowding effects are observed, thereby creating stringlike structures. Formation of the strings further enhances the nonlinear effects. A systematic study of these effects' dependence on temperature and total number of driven probe atoms is presented.

Jamming in systems with quenched disorder

We numerically study the effect of adding quenched disorder in the form of randomly placed pinning sites on jamming transitions in a disk packing that jams at a well-defined point J in the clean limit. Quenched disorder decreases the jamming density and introduces a depinning threshold. The onset of a finite threshold coincides with point J at the lowest pinning densities, but for higher pinning densities there is always a finite depinning threshold even well below jamming. We find that proximity to point J strongly affects the transport curves and noise fluctuations, and we observe a change from plastic behavior below jamming, where the system is highly heterogeneous, to elastic depinning above jamming. Many of the general features we find are related to other systems containing quenched disorder, including the peak effect observed in vortex systems.

Structural responses of quasi-two-dimensional colloidal fluids to excitations elicited by nonequilibrium perturbations

We investigate the response of a dense monodisperse quasi-two-dimensional colloid suspension when a particle is dragged by a constant velocity optical trap. Consistent with microrheological studies of other geometries, the perturbation induces a leading density wave and trailing wake. We also use a hybrid version of Stokesian dynamics simulations to parse direct colloid-colloid and hydrodynamic interactions. We go on to analyze the underlying individual particle-particle collisions in the experimental images. The displacements of particles occur in chains reminiscent of stress propagation in sheared granular materials. From these data, we can reconstruct steady-state dipolar-like flow patterns that were predicted for dilute suspensions and previously observed in granular analogs to our system. The decay of this field differs, however, from point Stokeslet calculations, indicating that the nonzero size of the colloids is important. Moreover, there is a pronounced angular dependence that corresponds to the surrounding colloid structure, which develops in response to the perturbation. Put together, our results show that the response of the complex fluid is highly anisotropic owing to the fact that the effects of the perturbation propagate through the structured medium via chains of colloid-colloid collisions.

Probability Densities of a Forced Probe Particle in Glass: Results from Mode Coupling Theory and Simulations of Active Microrheology

We investigate the displacements of a probe particle inside a glass, when a strong external force is applied to the probe (active nonlinear microrheology). Calculations within mode coupling theory are presented for glasses of hard spheres and compared to Langevin and Brownian dynamics simulations. Under not too strong forces where the probe remains trapped, the probe density distribution becomes anisotropic. It is shifted towards the direction of the force, develops an enhanced tail in that direction (signalled by a positive skewness), and exhibits different variances along and perpendicular to the force direction. A simple model of an harmonically trapped probe rationalizes the low force limit, with strong strain softening setting in at forces of the order of a few thermal energies per particle radius.