Nonlocal constitutive relation for steady granular flow

Insights into the rheology of cohesive granular media

An uninterrupted flow of powders is the key to smooth production operations of many industries. However, powders have more difficulty flowing than coarse, granular media like sand because of the interparticle cohesive interactions. What precisely controls the “flowability” of powders remains unclear. Here, we address this issue by performing numerical simulations of the flow of cohesive grains. We show that the cohesiveness during flow is not only controlled by the interparticle adhesion, but also by the stiffness and inelasticity of the grains. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow, i.e., higher “flowability.” This combined effect can be embedded in a single dimensionless number—a result that enriches our understanding of powder rheology.

Characterization and prediction of the “flowability” of powders are of paramount importance in many industries. However, our understanding of the flow of powders like cement or flour is sparse compared to the flow of coarse, granular media like sand. The main difficulty arises because of the presence of adhesive forces between the grains, preventing smooth and continuous flows. Several tests are used in industrial contexts to probe and quantify the “flowability” of powders. However, they remain empirical and would benefit from a detailed study of the physics controlling flow dynamics. Here, we attempt to fill the gap by performing intensive discrete numerical simulations of cohesive grains flowing down an inclined plane. We show that, contrary to what is commonly perceived, the cohesive nature of the flow is not entirely controlled by the interparticle adhesion, but that stiffness and inelasticity of the grains also play a significant role. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow. This observation is rationalized by introducing the concept of a dynamic, “effective” adhesive force, a single parameter, which combines the effects of adhesion, elasticity, and dissipation. Based on this concept, a rheological description of the flow is proposed for the cohesive grains. Our results elucidate the physics controlling the flow of cohesive granular materials, which may help in designing new approaches to characterize the “flowability” of powders.

Discrete Element Method Investigation of Binary Granular Flows with Different Particle Shapes

The effects of particle shape differences on binary mixture shear flows are investigated using the Discrete Element Method (DEM). The binary mixtures consist of frictionless rods and disks, which have the same volume but significantly different shapes. In the shear flows, stacking structures of rods and disks are formed. The effects of the composition of the mixture on the stacking are examined. It is found that the number fraction of stacking particles is smaller for the mixtures than for the monodisperse rods and disks. For binary mixtures with small particle shape differences, the mixture stresses are bounded by the stresses of the two corresponding monodisperse systems. However, for binary mixtures with large particle shape differences, the stresses of the mixtures can be larger than the stresses of the monodisperse systems at large solid volume fractions because larger differences in particle shape cause geometrical interference in packing, leading to stronger particle–particle interactions in the flow. The stresses in dense binary mixtures are found to be exponential functions of the order parameter, which is a measure of particle alignment. Based on the simulation results, an empirical expression for the bulk friction coefficient (ratio of the shear stress to normal stress) for dense binary flows is proposed by accounting for the effects of particle alignment and solid volume fraction.

Depletion attraction impairs the plasticity of emulsions flowing in a constriction

We study the elasto-plastic behavior of dense attractive emulsions under a mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration of surfactant micelles in the continuous phase. We find that such attractive forces are not sufficient to induce any measurable modification on the scalings between the local packing fraction and the deformation of the droplets. However, when the emulsions are flowed through 2D microfluidic constrictions, we uncover a measurable effect of attraction on their elasto-plastic response. Indeed, we measure higher levels of deformation inside the constriction for attractive droplets. In addition, we show that these measurements correlate with droplet rearrangements that are spatially delayed in the constriction for higher attraction forces.

Additive rheology of complex granular flows

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Granular materials are abundant in nature, but we haven’t fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

Force fluctuations at the transition from quasi-static to inertial granular flow

We analyse the rheology of gravity-driven, dry granular flows in experiments where individual forces within the flow bulk are measured. We release photoelastic discs at the top of an incline to create a quasi-static erodible bed over which flows a steady 2D avalanche. The flowing layers we produce are dense (φ ≈ 0.8), thin (h ≈ 10d), and in the slow to intermediate flow regime (I = 0.1 to 1). Using particle tracking and photoelastic force measurements we report coarse-grained profiles for packing fraction, velocity, shear rate, inertial number, and stress tensor components. In addition, we define a quantitative measure for the rate of generation of new force chain networks and we observe that fluctuations extend below the boundary between dense flow and quasi-static layers. Finally, we evaluate several existing definitions for granular fluidity, and make comparisons among them and the behaviour of our experimentally-measured stress tensor components. Our measurements of the non-dimensional stress ratio μ show that our experiments lie within the local rheological regime, yet we observe rearrangements of the force network extending into the quasi-static layer where shear rates vanish. This elucidates why non-local rheological models rely on the notion of stress diffusion, and we thus propose non-local effects may in fact be dependent on the local force network fluctuation rate.

Friction-mediated flow and jamming in a two-dimensional silo with two exit orifices

We show that the interparticle friction coefficient significantly influences the flow and jamming behavior of granular materials exiting through the orifice of a two-dimensional silo in the presence of another orifice located in its vicinity. The fluctuations emanating from a continuous flow through a larger orifice results in an intermittent flow through the smaller orifice consisting of sequential jamming and flowing events. The mean time duration of jammed and flow events, respectively, increase and decrease monotonically with increasing interparticle friction coefficient. The frequency of unjamming instances (n_{u}), however, shows a nonmonotonic behavior comprising an increase followed by a decrease with increasing friction coefficient. The decrease on either side of the maximum, then, represents a system moving progressively towards a permanently jammed or a permanently flowing state. The overall behavior shows a systematic dependence on the interorifice distance, which determines the strength of the fluctuations reaching the smaller orifice leading to unjamming instances. The probability distributions of jamming and flowing times are nearly similar for different combinations of friction coefficients and interorifice distances studied and, respectively, exhibit exponential and power-law tails.

Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient μ scales with the square root of the local Péclet number Pe provided that the particle diameter exceeds the particle mean free path. With decreasing Pe and granular temperature gradient M, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by M.

Photoelastic study of dense granular free-surface flows

In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime (I≤1), dense (φ≈0.8), and thin (h≈10d). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.

Mean force and fluctuations on a wall immersed in a sheared granular flow

In a sheared and confined granular flow, the mean force and the force fluctuations on a rigid wall are studied by means of numerical simulations based on the discrete element method. An original periodic immersed-wall system is designed to investigate a wide range of confinement pressure and shearing velocity imposed at the top of the flow, considering different obstacle heights. The mean pressure on the wall relative to the confinement pressure is found to be a monotonic function of the boundary macroscopic inertial number which encapsulates the confinement pressure, the shearing velocity, and the thickness of the sheared layer above the wall. The one-to-one relation is slightly affected by the length of the granular system. The force fluctuations on the wall are quantified through the analysis of both the distributions of grain-wall contact forces and the autocorrelation of force time series. The distributions narrow as the boundary macroscopic inertial number decreases, moving from asymmetric log-normal shape to nearly Gaussian-type shape. That evolution of the grain-wall force distributions is accompanied at the lowest inertial numbers by the occurrence of a system memory in terms of the force transmitted to the wall, provided that the system length is not too large. Moreover, the distributions of grain-wall contact forces are unchanged when the inertial number is increased above a critical value. All those results allow to clearly identify the transitions from quasistatic to dense inertial, and from dense inertial to collisional, granular flow regimes.

Nonlocal Effects in Inhomogeneous Flows of Soft Athermal Disks

We numerically investigate nonlocal effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave-number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with nonlocal constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.

Ultrasonic tracking of a sinking ball in a vibrated dense granular suspension

Observing and understanding the motion of an intruder through opaque dense suspensions such as quicksand remains a practical and conceptual challenge. Here we use an ultrasonic probe to monitor the sinking dynamics of a steel ball in a dense glass bead packing (3D) saturated by water. We show that the frictional model developed for dry granular media can be used to describe the ball motion induced by horizontal vibration. From this rheology, we infer the static friction coefficient and effective viscosity that decrease when increasing the vibration intensity. Our main finding is that the vibration-induced reduction of the yield stress and increase of the sinking depth are presumably due to micro-slips induced at the grain contacts but without visible plastic deformation due to macroscopic rearrangements, in contrast to dry granular packings. To explain these results, we propose a mechanism of acoustic lubrication that reduces the inter-particle friction and leads to a decrease of the yield stress. This scenario is different from the mechanism of liquefaction usually invoked in loosely packed quicksands where the vibration-induced compaction increases the pore pressure and decreases the confining pressure on the solid skeleton, thus reducing the granular resistance to external load.

Effective packing fraction for better resolution near the critical point of shear thickening suspensions

We present a technique for obtaining an effective packing fraction for discontinuous shear thickening suspensions near a critical point. It uses a measurable quantity that diverges at the critical point-in this case the inverse of the shear rate γ[over ̇]_{c}^{-1} at the onset of discontinuous shear thickening-as a proxy for packing fraction ϕ. We obtain an effective packing fraction for cornstarch and water by fitting γ[over ̇]_{c}^{-1}(ϕ) and then invert the function to obtain ϕ_{eff}(γ[over ̇]_{c}). We further include the dependence of γ[over ̇]_{c}^{-1} on the rheometer gap d to obtain the function ϕ_{eff}(γ[over ̇]_{c},d). This effective packing fraction ϕ_{eff} has better resolution near the critical point than the raw measured packing fraction ϕ by as much as an order of magnitude. Furthermore, ϕ_{eff} normalized by the critical packing fraction ϕ_{c} can be used to compare rheology data for cornstarch and water suspensions from different laboratory environments with different temperature and humidity. This technique can be straightforwardly generalized to improve resolution in any system with a diverging quantity near a critical point.

Flow-Arrest Transitions in Frictional Granular Matter

The transition between shear-flowing and shear-arrested states of frictional granular matter is studied using constant-stress discrete element simulations. By subjecting a dilute system of frictional grains to a constant external shear stress and pressure, friction-dependent critical shear stress and density are clearly identified with both exhibiting a crossover between low and high friction. The critical shear stress bifurcates two nonequilibrium steady states: (i) steady state shear flow characterized by a constant deformation rate, and (ii) shear arrest characterized by temporally decaying creep to a statically stable state. The onset of arrest below critical shear stress occurs at a time t_{c} that exhibits a heavy-tailed distribution, whose mean and variance diverge as a power law at the critical shear stress with a friction-dependent exponent that also exhibits a crossover between low and high friction. These observations indicate that granular arrest near critical shear stress is highly unpredictable and is strongly influenced by interparticle friction.

Energy Fluctuations in Slowly Sheared Granular Materials

Here we show the first experimental measurement of the particle-scale energy fluctuations ΔE in a slowly sheared layer of photoelastic disks. Starting from an isotropically jammed state, applying shear causes the shear-induced stochastic strengthening and weakening of particle-scale energies, whose statistics and dynamics govern the evolution of the macroscopic stress-strain curve. We find that the ΔE behave as a temperaturelike noise field, showing a novel, Boltzmann-type, double-exponential distribution at any given shear strain γ. Following the framework of the soft glassy rheology theory, we extract an effective temperature χ from the statistics of the energy fluctuations to interpret the slow startup shear (shear starts from an isotropically jammed state) of granular materials as an "aging" process: Starting below one, χ gradually approaches one as γ increases, similar to those of spin glasses, thermal glasses, and bulk metallic glasses.

X-ray rheography uncovers planar granular flows despite non-planar walls

Extremely useful techniques exist to observe the interior of deforming opaque materials, but these methods either require that the sample is replaced with a model material or that the motion is stopped intermittently. For example, X-ray computed tomography cannot measure the continuous flow of materials due to the significant scanning time required for density reconstruction. Here we resolve this technological gap with an alternative X-ray method that does not require such tomographs. Instead our approach uses correlation analysis of successive high-speed radiographs from just three directions to directly reconstruct three-dimensional velocities. When demonstrated on a steady granular system, we discover a compressible flow field that has planar streamlines despite curved confining boundaries, in surprising contrast to Newtonian fluids. More generally, our new X-ray technique can be applied using synchronous source/detector pairs to investigate transient phenomena in various soft matter such as biological tissues, geomaterials and foams.

Tracking the deformation of opaque materials under their surfaces is fascinating, yet a challenging task, which has been constrained to static conditions or model materials to date. Here, Baker et al. develop X-ray rheography to reconstruct three-dimensional velocity fields in general granular media.

Strain localization in dry sheared granular materials: A compactivity-based approach

Shear banding is widely observed in natural fault zones as well as in laboratory experiments on granular materials. Understanding the dynamics of strain localization under different loading conditions is essential for quantifying strength evolution of fault gouge and energy partitioning during earthquakes and characterizing rheological transitions and fault zone structure changes. To that end, we develop a physics-based continuum model for strain localization in sheared granular materials. The grain-scale dynamics is described by the shear transformation zone (STZ) theory, a nonequilibrium statistical thermodynamic framework for viscoplastic deformation in amorphous materials. Using a finite strain computational framework, we investigate the initiation and growth of complex shear bands under a variety of loading conditions and identify implications for strength evolution and the ductile to brittle transition. Our numerical results show similar localization patterns to field and laboratory observations and suggest that shear zones show more ductile response at higher confining pressures, lower dilatancy, and loose initial conditions. Lower pressures, higher dilatancy, and dense initial conditions favor a brittle response and larger strength drops. These findings shed light on a range of mechanisms for strength evolution in dry sheared granular materials and provide a critical input to physics-based multiscale models of fault zone instabilities.

Plastic flow and localization in an amorphous material: Experimental interpretation of the fluidity

We present a thorough study of the plastic response of a granular material progressively loaded. We study experimentally the evolution of the plastic field from a homogeneous one to a heterogeneous one and its fluctuations in terms of incremental strain. We show that the plastic field can be decomposed in two components evolving on two decoupled strain increment scales. We argue that the slowly varying part of the field can be identified with the so-called fluidity field introduced recently to interpret the rheological behavior of amorphous materials. This fluidity field progressively concentrates along a macroscopic direction corresponding to the Mohr-Coulomb angle.

Structural and topological nature of plasticity in sheared granular materials

Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for microscopic plasticity in disordered granular packings. The elementary plastic events occur through flip events which correspond to a neighbor switching process among these coplanar tetrahedra (or equivalently as the rotation motion of 4-ring disclinations). These events are discrete in space and possess specific orientations with the principal stress direction.

It is a general consensus that the structural defects are the plasticity carriers in amorphous solids, but its microscopic view remains largely unknown. Cao et a. show that highly distorted coplanar tetrahedra act as defects in granular packings, which flip under shear to carry local plasticity.

Spreading of a granular droplet under horizontal vibrations

By means of three-dimensional discrete element simulations, we study the spreading of a granular droplet on a horizontally vibrated plate. Apart from a short transient with a parabolic shape, the droplet adopts a triangular profile during the spreading. The dynamics of the spreading is governed by two distinct regimes: a superdiffusive regime in the early stages driven by surface flow followed by a second one which is subdiffusive and governed by bulk flow. The plate bumpiness is found to alter only the spreading rate but plays a minor role on the shape of the granular droplet and on the scaling laws of the spreading. Importantly, we show that in the subdiffusive regime, the effective friction between the plate and the granular droplet can be interpreted in the framework of the μ(I)-rheology.

Critical scaling near the yielding transition in granular media

We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low-inertial-number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress Σ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied Σ, isotropically prepared states with size L must undergo a total strain γ_{ms}(Σ,L). The number density of MS packings (∝γ_{ms}^{-1}) vanishes for Σ>Σ_{c}≈0.11 according to a critical scaling form with a length scale ξ∝|Σ-Σ_{c}|^{-ν}, where ν≈1.7-1.8. Above the yield stress (Σ>Σ_{c}), no MS packings that can support Σ exist in the large-system limit L/ξ≫1. MS packings generated via shear possess anisotropic force and contact networks, suggesting that Σ_{c} is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.

Size-dependence of the flow threshold in dense granular materials

The flow threshold in dense granular materials is typically modeled by local, stress-based criteria. However, grain-scale cooperativity leads to size effects that cannot be captured with local conditions. In a widely studied example, flows of thin layers of grains down an inclined surface exhibit a size effect whereby thinner layers require more tilt to flow. In this paper, we consider the question of whether the size-dependence of the flow threshold observed in inclined plane flow is configurationally general. Specifically, we consider three different examples of inhomogeneous flow - planar shear flow with gravity, annular shear flow, and vertical chute flow - using two-dimensional discrete-element method calculations and show that the flow threshold is indeed size-dependent in these flow configurations, displaying additional strengthening as the system size is reduced. We then show that the nonlocal granular fluidity model - a nonlocal continuum model for dense granular flow - is capable of quantitatively capturing the observed size-dependent strengthening in all three flow configurations.

Quantifying flow and stress in ice mélange, the world's largest granular material

Tidewater glacier fjords are often filled with a collection of calved icebergs, brash ice, and sea ice. For glaciers with high calving rates, this "mélange" of ice can be jam-packed, so that the flow of ice fragments is mostly determined by granular interactions. In the jammed state, ice mélange has been hypothesized to influence iceberg calving and capsize, dispersion and attenuation of ocean waves, injection of freshwater into fjords, and fjord circulation. However, detailed measurements of ice mélange are lacking due to difficulties in instrumenting remote, ice-choked fjords. Here we characterize the flow and associated stress in ice mélange, using a combination of terrestrial radar data, laboratory experiments, and numerical simulations. We find that, during periods of terminus quiescence, ice mélange experiences laminar flow over timescales of hours to days. The uniform flow fields are bounded by shear margins along fjord walls where force chains between granular icebergs terminate. In addition, the average force per unit width that is transmitted to the glacier terminus, which can exceed 10⁷ N/m, increases exponentially with the mélange length-to-width ratio. These "buttressing" forces are sufficiently high to inhibit the initiation of large-scale calving events, supporting the notion that ice mélange can be viewed as a weak granular ice shelf that transmits stresses from fjord walls back to glacier termini.

Nonlocal rheology of dense granular flow in annular shear experiments

The flow of dense granular materials at low inertial numbers cannot be fully characterized by local rheological models; several nonlocal rheologies have recently been developed to address these shortcomings. To test the efficacy of these models across different packing fractions and shear rates, we perform experiments in a quasi-2D annular shear cell with a fixed outer wall and a rotating inner wall, using photoelastic particles. The apparatus is designed to measure both the stress ratio μ (the ratio of shear to normal stress) and the inertial number I through the use of a torque sensor, laser-cut leaf springs, and particle-tracking. We obtain μ(I) curves for several different packing fractions and rotation rates, and successfully find that a single set of model parameters is able to capture the full range of data collected once we account for frictional drag with the bottom plate. Our measurements confirm the prediction that there is a growing lengthscale at a finite value μs, associated with a frictional yield criterion. Finally, we newly identify the physical mechanism behind this transition at μs by observing that it corresponds to a drop in the susceptibility to force chain fluctuations.

Archimedes' law explains penetration of solids into granular media

Understanding the response of granular matter to intrusion of solid objects is key to modelling many aspects of behaviour of granular matter, including plastic flow. Here we report a general model for such a quasistatic process. Using a range of experiments, we first show that the relation between the penetration depth and the force resisting it, transiently nonlinear and then linear, is scalable to a universal form. We show that the gradient of the steady-state part, K ϕ , depends only on the medium's internal friction angle, ϕ, and that it is nonlinear in μ = tan ϕ, in contrast to an existing conjecture. We further show that the intrusion of any convex solid shape satisfies a modified Archimedes' law and use this to: relate the zero-depth intercept of the linear part to K ϕ and the intruder's cross-section; explain the curve's nonlinear part in terms of the stagnant zone's development.

Erosion and deposition processes in surface granular flows

We report on experiments aiming at characterizing erosion and deposition processes on a tilted granular bed. We investigate the existence of the neutral angle, that is, the critical angle at which erosion exactly balances accretion after the passage of a granular avalanche of a finite mass. Experiments show in particular that the neutral angle depends on both avalanche mass and shape but is rather insensitive to the bed length. This result strongly suggests that the effective friction between the static and mobile granular phases cannot be taken as an intrinsic property that is only material dependent but should be considered a flow-dependent property. Interestingly, for a given avalanche mass, the net erosion rate increases linearly with the angular deviation from the neutral angle. We also compare our data with the predictions of the erosion-deposition model introduced by Bouchaud, Cates, Ravi Prakash, and Edwards (BCRE) [J. Phys. I 4, 1283 (1994)JPGCE81155-430410.1051/jp1:1994195]. We show that the predictions drawn from the modified version of the BCRE model proposed by Boutreux and de Gennes, in which the local erosion rate between the static and mobile phases is independent of the flow thickness, are in remarkable agreement with the experimental results.

Bulk and local rheology in a dense and vibrated granular suspension

In this paper, we investigate experimentally the dynamics of particles in dense granular suspensions when both shear and external vibrations are applied. We study in detail how vibrations affect particle reorganization at the local scale and modify the apparent rheology. The nonlocal nature of the rheology when no vibrations are applied is evidenced, in agreement with previous numerical studies from the literature. It is also shown that vibrations induce structural reorganizations, which tend to homogenize the system and cancel the nonlocal properties.

Relaxation-type nonlocal inertial-number rheology for dry granular flows

We propose a constitutive model to describe the nonlocality, hysteresis, and several flow features of dry granular materials. Taking the well-known inertial number I as a measure of sheared-induced local fluidization, we derive a relaxation model for I according to the evolution of microstructure during avalanche and dissipation processes. The model yields a nonmonotonic flow law for a homogeneous flow, accounting for hysteretic solid-fluid transition and intermittency in quasistatic flows. For an inhomogeneous flow, the model predicts a generalized Bagnold shear stress revealing the interplay of two microscopic nonlocal mechanisms: collisions among correlated structures and the diffusion of fluidization within the structures. In describing a uniform flow down an incline, the model reproduces the hysteretic starting and stopping heights and the Pouliquen flow rule for mean velocity. Moreover, a dimensionless parameter reflecting the nonlocal effect on the flow is discovered, which controls the transition between Bagnold and creeping flow dynamics.

Sidewall-friction-driven ordering transition in granular channel flows: Implications for granular rheology

We report a transition from a disordered state to an ordered state in the flow of nearly monodisperse granular matter flowing in an inclined channel with planar slide walls and a bumpy base, using discrete element method simulations. For low particle-sidewall friction coefficients, the flowing particles are disordered, however, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cross section of the channel, with the highest ordering near the sidewalls. The flow transition significantly affects the local rheology-the effective friction coefficient is lower, and the packing fraction is higher, in the ordered state compared to the disordered state. A simple model, incorporating the extent of local ordering, is shown to describe the rheology of the system.

Microstructures and mechanics in the colloidal film drying process

We use Brownian Dynamics (BD) simulations and continuum models to study the microstructures and mechanics in the colloidal film drying process. Colloidal suspensions are compressed between a planar moving interface and a stationary substrate. In the BD simulations, we develop a new Energy Minimization Potential-Free (EMPF) algorithm to enforce the hard-sphere potential in confined systems and to accurately measure the stress profile. The interface moves either at a constant velocity U_w or via a constant imposed normal stress Σ_e. Comparing the interface motions to the particle Brownian motion defines the Péclet numbers Pe_U = U_wa/d₀ and Pe_Σ = Σ_ea³/k_BT, respectively, where d₀ = k_BT/ζ with k_BT the thermal energy scale, ζ the single-particle resistance, and a the particle radius. With a constant interface velocity, thermodynamics drives the suspension behavior when Pe_U ≪ 1, and homogeneous crystallization appears when the gap spacing between the two boundaries pushes the volume fraction above the equilibrium phase boundary. In contrast, when Pe_U ≫ 1, local epitaxial crystal growth appears adjacent to the moving interface even for large gap sizes. Interestingly, the most amorphous film microstructures are found at moderate Pe_U. The film stress profile develops sharp transitions and becomes step-like with growing Péclet number. With a constant imposed stress, the interface stops moving as the suspension pressure increases and the microstructural and mechanical behaviors are similar to the constant velocity case. Comparison with the simulations shows that the model accurately captures the stress on the moving interface, and quantitatively resolves the local stress and volume fraction distributions for low to moderate Péclet numbers. This work demonstrates the critical role of interface motion on the film microstructures and stresses.

Granular materials flow like complex fluids

Granular materials such as sand, powders and foams are ubiquitous in daily life and in industrial and geotechnical applications. These disordered systems form stable structures when unperturbed, but in the presence of external influences such as tapping or shear they 'relax', becoming fluid in nature. It is often assumed that the relaxation dynamics of granular systems is similar to that of thermal glass-forming systems. However, so far it has not been possible to determine experimentally the dynamic properties of three-dimensional granular systems at the particle level. This lack of experimental data, combined with the fact that the motion of granular particles involves friction (whereas the motion of particles in thermal glass-forming systems does not), means that an accurate description of the relaxation dynamics of granular materials is lacking. Here we use X-ray tomography to determine the microscale relaxation dynamics of hard granular ellipsoids subject to an oscillatory shear. We find that the distribution of the displacements of the ellipsoids is well described by a Gumbel law (which is similar to a Gaussian distribution for small displacements but has a heavier tail for larger displacements), with a shape parameter that is independent of the amplitude of the shear strain and of the time. Despite this universality, the mean squared displacement of an individual ellipsoid follows a power law as a function of time, with an exponent that does depend on the strain amplitude and time. We argue that these results are related to microscale relaxation mechanisms that involve friction and memory effects (whereby the motion of an ellipsoid at a given point in time depends on its previous motion). Our observations demonstrate that, at the particle level, the dynamic behaviour of granular systems is qualitatively different from that of thermal glass-forming systems, and is instead more similar to that of complex fluids. We conclude that granular materials can relax even when the driving strain is weak.

Vortices Enhance Diffusion in Dense Granular Flows

This Letter introduces unexpected diffusion properties in dense granular flows and shows that they result from the development of partially jammed clusters of grains, or granular vortices. Transverse diffusion coefficients D and average vortex sizes ℓ are systematically measured in simulated plane shear flows at differing inertial numbers I revealing (i) a strong deviation from the expected scaling D∝d^{2}γ[over ˙] involving the grain size d and shear rate γ[over ˙] and (ii) an increase in average vortex size ℓ at low I, following ℓ∝dI^{-1/2} but limited by the system size. A general scaling D∝ℓdγ[over ˙] is introduced that captures all the measurements and highlights the key role of vortex size. This leads to establishing a scaling for the diffusivity in dense granular flow as D∝d^{2}sqrt[γ[over ˙]/t_{i}] involving the geometric average of shear time 1/γ[over ˙] and inertial time t_{i} as the relevant time scale. Analysis of grain trajectories is further evidence that this diffusion process arises from a vortex-driven random walk.

Force fluctuations on a wall in interaction with a granular lid-driven cavity flow

The force fluctuations experienced by a boundary wall subjected to a lid-driven cavity flow are investigated by means of numerical simulations based on the discrete-element method. The time-averaged dynamics inside the cavity volume and the resulting steady force on the wall are governed by the boundary macroscopic inertial number, the latter being derived from the shearing velocity and the confinement pressure imposed at the top. The force fluctuations are quantified through measuring both the autocorrelation of force time series and the distributions of grain-wall forces, at distinct spatial scales from particle scale to wall scale. A key result is that the grain-wall force distributions are entirely driven by the boundary macroscopic inertial number, whatever the spatial scale considered. In particular, when the wall scale is considered, the distributions are found to evolve from nearly exponential to nearly Gaussian distributions by decreasing the macroscopic inertial number. The transition from quasistatic to dense inertial flow is well identified through remarkable changes in the shapes of the distributions of grain-wall forces, accompanied by a loss of system memory in terms of the mesoscale force transmitted toward the wall.

Liquidlike sloshing dynamics of monodisperse granulate

Analogies between fluid flows and granular flows are useful because they pave the way for continuum treatments of granular media. However, in practice it is impossible to predict under what experimental conditions the dynamics of fluids and granulates are qualitatively similar. In the case of unsteadily driven systems no such analogy is known. For example, in a partially filled container subject to horizontal oscillations liquids slosh, whereas granular media of complex particles exhibit large-scale convection rolls. We here show that smooth monodisperse steel spheres exhibit liquidlike sloshing dynamics. Our findings highlight the role of particle material and geometry for the dynamics and phase transitions of the system.

Transport analogy for segregation and granular rheology

Here, we show a direct connection between density-based segregation and granular rheology that can lead to insight into both problems. Our results exhibit a transition in the rate of segregation during simple shear that occurs at I∼0.5 and mimics a coincident regime change in flow rheology. We propose scaling arguments that support a packing fraction criterion for this transition that can both explain our segregation results as well as unify existing literature studies of granular rheology. By recasting a segregation model in terms of rheological parameters, we establish an approach that not only collapses results for a wide range of conditions, but also yields a direct relationship between the coordination number z and the segregation velocity. Moreover, our approach predicts the precise location of the observed regime change or saturation. This suggests that it is possible to rationally design process operating conditions that lead to significantly lower segregation extents. These observations can have a profound impact on both the study of granular flow or mixing as well as industrial practice.

Non-trivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins of non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

Viscorotational shear instability of Keplerian granular flows

The linear stability of viscous Keplerian flow around a gravitating center is studied using the rheological granular fluid model. The linear rheological instability triggered by the interplay of the shear rheology and Keplerian differential rotation of incompressible dense granular fluids is found. Instability sets in in granular fluids, where the viscosity parameter grows faster than the square of the local shear rate (strain rate) at constant pressure. Found instability can play a crucial role in the dynamics of dense planetary rings and granular flows in protoplanetary disks.