Nonlocal rheological properties of granular flows near a jamming limit

Signature of Transition between Granular Solid and Fluid: Rate-Dependent Stick Slips in Steady Shearing

Despite extensive studies on either smooth granular-fluid flow or the solidlike deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of interparticle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers J decades below reported values, we answer how a granular system can transition to the regime sustained by solid-to-solid friction that goes beyond existing paradigms based on suspension rheology.

Rheological properties of composite polymers and hybrid nanocomposites

This paper summarizes a review of the viscosimetric, viscoelastic and rheological properties of polymers and hybrid nanocomposite polymers. Hybrid nanocomposites can be combined from natural fibers or synthetic fibers and/or both. The hybrid nanocomposite polymer offers the designer the opportunity to achieve the required characteristics to a considerable extent controlled by the choice of appropriate fibers or fillers and the polymer architecture. The rheological behavior of hybrid nanocomposite depends on fiber content, fiber length, fiber orientation, fiber-to-matrix bonding, fiber configuration and filler, respectively. Further, rheological properties of hybrid nanocomposite polymers by introducing various charges were examined discussed.

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.

Nonlocal Elasticity near Jamming in Frictionless Soft Spheres

We use simulations of frictionless soft sphere packings to identify novel constitutive relations for linear elasticity near the jamming transition. By forcing packings at varying wavelengths, we directly access their transverse and longitudinal compliances. These are found to be wavelength dependent, in violation of conventional (local) linear elasticity. Crossovers in the compliances select characteristic length scales, which signify the appearance of nonlocal effects. Two of these length scales diverge as the pressure vanishes, indicating that critical effects near jamming control the breakdown of local elasticity. We expect these nonlocal constitutive relations to be applicable to a wide range of weakly jammed solids, including emulsions, foams, and granulates.

Granular avalanches down inclined and vibrated planes

In this article, we study granular avalanches when external mechanical vibrations are applied. We identify conditions of flow arrest and compare with the ones classically observed for nonvibrating granular flows down inclines [Phys. Fluids 11, 542 (1999)PHFLE61070-663110.1063/1.869928]. We propose an empirical law to describe the thickness of the deposits with the inclination angle and the vibration intensity. The link between the surface velocity and the depth of the flow highlights a competition between gravity and vibrations induced flows. We identify two distinct regimes: (a) gravity-driven flows at large angles where vibrations do not modify dynamical properties but the deposits (scaling laws in this regime are in agreement with the literature for nonvibrating granular flows) and (b) vibrations-driven flows at small angles where no flow is possible without applied vibrations (in this last regime, the flow behavior can be properly described by a vibration induced activated process). We show, in this study, that granular flows down inclined planes can be finely tuned by external mechanical vibrations.

Enstrophy cascades in two-dimensional dense granular flows

Employing two-dimensional molecular dynamics simulations of dense granular materials under simple shear deformations, we investigate vortex structures of particle rearrangements. Introducing vorticity fields as a measure of local spinning motions of the particles, we observe their heterogeneous distributions, where statistics of vorticity fields exhibit the highly non-Gaussian behavior and typical domain sizes of vorticity fields significantly increase if the system is yielding under quasistatic deformations. In such dense granular flows, a power-law decay of vorticity spectra can be observed at mesoscopic scale, implying anomalous local structures of kinetic energy dissipation. We explain the power-law decay, or enstrophy cascades in dense granular materials, by a dimensional analysis, where the dependence of vorticity spectra not only on the wave number, but also on the shear rate, is well explained. From our dimensional analyses, the scaling of granular temperature and rotational kinetic energy is also predicted.

Anomalous energy cascades in dense granular materials yielding under simple shear deformations

By using molecular dynamics (MD) simulations of dense granular particles in two dimensions, we study turbulent-like structures of their non-affine velocities under simple shear deformations. We find that the spectrum of non-affine velocities, introduced as an analog of the energy spectrum for turbulent flows, exhibits the power-law decay if the system is yielding in a quasi-static regime, where large-scale collective motions and inelastic interactions of granular particles are crucial for the anomalous cascade of kinetic energy. Based on hydrodynamic equations of dense granular materials, which include both kinetic and contact contributions in constitutive relations, we derive a theoretical expression for the spectrum, where a good agreement between the result of MD simulations and theoretical prediction is established over a wide range of length scales.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology μ(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

Hydrodynamic instabilities in shear flows of dry cohesive granular particles

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett., 2005, 94, 054501] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. By numerically solving the dynamic van der Waals model, we observed various heterogeneous structures of density fields in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we found that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, p, and the volume fraction, ϕ, satisfy ∂p/∂ϕ < 0.

Nonlocal effects in sand flows on an inclined plane

The flow of sand on a rough inclined plane is investigated experimentally. We directly show that a jammed layer of grains spontaneously forms below the avalanche. Its properties and its relation with the rheology of the flowing layer of grains are presented and discussed. In a second part, we study the dynamics of erosion and deposition solitary waves in the domain where they are transversally stable. We characterize their shapes and velocity profiles. We relate their translational velocity to the stopping height and to the mass trapped in the avalanche. Finally, we use the velocity profile to get insight into the rheology very close to the jamming limit.

Friction and the oscillatory motion of granular flows

This contribution reports on numerical simulations of two-dimensional granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibit spontaneous oscillatory motion in generic flow conditions, and in this case, whether the frictional properties of the contacts between grains may affect the existence or the characteristics of this oscillatory motion. The analysis of different series of simulations shows that the flow develops an oscillatory motion with a well-defined frequency which increases like the inverse of the velocity's square root. We show that the oscillation is essentially a surface phenomenon. The amplitude of the oscillation is higher for lower volume fractions and can thus be related to the flow velocity and grains' friction properties. The study of the influence of the periodic geometry of the simulation cell shows no significant effect. These results are discussed in relation to sonic sands.

Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

The influence of grain angularity on the properties of dense flows down a rough inclined plane are investigated. Three-dimensional numerical simulations using the nonsmooth contact dynamics method are carried out with both spherical (rounded) and polyhedral (angular) grain assemblies. Both sphere and polyhedra assemblies abide by the flow start and stop laws, although much higher tilt angle values are required to trigger polyhedral grain flow. In the dense permanent flow regime, both systems show similarities in the bulk of the material (away from the top free surface and the substrate), such as uniform values of the solid fraction, inertial number and coordination number, or linear dependency of the solid fraction and effective friction coefficient with the inertial number. However, discrepancies are also observed between spherical and polyhedral particle flows. A dead (or nearly arrested) zone appears in polyhedral grain flows close to the rough bottom surface, reflected by locally concave velocity profiles, locally larger coordination number and solid fraction values, smaller inertial number values. This dead zone disappears for smooth bottom surfaces. In addition, unlike sphere assemblies, polyhedral grain assemblies exhibit significant normal stress differences, which increase close to the substrate.

Hysteresis in a hydrodynamic model of dense granular flows

A hydrodynamic model for dense granular flows, previously developed for confined flows, has been extended to address free surface flow down an inclined chute. Results show that the model can predict the existence of two critical inclination angles, namely, the avalanche starting angle θ(start) above which the granular bed begins flowing from an initially jammed configuration, and an avalanche stopping angle θ(stop), which is the minimum to maintain flowing conditions, in agreement with experiments and numerical simulations available from the literature. The dependence of these critical angles on the bed depth is also analytically formulated, reflecting the expected qualitative behavior. Such a hysteretic behavior is specific of granular flow and its prediction provides indications of consistence of the modeling approach. The improved model also captures the scaling of the velocity profiles down the bed depth.

Shallow granular flows

Many processes in geophysical and industrial settings involve the flow of granular materials down a slope. In order to investigate the granular dynamics, we report a series of laboratory experiments conducted by releasing grains at a steady rate from a localized source on a rough inclined plane. Different types of dense granular flow are observed by varying the flow rate at the source and the slope of the inclined plane. The two cases of steady flow confined by levees and the flow of avalanches down the plane are examined. The width of the steady flow increases linearly with the prescribed flow rate, which does not appreciably affect the characteristic depth or surface velocity of the bulk flow. When the flow rate is just below that required for sustaining the steady flow, avalanches are triggered at regular intervals. The avalanches maintain their shape, size, and speed down the inclined plane. We propose a simple model of steady flow that is consistent with our observations and discuss the challenges associated with the theoretical treatment of avalanche dynamics.

Chaotic mixing via streamline jumping in quasi-two-dimensional tumbled granular flows

We study, numerically and analytically, the singular limit of a vanishing flowing layer in tumbled granular flows in quasi-two-dimensional rotating containers. The limiting behavior is found to be identical under the two versions of the kinematic continuum model of such flows, and the transition to the limiting dynamics is analyzed in detail. In particular, we formulate the no-shear-layer dynamical system as a piecewise isometry. It is shown how such a discontinuous map, through the concordant mechanism of streamline jumping, leads to the physical mixing of granular matter. The dependence of the dynamics of Lagrangian particle trajectories on the tumbler fill fraction is also established through Poincaré sections, and, in the special case of a half-full tumbler, chaotic behavior is shown to disappear completely in the singular limit. At other fill levels, stretching in the sense of shear strain is replaced by spreading due to streamline jumping. Finally, we use finite-time Lyapunov exponents to establish the manifold structure and understand "how chaotic" the limiting piecewise isometry is.

Rheology of a sonofluidized granular packing

We report experimental measurements on the rheology of a dry granular material under a weak level of vibration generated by sound injection. First, we measure the drag force exerted on a wire moving in the bulk. We show that when the driving vibration energy is increased, the effective rheology changes drastically: going from a non-linear dynamical friction behavior --weakly increasing with the velocity-- up to a linear force-velocity regime. We present a simple heuristic model to account for the vanishing of the stress dynamical threshold at a finite vibration intensity and the onset of a linear force-velocity behavior. Second, we measure the drag force on spherical intruders when the dragging velocity, the vibration energy, and the diameters are varied. We evidence a so-called "geometrical hardening" effect for smaller-size intruders and a logarithmic hardening effect for the velocity dependence. We show that this last effect is only weakly dependent on the vibration intensity.

Patterns in flowing sand: understanding the physics of granular flow

Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental and numerical results that show the formation of longitudinal stripes that arise from instability of the uniform flowing state of granular media on a rough inclined plane. The form of the stripes depends critically on the mean density of the flow with a robust form of stripes at high density that consists of fast sliding pluglike regions (stripes) on top of highly agitated boiling material--a configuration reminiscent of the Leidenfrost effect when a droplet of liquid lifted by its vapor is hovering above a hot surface.

Effect of noise on solid-to-liquid transition in small granular systems under shear

The effect of noise on the solid-to-liquid transition of a dense granular assembly under planar shear is studied numerically using soft-particle molecular dynamics simulations in two dimensions. We focus on small systems in a thin planar Couette cell, examining the bistable region while increasing shear, with varying amounts of random noise, and determine statistics of the shear required for fluidization. In the absence of noise, the threshold value of the shear stress depends on the preparation of the system and has a broad distribution. However, adding force fluctuations both lowers the mean threshold value of the shear stress and decreases its variability. This behavior is interpreted as thermoactivated escape through a fluctuating barrier.