One great challenge of modeling granular systems lies in capturing the rheologic dependencies on scale. For example, there are marked differences between quasi-static, intermediate, and rapid flow regimes. In this study, we demonstrate that assumptions for infinite stiffness of rigid particles, an assumption upon which the state-of the-art ($μ(I)$-rheology) modeling approaches are constructed, must be relaxed in order to recover the physical mechanisms behind many scale-dependent and non-local rheological effects. Any relaxation of the infinite stiffness assumption allows for particles to compress in series, whereby the number of simultaneously compressed particles controls the extent to which end-member particles experience a modified coefficient of effective friction, analogous to reduced stiffness for springs in series. To demonstrate the importance of such a mechanism in setting the dynamics for dense rigid granular systems, we show that modifying simple models to include the kinematics introduced by compression in series captures the emergence of thin layer stability, a widely observed yet incompletely explained non-local granular phenomenon. We also discuss, in general, how knowledge of the contact network and softness provides a potential physical basis for the diffusion of granular temperature.
When dealing with unsaturated wet granular materials, a fundamental question is: what is the effect of capillary cohesion on the bulk flow and yield behavior? We inwestigate the dense flow rheology of unsaturated granular materials through experiments and discrete element simulations of homogeneous, simple annular shear flows of frictional, cohesive, spherical particles.
We probe the rheology of weakly vibrated granular flows as function of flow rate, vibration strength and pressure by performing experiments in a vertically vibrated split-bottom shear cell. For slow flows, we establish the existence of a novel vibration dominated granular flow regime, where the driving stresses smoothly vanish as the driving rate is diminished. We distinguish three qualitatively different vibration dominated rheologies, most strikingly a regime where the shear stresses no longer are proportional to the pressure.
In this study we characterize the rheology of fluidized granular matter subject to secondary forcing. Our approach consists of first fluidizing granular matter in a drum half filled with grains via simple rotation, and then superimposing oscillatory shear perpendicular to the downhill flow direction. The response of the system is mostly linear, with a phase lag between the grain motion and the oscillatory forcing. The rheology of the system can be well characterize by the GDR-Midi model if the system is forced with slow oscillations. The model breaks down when the forcing timescale becomes com…
We present a phenomenological model for granular suspension rheology in which particle interactions enter as constraints to relative particle motion. By considering constraints that are formed and released by stress respectively, we derive a range of experimental flow curves in a single treatment and predict singularities in viscosity and yield stress consistent with literature data. Fundamentally, we offer a generic description of suspension flow that is independent of bespoke microphysics.
The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is foun…
We report a transition from a disordered state to an ordered state in the flow of nearly mono-disperse granular matter flowing in an inclined channel with a bumpy base, in discrete element method simulations. For low particle-sidewall friction coefficients, the particles are disordered and the Bagnold velocity profile is obtained. 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 cro…
We numerically and theoretically investigate how the softness of particles affects the rheology of sheared dilute granular gases. We find that the kinetic theory predicts the deviation of the flow curve from the Bagnold scaling, and it works well below a certain shear rate when we compare with the simulation results. It is also found that there is no theoretical solution above this shear rate, which is because the energy loss due to inelastic collisions cannot be balanced with the energy injection by the shear.
We establish that the rheological curve of dry granular media is non-monotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the non-monotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the non-monotonic flow curve governs the yielding behavior of granular media. Finally, we show that non-monotonic flow curves can be seen in at least two different flow geometries and for several granular materials.
This paper is devoted to the basic question of what factors determine the strain field in a quasi static granular flow. It is shown that using stress - strain rate relations is not the proper way to understand quasi static rheology. An alternative approach is discussed where the local deformation is regarded as the cause of deformation in the vicinity. We suggest a continuum model where the local shear strain is proportional to its Laplacian and the proportionality factor is determined by the local stress. The predicted behavior is tested in a three dimensional shear cell by means of computer …
The steady shear rheology of granular materials is investigated in slow quasi-static states and inertial flows. The effect of the gravity field and contact stiffness, which are conventionally trivialized is the focus of this study. Series of Discrete Element Method simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various gravity fields and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate timescales describes the flow rheology, we find that a second dimensionless number, the ratio of s…
We use large scale computer simulations and finite size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size, and study carefully the asymptotic limits of large system sizes and infinitely hard particle repulsion. Extending earlier analysis by about two orders of magnitude, we first study the asymptotic behavior of the shear viscosity in the hard particle limit. We co…
Rheological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that the shear stress, the pressure, and the kinetic temperature obey critical scaling near the jamming transition point, which is considered as a critical point. These scaling laws have some peculiar properties in view of conventional critical phenomena because the exponents depend on the interparticle force models so that they are not universal. It is also found that these scaling laws imply the relation between the exponents that describe the growing correlation length.
Shear cell simulations and experiments of weakly wetted particles (a few volume percent liquid binders) are compared, with the goal to understand their flow rheology. Application examples are cores for metal casting by core shooting made of sand and liquid binding materials. The experiments are carried out with a Couette-like rotating viscometer. The weakly wetted granular materials are made of quartz sand and small amounts of Newtonian liquids. For comparison, experiments on dry sand are also performed with a modified configuration of the viscometer. The numerical model involves spherical, mo…
We investigate the rheology of granular materials via molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional, noncohesive spheres. In agreement with previous results for frictionless particles, we observe three flow regimes existing in different domains of particle volume fraction and shear rate, with all stress data collapsing upon scaling by powers of the distance to the jamming point. Though this jamming point is a function of the interparticle friction coefficient, the relation between pressure and strain rate at this point is found to be independent of frict…
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 line…
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 …
Despite there being an infinite variety of types of flow, most rheological studies focus on a single type such as simple shear. Using discrete element simulations, we explore bulk granular systems in a wide range of flow types at large strains and characterize invariants of the stress tensor for different inertial numbers and interparticle friction coefficients. We identify a strong dependence on the type of flow which grows with increasing inertial number or friction. Standard models of yielding, repurposed to describe the dependence of the stress on flow type in steady-state flow and at fini…
We study the rheology of dry and wet granular materials in the steady quasistatic regime using the Discrete Element Method (DEM) in a split-bottom ring shear cell with focus on the macroscopic friction. The aim of our study is to understand the local rheology of bulk flow at various positions in the shear band, where the system is in critical state. The general(ized) rheology has four dimensionless control parameters that relate the time scales of five significant phenomena, namely, the time scales related to confining pressure $t_p$, shear rate $t_{\dotγ}$, particle stiffness $t_k$, gravity $…
The constitutive relations of a dense granular flow composed of self-propelling frictional hard particles are investigated by means of DEM numerical simulations. We show that the rheology, which relates the dynamical friction $μ$ and the volume fraction $ϕ$ to the inertial number $I$, depends on a dimensionless number $\mathcal{A}$, which compares the active force to the confining pressure. Two liquid/solid transitions -- in the Maxwell rigidity sense -- are observed. As soon as the activity is turned on, the packing becomes an `active solid' with a mean number of particle contacts larger than…
Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional $μ(I)$-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakeni…
Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary condition, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the later is selected from among 6 walls with various roughness, local concavity, and compliance. W…
Recent progresses in understanding the behavior of dense granular flows are presented. After presenting a bulk rheology of granular materials, I focus on the new developments to account for non-local effects, and on ongoing research concerning the surface rheology and the evolution of mechanical properties for heterogeneous systems.
The rheology of a two-dimensional granular gas under a plane shear is investigated. From the comparison among the discrete element method, the simulation of a set of hydrodynamic equation, and the analytic solution of the steady equation of the hydrodynamic equations, it is confirmed that the fluid equations derived from the kinetic theory give us accurate results even in relatively high density cases.
Nonlocal rheologies allow for the modeling of granular flows from the creeping to intermediate flow regimes, using a small number of parameters. In this paper, we report on experiments testing how particle properties affect model parameters, using particles of three different shapes (circles, ellipses, and pentagons) and three different materials, including one which allows for measurements of stresses via photoelasticity. Our experiments are performed on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall. Each type of particle is found to exhibit flows which are w…
In this paper we study the steady uniform flows that develop when granular material is released from a hopper on top of a static pile in a channel. We more specifically focus on the role of side walls by carrying out experiments in setup of different widths, from narrow channels 20 particle diameters wide to channels 600 particle diameters wide. Results show that steady flows on pile are entirely controlled by side wall effects. A theoretical model, taking into account the wall friction and based on a simple local constitutive law recently proposed for other granular flow configurations (GDR M…
We present an experimental investigation on the rheological behavior of model granular media made of nearly elastic spherical particles. The experiments are performed in a cylindrical Couette geometry and the experimental device is placed inside an airplane undergoing parabolic flights to cancel the effect of gravity. The corresponding curves, shear stress versus shear rate, are presented and a comparison with existing theories is proposed. The quadratic dependence on the shear rate is clearly shown and the behavior as a function of the solid volume fraction of particles exhibits a power law f…
We develop the rheology of a dilute granular gas mixture. Motivated by the interaction of charged granular particles, we assume that the grains interact via a square shoulder and well potential. Employing kinetic theory, we compute the temperature and the shear viscosity as functions of the shear rate. Numerical simulations confirm our results above the critical shear rate. At a shear rate below a critical value, clustering of the particles occurs.
We study the rheology and distribution of interparticle contact lifetimes for gravity-driven, dense granular flows of non-cohesive particles down an inclined plane using large-scale, three dimensional, granular dynamics simulations. Rather than observing a large number of long-lived contacts as might be expected for dense flows, brief binary collisions predominate. In the hard particle limit, the rheology conforms to Bagnold scaling, where the shear stress is quadratic in the strain rate. As the particles are made softer, however, we find significant deviations from Bagnold rheology; the mater…
Dense suspensions are widespread in nature, manufacturing and process engineering. Particle-based simulations have proven to be an invaluable complement to experimental rheological characterisation, serving as a virtual rheometer that enables rapid exploration of parameter space and detailed scrutiny of microscopic dynamics. To maximise the utility of such simulations, it can be advantageous to exploit pre-existing, well-optimised, well-documented codes. Here we provide a simple description of how to use LAMMPS to study the rheology of dense, granular suspensions.
We study the rheology of dense granular flows for frictionless spherocylinders by means of 3D numerical simulations. As in the case of spherical particles, the effective friction $μ$ is an increasing function of the inertial number $I$, and we systematically investigate the dependence of $μ$ on the particle aspect ratio $Q$, as well as that of the normal stress differences, the volume fraction and the coordination number. We show in particular that the quasi-static friction coefficient is non-monotonic with $Q$: from the spherical case $Q=1$, it first sharply increases, reaches a maximum aroun…
We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined.
This work generalises the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)] to the determination of the pressure. We focus on the Bagnold regime, and provide theoretical support to the empirical $μ(\mathcal{I})$ rheology laws, that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the $μ(\mathcal{I})$ laws apply.
We probe the secondary rheology of granular media, by imposing a main flow and immersing a vane-shaped probe into the slowly flowing granulate. The secondary rheology is then the relation between the exerted torque T and rotation rate ωof our probe. In the absence of any main flow, the probe experiences a clear yield-stress, whereas for any finite flow rate, the yield stress disappears and the secondary rheology takes on the form of a double exponential relation between ωand T. This secondary rheology does not only depend on the magnitude of T, but is anisotropic --- which we show by varying t…
In this letter, we investigate the transient rheological behavior of immersed granular flows using both experiments of submerged granular column collapses and corresponding numerical simulations. The simulations are performed with the lattice-Boltzmann method (LBM) coupled with the discrete element method (DEM) and provide a significant amount of data of the stress and deformation conditions at different positions and times during the granular collapse. We derive a new dimensionless number $\mathcal{G}$ that can unify the rheology of transient granular flows in different regimes for all the si…
The rheology of cohesive granular materials, under a constant pressure condition, is studied using molecular dynamics simulations. Depending on the shear rate, pressure, and interparticle cohesiveness, the system exhibits four distinctive phases: uniform shear, oscillation, shear-banding, and clustering. The friction coefficient is found to increase with the inertial number, irrespective of the cohesiveness. The friction coefficient becomes larger for strong cohesion. This trend is explained by the anisotropies of the coordination number and angular distribution of the interparticle forces. In…
We study granular suspensions under a variety of extensional deformations and simple shear using numerical simulations. The viscosity and Trouton's ratio (the ratio of extensional to shear viscosity) are computed as functions of solids volume fraction $ϕ$ close to the limit of zero inertia. Suspensions of frictionless particles follow a Newtonian Trouton's ratio for $ϕ$ all the way up to $ϕ_0$, a universal jamming point that is independent of deformation type. In contrast, frictional particles lead to a deformation-type-dependent jamming fraction $ϕ_m$, which is largest for shear flows. Trouto…
Understanding the dynamics of fluid-driven sediment transport remains challenging, as it is an intermediate region between a granular material and a fluid flow. Boyer \textit{et al.}\citep{Boyer2011} proposed a local rheology unifying dense dry-granular and viscous-suspension flows, but it has been validated only for neutrally-buoyant particles in a confined system. Here we generalize the Boyer \textit{et al.}\citep{Boyer2011} model to account for the weight of a particle by addition of a pressure $P_0$, and test the ability of this model to describe sediment transport in an idealized laborato…
The rheology of 2D steady surface flow of cohesionless cylinders in a rotating drum is investigated through {\em Non Smooth Contact Dynamics} simulations. Profile of volume fraction, translational and angular velocity, rms velocity, strain rate and stress tensor were measured at the midpoint along the length of the surface flowing layer where the flow is generally considered as steady and homogeneous. Analysis of these data and their inter-relations suggest the local inertial number - defined as the ratio between local inertial forces and local confinement forces - to be the relevant dimension…
The steady flow of spherical particles in a rectangular bin is studied using the Discrete Element Method (DEM) for different flow rates of the particles from the bin, in the slow flow regime. The flow has two non-zero velocity components and is more complex than the widely studied unidirectional shear flows. The objective of the study is to characterize, in detail, the local rheology of the flowing material. The flow is shown to be nearly constant density, with a symmetric stress tensor and the principal directions of the stress and rate of strain tensors nearly colinear. The local rheology is…
Understanding the rheology of granular assemblies is important for natural and engineering systems, but the relationship between inter-particle friction (or microscopic friction) and macroscopic friction is still not well understood. In this study, using the the discrete element method (DEM) with spherical particles and realistic contact laws, we investigate the mechanics of granular systems with a wide range of inter-particle frictional coefficients and aim to establish a friction-dependent rheology for dry granular flows. The corresponding results show that increasing inter-particle friction…
The rheology of dense granular flows is often seen as dependent on the nature of the energy landscape defining the modes of energy relaxation under shear. We investigate numerically the transition from soft to rigid particles, varying $S$, their stiffness compared to the confining pressure over three decades and the inertial number $I$ of the shear flow over five decades. We show that the rheological constitutive relation, characterized by a dynamical friction coefficient of the form $μ(I)=μ_c + a I^α$ is marginally affected by the particle stiffness, with constitutive parameters being essenti…
This work utilizes soft-particle discrete element simulations to examine the rheology of steady two-dimensional granular flows with reference to a unidirectional shear flow, which has been extensively employed for validating the local visco-plastic model of Jop et al. [Nature 441, 727--730 (2006)]. The $μ$-$I$ scaling proposed by Jop et al. is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies, however, each flow type results in a different curve. Here $μ$, ratio of the shear stress magnitude to the pressure, is the friction coefficient and $I$ …
Rheology of a dilute cohesive granular gas is theoretically and numerically studied. The flow curve between the shear viscosity and the shear rate is derived from the inelastic Boltzmann equation for particles having square-well potentials in a simple shear flow. It is found that (i) the stable uniformly sheared state only exists above a critical shear rate and (ii) the viscosity in the uniformly sheared flow is almost identical to that for uniformly sheared flow of hard core granular particles. Below the critical shear rate, clusters grow with time, in which the viscosity can be approximated …
We investigate the link between particle-scale dynamics and bulk behaviors of thickly-coated particle-fluid flows using computational simulations. We find that, similar to dense fully-saturated slurries, the form the rheology takes in these systems can carry signatures of interparticle collisions and/or interparticle viscous dynamics that vary solid fraction. However, we find significant qualitative and quantitative differences in the transitions of the system between what might be called viscous, collisional, and visco-collisional behaviors. We show how these transitions arise from changes in…
In this communication, we present a new lengthscale-based rheology for dense sheared particle suspensions as they transition from inertial- to viscous-dominated. We derive a lengthscale ratio using straightforward physics-based considerations for a particle subjected to pressure and drag forces. In doing so, we demonstrate that an appropriately chosen length-scale ratio intrinsically provides a consistent relationship between normal stress and system proximity to its ''jammed'' or solid-like state, even as a system transitions between inertial and viscous states, captured by a variable Stokes …
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；College of Physics, Chengdu University of Technology（成都理工大学物理学院）；Med-X Research Institute and School of Biomedical Engineering, Shanghai Jiao Tong University（上海交通大学Med-X研究院与生物医学工程学院）；School of Physics, East China Normal University（华东师范大学物理系）；Jiangsu First-Imaging Medical Equipment Co., Ltd.（江苏首影医疗设备有限公司）；State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology（成都大学地质灾害防治与地质环境国家重点实验室）
The rheology of surface granular flows is investigated by means of measurements of velocity and number density profiles in a quasi-two-dimensional rotating cylinder, half-filled with mono-disperse steel balls. The measurements are made at the center of the cylinder, where the flow is fully-developed, using streakline photography and image analysis . The stress profile is computed from the number density profile using a force balance taking into account wall friction. The profiles for the mean velocity superimpose when distance is scaled by the particle diameter and the velocity by a characteri…
