Static friction phenomena in granular materials: Coulomb law versus particle geometry

The uncertainty inherent to DEM simulations of interlocking particles

In industrial applications, the handling of heterogeneous mixtures of phases and materials poses challenges for direct measurements and experiments, necessitating complementary modeling approaches. The Discrete Element Method (DEM) is commonly used for simulating the flow of granular systems, typically with spherical particles. However, certain applications, such as recycled polymers and batteries, require alternative non-convex particle representations in DEM simulations. Tetrapods are a promising shape candidate for modeling the flow behavior of such materials, as well as the associated uncertainty. We investigate the impact of the tetrapods' properties on the outcome and uncertainty inherent to DEM-based simulations. We demonstrate that tetrapods are effective for modeling interlocking materials, with their shape and size parameter significantly affecting interlocking behavior. Most interestingly, we can correlate the shape and size of tetrapods to the uncertainty inherent to our simulations. Specifically, we find that this uncertainty is positively correlated with both tetrapod size and the interlocking parameter ξ/D that quantifies their non-convexity. Lastly, we provide guidelines for selecting optimal tetrapod parameter sets for accurately modeling materials based on mean and variability measured in experiments.

Influence of the frequency on undulatory swimming speed in granular media

Sand is a highly dissipative system, where the local spatial arrangements and densities depend strongly on the applied forces, resulting in fluid-like or solid-like behaviour. This makes sand swimming challenging and intriguing, raising questions about the nature of the motion and how to optimize the design of artificial swimmers able to swim in sand. Recent experiments suggest that lateral undulatory motion enables efficient locomotion, with a non-monotonic dependence of the swimming speed on the undulatory frequency and the height of the sediment bed. Here, we propose a 2D granular model, where the effect of the sediment height is modeled by an effective frictional force with the substrate. We show that the optimal frequency coincides with the second vibrational mode of the swimmer and explain the underlying mechanism through a characterization of the rheology of the medium. Potential implications in the design of artificial swimmers are discussed.

Triggering avalanches by transverse perturbations in a rotating drum

We study the role of small-scale perturbations in the onset of avalanches in a rotating drum in the stick-slip regime. By vibrating the system along the axis of rotation with an amplitude orders of magnitude smaller than the particles’ diameter, we found that the order parameter that properly describes the system is the kinetic energy. We also show that, for high enough frequencies, the onset of the avalanche is determined by the amplitude of the oscillation, contrary to previous studies that showed that either acceleration or velocity was the governing parameter. Finally, we present a theoretical model that explains the transition between the continuous and discrete avalanche regimes as a supercritical Hopf bifurcation.

Simple particle shapes for DEM simulations of railway ballast: influence of shape descriptors on packing behaviour

ABSTRACT

In any DEM simulation, the chosen particle shape will greatly influence the simulated material behaviour. For a specific material, e.g. railway ballast, it remains an open question how to model the particle shape, such that DEM simulations are computationally efficient and simulation results are in good accordance with measurements. While DEM shape modelling for railway ballast is well addressed in the literature, approaches mainly aim at approximating the stones' actual shape, resulting in rather complex and thus inefficient particle shapes. In contrast, very simple DEM shapes will be constructed, clumps of three spheres, which aim to approximate shape descriptors of the considered ballast material. In DEM simulations of the packing behaviour, a set of clump shapes is identified, which can pack at porosities observed at track sites, as well as in lab tests. The relation between particle shape (descriptors) and obtained packing (characteristic) is investigated in a correlation analysis. The simulated packing's porosity is strongly correlated to four shape descriptors, which are also strongly correlated among each other. Thus, to derive simple shape models of a given particle shape, matching one of these shape descriptors, might be a good first step to bring simulated porosities closer to measured ones. The conducted correlation analysis also shows that packing's coordination number and isotropic fabric are correlated to more shape descriptors, making it more difficult to estimate the effect of particle shape on these quantities.

Dissipation of Energy by Dry Granular Matter in a Rotating Cylinder

We study experimentally the dissipation of energy in a rotating cylinder which is partially filled by granular material. We consider the range of angular velocity corresponding to continous and stationary flow of the granulate. In this regime, the stationary state depends on the angular velocity and on the filling mass. For a wide interval of filling levels we find a universal behavior of the driving torque required to sustain the stationary state as a function of the angular velocity. The result may be of relevance to industrial applications, e.g. to understand the power consumption of ball mills or rotary kilns and also for damping applications where mechanical energy has to be dissipated in a controlled way.

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.

Process modeling in the pharmaceutical industry using the discrete element method

The discrete element method (DEM) is widely used to model a range of processes across many industries. This paper reviews current DEM models for several common pharmaceutical processes including material transport and storage, blending, granulation, milling, compression, and film coating. The studies described in this review yielded interesting results that provided insight into the effects of various material properties and operating conditions on pharmaceutical processes. Additionally, some basic elements common to most DEM models are overviewed. A discussion of some common model extensions such as nonspherical particle shapes, noncontact forces, and interstitial fluids is also presented. While these more complex systems have been the focus of many recent studies, considerable work must still be completed to gain a better understanding of how they can affect the processing behavior of bulk solids.

Effects of friction and disorder on the quasistatic response of granular solids to a localized force

The response to a localized force provides a sensitive test for models of stress transmission in granular solids. Elasto-plastic models, traditionally used by engineers, have been challenged by theories and experiments that suggest a wavelike (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Simulations of two-dimensional granular systems subject to a localized external force have been employed to examine the nature of stress transmission in these systems as a function of the magnitude of this force, the frictional parameters, and degree of disorder. The results indicate that in large systems (as considered by engineers) the response is close to that predicted by isotropic elasticity, whereas for small systems (or strongly forced ones) it is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding and gives rise to hyperboliclike stress propagation. The larger the static friction, the more extended the range of forces for which the response is elastic, and the smaller the anisotropy. Increase in the degree of polydispersity (in the studied range, up to 25%) decreases the range of elastic response. This paper is an extension of a previously published Letter [C. Goldenberg and I. Goldhirsch, Nature (London) 435, 188 (2005)].

Friction versus texture at the approach of a granular avalanche

We perform an analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilization in a simulated two-dimensional packing. In this way, we recover the bimodal character of granular texture and the coexistence of weak and strong phases in the sense of distinct contacts populations. Moreover, we show the existence of a well-defined subset of contacts within the weak contact network. These contacts are characterized by their important friction and form a highly coherent population in terms of fabric. They play an antagonistic role with respect to force chains. Thus, we are able to discriminate between incoherent contacts and coherent contacts in the weak phase and to specify the role that the latter plays in the destabilization process.

Friction measurements in granular media

We present some experimental results, estimating the lateral stress response to a longitudinal stress applied to an ideal granular system as a function of friction parameters. Structural effects are taken into account through the use of an angle of contact distribution. The two-dimensional model, based on mainly equally sized cylinder granules allows one to derive a dependency of the friction between single granules and the overall angle of friction, which is commonly used to describe the macroscopic behavior of granulate material.

Ratchet-induced segregation and transport of nonspherical grains

We consider through simulations the behavior of elongated grains on a vibrating ratchet-shaped base. We observe differences in layer velocity profile and in net grain velocity for grains that are composed of one, two, or three collinear spheres. In the case of mixtures of different species of grains, we demonstrate layer-by-layer variation in the average velocity as well as layer segregation of species, and show that horizontal separation of the species can be achieved using this geometry. We also find that the addition of a small number of shorter grains to a sample of long grains provides a lubrication effect that increases the velocity of the long grains.

Navier-Stokes simulation with constraint forces: finite-difference method for particle-laden flows and complex geometries

Building on an idea of Fogelson and Peskin [J. Comput. Phys. 79, 50 (1988)] we describe the implementation and verification of a simulation technique for systems of non-Brownian particles in fluids at Reynolds numbers up to about 20 on the particle scale. This direct simulation technique fills a gap between simulations in the viscous regime and high-Reynolds-number modeling. It also combines sufficient computational accuracy with numerical efficiency and allows studies of several thousand, in principle arbitrarily shaped, extended and hydrodynamically interacting particles on regular work stations. We verify the algorithm in two and three dimensions for (i) single falling particles and (ii) a fluid flowing through a bed of fixed spheres. In the context of sedimentation we compute the volume fraction dependence of the mean sedimentation velocity. The results are compared with experimental and other numerical results both in the viscous and inertial regime and we find very satisfactory agreement.

The rotating bucket of sand: Experiment and theory

The surface shape of a bucket of sand rotating about its cylindrical axis is studied experimentally and theoretically. Focusing on fast time scales on which surface shape is determined by avalanches, we identify three regimes of behavior. At intermediate and high frequencies, the surface shape is always at its critical shape determined by the Coulomb yield condition. The low frequency behavior displays an unexpected subcritical region at the center of the bucket. To understand this central region, we adapt a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. The model indicates that the subcritical region is due to a nonlinear instability mechanism. (c) 1999 American Institute of Physics.