Granular flow down an inclined plane: Bagnold scaling and rheology

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.

Force distributions in frictional granular media

We report a joint experimental and theoretical investigation of the probability distribution functions (PDFs) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint PDF of normal and tangential forces together, and the marginal PDFs of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. Excellent agreements with both experimental and simulation data are reported. The proposed joint PDF predicts giant slip events at low pressures, again in agreement with observations.

Dry granular avalanche impact force on a rigid wall: Analytic shock solution versus discrete element simulations

The present paper investigates the mean impact force exerted by a granular mass flowing down an incline and impacting a rigid wall of semi-infinite height. First, this granular flow-wall interaction problem is modeled by numerical simulations based on the discrete element method (DEM). These DEM simulations allow computing the depth-averaged quantities-thickness, velocity, and density-of the incoming flow and the resulting mean force on the rigid wall. Second, that problem is described by a simple analytic solution based on a depth-averaged approach for a traveling compressible shock wave, whose volume is assumed to shrink into a singular surface, and which coexists with a dead zone. It is shown that the dead-zone dynamics and the mean force on the wall computed from DEM can be reproduced reasonably well by the analytic solution proposed over a wide range of slope angle of the incline. These results are obtained by feeding the analytic solution with the thickness, the depth-averaged velocity, and the density averaged over a certain distance along the incline rather than flow quantities taken at a singular section before the jump, thus showing that the assumption of a shock wave volume shrinking into a singular surface is questionable. The finite length of the traveling wave upstream of the grains piling against the wall must be considered. The sensitivity of the model prediction to that sampling length remains complicated, however, which highlights the need of further investigation about the properties and the internal structure of the propagating granular wave.

Rheology of dilute cohesive granular gases

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 by that for the hard-core fluids if we replace the diameter of the particle by the mean diameter of clusters.

Continuum modelling of segregating tridisperse granular chute flow

Segregation and mixing of size multidisperse granular materials remain challenging problems in many industrial applications. In this paper, we apply a continuum-based model that captures the effects of segregation, diffusion and advection for size tridisperse granular flow in quasi-two-dimensional chute flow. The model uses the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The predictions from the model are consistent with experimentally validated discrete element method (DEM) simulations over a wide range of flow conditions and particle sizes. The degree of segregation depends on the Péclet number, Pe, defined as the ratio of the segregation rate to the diffusion rate, the relative segregation strength κ_ij between particle species i and j, and a characteristic length L, which is determined by the strength of segregation between smallest and largest particles. A parametric study of particle size, κ_ij , Pe and L demonstrates how particle segregation patterns depend on the interplay of advection, segregation and diffusion. Finally, the segregation pattern is also affected by the velocity profile and the degree of basal slip at the chute surface. The model is applicable to different flow geometries, and should be easily adapted to segregation driven by other particle properties such as density and shape.

Controlled Viscosity in Dense Granular Materials

We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency, we observe a reentrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material that we rationalize by relating this frequency to the balance between dissipative and inertial forces in the system. Molecular dynamics simulations well reproduce the experimental data, confirming the suggested theoretical picture.

Thermal transport in binary colloidal glasses: Composition dependence and percolation assessment

The combination of various types of materials is often used to create superior composites that outperform the pure phase components. For any rational design, the thermal conductivity of the composite as a function of the volume fraction of the filler component needs to be known. When approaching the nanoscale, the homogeneous mixture of various components poses an additional challenge. Here, we investigate binary nanocomposite materials based on polymer latex beads and hollow silica nanoparticles. These form randomly mixed colloidal glasses on a sub-μm scale. We focus on the heat transport properties through such binary assembly structures. The thermal conductivity can be well described by the effective medium theory. However, film formation of the soft polymer component leads to phase segregation and a mismatch between existing mixing models. We confirm our experimental data by finite element modeling. This additionally allowed us to assess the onset of thermal transport percolation in such random particulate structures. Our study contributes to a better understanding of thermal transport through heterostructured particulate assemblies.

Compliant contact versus rigid contact: A comparison in the context of granular dynamics

We summarize and numerically compare two approaches for modeling and simulating the dynamics of dry granular matter. The first one, the discrete-element method via penalty (DEM-P), is commonly used in the soft matter physics and geomechanics communities; it can be traced back to the work of Cundall and Strack [P. Cundall, Proc. Symp. ISRM, Nancy, France 1, 129 (1971); P. Cundall and O. Strack, Geotechnique 29, 47 (1979)GTNQA80016-850510.1680/geot.1979.29.1.47]. The second approach, the discrete-element method via complementarity (DEM-C), considers the grains perfectly rigid and enforces nonpenetration via complementarity conditions; it is commonly used in robotics and computer graphics applications and had two strong promoters in Moreau and Jean [J. J. Moreau, in Nonsmooth Mechanics and Applications, edited by J. J. Moreau and P. D. Panagiotopoulos (Springer, Berlin, 1988), pp. 1-82; J. J. Moreau and M. Jean, Proceedings of the Third Biennial Joint Conference on Engineering Systems and Analysis, Montpellier, France, 1996, pp. 201-208]. The DEM-P and DEM-C are manifestly unlike each other: They use different (i) approaches to model the frictional contact problem, (ii) sets of model parameters to capture the physics of interest, and (iii) classes of numerical methods to solve the differential equations that govern the dynamics of the granular material. Herein, we report numerical results for five experiments: shock wave propagation, cone penetration, direct shear, triaxial loading, and hopper flow, which we use to compare the DEM-P and DEM-C solutions. This exercise helps us reach two conclusions. First, both the DEM-P and DEM-C are predictive, i.e., they predict well the macroscale emergent behavior by capturing the dynamics at the microscale. Second, there are classes of problems for which one of the methods has an advantage. Unlike the DEM-P, the DEM-C cannot capture shock-wave propagation through granular media. However, the DEM-C is proficient at handling arbitrary grain geometries and solves, at large integration step sizes, smaller problems, i.e., containing thousands of elements, very effectively. The DEM-P vs DEM-C comparison is carried out using a public-domain, open-source software package; the models used are available online.

Synchronized oscillations and acoustic fluidization in confined granular materials

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency.

Effect of particle stiffness on contact dynamics and rheology in a dense granular flow

Dense granular flows have been well described by the Bagnold rheology, even when the particles are in the multibody contact regime and the coordination number is greater than 1. This is surprising, because the Bagnold law should be applicable only in the instantaneous collision regime, where the time between collisions is much larger than the period of a collision. Here, the effect of particle stiffness on rheology is examined. It is found that there is a rheological threshold between a particle stiffness of 10^{4}-10^{5} for the linear contact model and 10^{5}-10^{6} for the Hertzian contact model above which Bagnold rheology (stress proportional to square of the strain rate) is valid and below which there is a power-law rheology, where all components of the stress and the granular temperature are proportional to a power of the strain rate that is less then 2. The system is in the multibody contact regime at the rheological threshold. However, the contact energy per particle is less than the kinetic energy per particle above the rheological threshold, and it becomes larger than the kinetic energy per particle below the rheological threshold. The distribution functions for the interparticle forces and contact energies are also analyzed. The distribution functions are invariant with height, but they do depend on the contact model. The contact energy distribution functions are well fitted by Gamma distributions. There is a transition in the shape of the distribution function as the particle stiffness is decreased from 10^{7} to 10^{6} for the linear model and 10^{8} to 10^{7} for the Hertzian model, when the contact number exceeds 1. Thus, the transition in the distribution function correlates to the contact regime threshold from the binary to multibody contact regime, and is clearly different from the rheological threshold. An order-disorder transition has recently been reported in dense granular flows. The Bagnold rheology applies for both the ordered and disordered states, even though the rheological constants differ by orders of magnitude. The effect of particle stiffness on the order-disorder transition is examined here. It is found that when the particle stiffness is above the rheological threshold, there is an order-disorder transition as the base roughness is increased. The order-disorder transition disappears after the crossover to the soft-particle regime when the particle stiffness is decreased below the rheological threshold, indicating that the transition is a hard-particle phenomenon.

Additively manufactured hierarchical stainless steels with high strength and ductility

Many traditional approaches for strengthening steels typically come at the expense of useful ductility, a dilemma known as strength-ductility trade-off. New metallurgical processing might offer the possibility of overcoming this. Here we report that austenitic 316L stainless steels additively manufactured via a laser powder-bed-fusion technique exhibit a combination of yield strength and tensile ductility that surpasses that of conventional 316L steels. High strength is attributed to solidification-enabled cellular structures, low-angle grain boundaries, and dislocations formed during manufacturing, while high uniform elongation correlates to a steady and progressive work-hardening mechanism regulated by a hierarchically heterogeneous microstructure, with length scales spanning nearly six orders of magnitude. In addition, solute segregation along cellular walls and low-angle grain boundaries can enhance dislocation pinning and promote twinning. This work demonstrates the potential of additive manufacturing to create alloys with unique microstructures and high performance for structural applications.

Rattler-induced aging dynamics in jammed granular systems

Granular materials jam when developing a network of contact forces able to resist the applied stresses. Through numerical simulations of the dynamics of the jamming process, we show that the jamming transition does not occur when the kinetic energy vanishes. Rather, as the system jams, the kinetic energy becomes dominated by rattler particles, which scatter within their cages. The relaxation of the kinetic energy in the jammed configuration exhibits a double power-law decay, which we interpret in terms of the interplay between backbone and rattler particles.

Rheology of dense granular flows for elongated particles

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 quasistatic friction coefficient is nonmonotonic with Q: from the spherical case Q=1, it first sharply increases, reaches a maximum around Q≃1.05, and then gently decreases until Q=3, passing its initial value at Q≃2. We provide a microscopic interpretation for this unexpected behavior through the analysis of the distribution of dissipative contacts around the particles: as compared to spheres, slightly elongated grains enhance contacts in their central cylindrical band, whereas at larger aspect ratios particles tend to align and dissipate by preferential contacts at their hemispherical caps.

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.

River-bed armouring as a granular segregation phenomenon

River bed-load transport is a kind of dense granular flow, and such flows are known to segregate grains. While gravel-river beds typically have an “armoured” layer of coarse grains on the surface, which acts to protect finer particles underneath from erosion, the contribution of granular physics to river-bed armouring has not yet been investigated. Here we examine these connections in a laboratory river with bimodal sediment size, by tracking the motion of particles from the surface to deep inside the bed, and find that armour develops by two distinct mechanisms. Bed-load transport in the near-surface layer drives rapid, shear rate-dependent advective segregation. Creeping grains beneath the bed-load layer give rise to slow but persistent diffusion-dominated segregation. We verify these findings with a continuum phenomenological model and discrete element method simulations. Our experiments suggest that some river-bed armouring may be due to granular segregation from below—rather than fluid-driven sorting from above—while also providing new insights on the mechanics of segregation that are relevant to a wide range of granular flows.

River beds often exhibit armouring, in which formation of a coarse surface layer shields the finer underlying grains from erosion. Here, using experiments in a laboratory river and discrete and continuum models, the authors demonstrate that river-bed armouring is driven by vertical granular segregation.

Local and global avalanches in a two-dimensional sheared granular medium

We present the experimental and numerical studies of a two-dimensional sheared amorphous material composed of bidisperse photoelastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale-free distributions for these global and local avalanches denoted by power laws whose cutoffs vary with interparticle friction and packing fraction. Different exponents are found for these power laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered by the shear bands. A simple relation independent of the intensity is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from mean-field and depinning theories.

Segregation of a binary granular mixture in a vibrating sawtooth base container

A granular mixture of identical particles of different densities can be segregated when the system is shaken. We present an efficient method of continuously segregating a flow of randomly mixed identical spherical particles of different densities by shaking them in a quasi-two-dimensional container with a sawtooth-shaped base. Using numerical simulation we study the effect of direction of shaking (horizontal/vertical), geometry of the sawtooth, and the friction coefficient between the grains and the container walls on the segregation quality. Finally by performing experiments on the same system we compare our simulation results with the experimental results. The good agreement between our simulation and experiment indicates the validity of our simulation approach and will provide a practical way for granular segregation in industrial applications.

Force Transmission Modes of Non-Cohesive and Cohesive Materials at the Critical State

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for “bottom up” prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.

Direct numerical simulation of turbulent boundary layer with fully resolved particles at low volume fraction

In the present work, a direct numerical simulation (DNS) of dilute particulate flow in a turbulent boundary layer has been conducted, containing thousands of finite-sized solid rigid particles. The particle surfaces are resolved with the multi-direct forcing immersed-boundary method. This is, to the best of the authors' knowledge, the first DNS study of a turbulent boundary layer laden with finite-sized particles. The particles have a diameter of approximately 11.3 wall units, a density of 3.3 times that of the fluid, and a solid volume fraction of 1/1000. The simulation shows that the onset and the completion of the transition processes are shifted earlier with the inclusion of the solid phase and that the resulting streamwise mean velocity of the boundary layer in the particle-laden case is almost consistent with the results of the single-phase case. At the same time, relatively stronger particle movements are observed in the near-wall regions, due to the driving of the counterrotating streamwise vortexes. As a result, increased levels of dissipation occur on the particle surfaces, and the root mean square of the fluctuating velocities of the fluid in the near-wall regions is decreased. Under the present parameters, including the particle Stokes number St⁺ = 24 and the particle Reynolds number Re_p = 33 based on the maximum instantaneous fluid-solid velocity lag, no vortex shedding behind the particle is observed. Lastly, a trajectory analysis of the particles shows the influence of turbophoresis on particle wall-normal concentration, and the particles that originated between y⁺ = 60 and 2/3 of the boundary-layer thickness are the most influenced.

Micromechanical Origin of Particle Size Segregation

We computationally study the micromechanics of shear-induced size segregation and propose distinct migration mechanisms for individual large and small particles. While small particles percolate through voids without enduring contacts, large particles climb under shear through their crowded neighborhoods with anisotropic contact network. Particle rotation associated with shear is necessary for the upward migration of large particles. Segregation of large particles can be suppressed with inadequate friction, or with no rotation; increasing interparticle friction promotes the migration of large particles, but has little effect on the percolation of small particles.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for "bottom up" prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.