We report on direct measurements of the basal force components for granular material flowing down a smooth incline. We investigate granular flows for a large range of inclination angles from teta=13.4° to 83.6° and various gate opening of the chute. We find that the effective basal friction coefficient, muB, obtained from the ratio of the longitudinal force to the normal one exhibits a systematic increase with increasing slope angle and a significant weakening with increasing particle hold-up H (the depth-integrated particle volume fraction). At low angles, the basal friction is slightly less than or equal to tan(teta). The deviation from tan(teta) can be interpreted as a contribution from the side-wall to the overall friction. At larger angles, the basal friction muB saturates at an asymptotic value that is dependent on the gate opening of the chute. Importantly, our data confirm the outcomes of recent discrete numerical simulations. First, for steady and fully developed flows as well as for moderately accelerated ones, the variation of the basal friction can be captured through a unique dimensionless number, the Froude number Fr, defined as Fr=U/(gHcos(teta))^1/2, where U is the mean flow velocity. Second, the mean velocity scales with the particle hold-up H with a power exponent close to 1/4, contrasting with the Bagnold scaling (U~H^3/2).
Inelastic grains in a flow under gravitation tend to collapse into states in which the relative normal velocities of two neighboring grains is zero. If the time scale for this gravitational collapse is shorter than inverse strain rates in the flow, we propose that this collapse will lead to the formation of ``granular eddies", large scale condensed structures of particles moving coherently with one another. The scale of these eddies is determined by the gradient of the strain rate. Applying these concepts to chute flow of granular media, (gravitationally driven flow down inclined planes) we pr…
Reverse segregation and self-organization in inclined chute flows of bidisperse granular mixtures
Sandia National Laboratories（桑迪亚国家实验室）；Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室计算科学与工程中心）；School of Math, Science, and Engineering, Central New Mexico Community College（新墨西哥中部社区学院数理工程学院）
In a recent article (Forterre, PRL, 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we have proposed an instability mechanism based on the coupling between the flow and the granular temperature in rapid granular flows. In order to investigate the relevance of the proposed mechanism, we perform in the present paper a three-dimensional linear stability analysis of steady uniform flows down inclined planes using the kinetic theory of granular flows.…
Base roughness plays an important role to the dynamics of granular flows but is yet poorly understood due to the difficulty of its quantification. For a bumpy base made by spheres, at least two factors should be considered to characterize its geometric roughness, namely the size ratio of base- to flow-particles and the packing of base particles. In this paper, we propose a definition of base roughness, Ra, which is a function of both the size ratio and the packing arrangement of base particles. The function is generalized for random and regular packing of multi-layered spheres, where the range…
We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time $\dt$ used …
We report on the scaling between the lift force and the velocity lag experienced by a single particle of different size in a monodisperse dense granular chute flow. The similarity of this scaling to the Saffman lift force in (micro) fluids, suggests an inertial origin for the lift force responsible for segregation of (isolated, large) intruders in dense granular flows. We also observe an anisotropic pressure/stress field surrounding the particle, which potentially lies at the origin of the velocity lag. These findings are relevant for modelling and theoretical predictions of particle-size segr…
Recent numerical work has shown that high-speed confined granular flows down inclines exhibit a rich variety of flow patterns, including dense unidirectional flows, flows with longitudinal vortices and supported flows characterized by a dense core surrounded by a dilute hot granular gas (Brodu et al, JFM 2015). Here, we revisit the results obtained by Brodu et al. (JFM, 2015) and present new features characterizing these flows. In particular, we provide vertical and transverse profiles for the packing fraction, velocity and granular temperature.We also characterize carefully the transition bet…
Granular material flowing on complex topographies are ubiquitous in industrial and geophysical situations. In this paper, we study the small-scale model of a granular layer flowing on a rough incline. The shape of a granular front is solved analytically by using a 1D Savage-Hutter's model based on depth-averaged mass and momentum equations with the fractional expression for the frictional rheology $μ(I)$. Unlike previous studies where a "plug flow" is assumed, a free shape factor $α$ describing the vertical velocity profile, is taken into account to determine the solution. Such a way, we put i…
When a granular mixture involving grains of different sizes is shaken, sheared, mixed, or left to flow, grains tend to separate by sizes in a process known as size segregation. In this study, we explore the size segregation mechanism in granular chute flows in terms of pressure distribution and granular micro-structure. Therefore, 2D discrete numerical simulations of bi-disperse granular chute flows are systematically analysed. Based on the theoretical models by Gray and Thornton 2005 and Hill and Tan 2014, we explore the stress partition in the phases of small and large grains, discriminating…
We propose an explanation for the onset of oscillations seen in numerical simulations of dense, inclined flows of inelastic, frictional spheres. It is based on a phase transition between disordered and ordered collisional states that may be interrupted by the formation of force chains. Low frequency oscillations between ordered and disordered states take place over weakly bumpy bases; higher-frequency oscillations over strongly bumpy bases involve the formation of particle chains that extend to the base and interrupt the phase change. The predicted frequency and amplitude of the oscillations i…
Macroscopic and microscopic properties of dense granular layers flowing down inclined planes are obtained from Discrete-Element-Method simulations for both frictionless and frictional grains. Three fundamental observations for dense granular flows are recovered, namely the occurrence of a critical stress, the Bagnold velocity profile, as well as well-defined friction and dilatancy laws. The microscopic aspects of the grain motion highlight the formation of transient clusters. From this microscopic picture, we derive a theoretical scaling model without any empirical input that explains quantita…
We report experiments on the overall phase diagram of granular flows on an incline with emphasis on high inclination angles where the mean layer velocity approaches the terminal velocity of a single particle free falling in air. The granular flow was characterized by measurements of the surface velocity, the average layer height, and the mean density of the layer as functions of the hopper opening, the plane inclination angle and the downstream distance x of the flow. At high inclination angles the flow does not reach an x-invariant steady state over the length of the inclined plane. For low v…
The collapse of an inclined cohesive granular layer triggered by a certain perturbation can be a model for not only landslides on Earth but also relaxations of asteroidal surface terrains. To understand such terrain dynamics, we conduct a series of experiments of a solid-projectile impact onto an inclined wet granular layer with various water contents and inclination angles. As a result, we find two types of outcomes: "crater formation" and "collapse". The "collapse" phase is observed when the inclination angle is close to the maximum stable angle and the impact-induced vibration at the bottom…
Granulates are ubiquitous in nature and technology, but despite their great importance, their dynamics are by far less well understood than those of liquids. We demonstrate in an almost compactly filled flat (Hele-Shaw) cell, where slow horizontal rotation simulates a variable gravitational force, that unexpected dynamic structures may arise under geometrical restrictions. The cell motion drives regular flow in the compact interior, and convection rolls combine with segregation. The container fill level is crucial for the dynamic regime. A transition from chute flow at lower fill levels to con…
Avalanche experiments on an erodible substrate are treated in the framework of ``partial fluidization'' model of dense granular flows. The model identifies a family of propagating soliton-like avalanches with shape and velocity controlled by the inclination angle and the depth of substrate. At high inclination angles the solitons display a transverse instability, followed by coarsening and fingering similar to recent experimental observation. A primary cause for the transverse instability is directly related to the dependence of soliton velocity on the granular mass trapped in the avalanche.
We report and analyze the results of numerical studies of dense granular flows in two and three dimensions, using both linear damped springs and Hertzian force laws between particles. Chute flow generically produces a constant density profile that satisfies scaling relations suggestive of a Bagnold grain inertia regime. The type of force law has little impact on the behavior of the system. Bulk and surface flows differ in their failure criteria and flow rheology, as evidenced by the change in principal stress directions near the surface. Surface-only flows are not observed in this geometry.
The integral method can be used to model accurately flows down an inclined plane. Such a method consists in projecting the full 3D equations on a lower dimensional representation. The vertical velocity profiles have their functional form fixed, based from the exact solution of homogeneous steady flows. This projection is achieved by integration of the momentum equation over the flow depth -- Saint-Venant approach. Here we generalize the viscous case to two non-newtonian constitutive relations: a Prandtl-like turbulent closure and a local granular rheology. We discuss one application in each ca…
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused …
We investigate the mechanical properties of inclined frictional granular layers prepared with different protocols by means of DEM numerical simulations. We perform an orthotropic elastic analysis of the stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle $α$ with respect to the critical angle $α_c$. We find that the shear modulus of the system decreases with $α$, but tends to a finite value as $α\to α_c$. We also study the behaviour of various microscopic quantities with $α$, an…
We study the granular segregation in a tapered rotating drum by means of simulations. In this geometry, both radial and axial segregation appear, the strength of which depends on the filling fraction. We study the effect of the drum's tapering angle on the segregation speed and show that, coherently with several recent studies, the axial segregation is due to the combined effect of the radial segregation and the shape of the drum. We show that the axial segregation behaves in a way analogous to the one found in chute flows, and corresponds to previous theories for shallow gravity driven surfac…
The problem of the spreading of a granular mass released at the top of a rough inclined plane was investigated. We experimentally measure the evolution of the avalanche from the initiation up to the deposit using a Moiré image processing technique. The results are quantitatively compared with the prediction of an hydrodynamic model based on depth averaged equations. In the model, the interaction between the flowing layer and the rough bottom is described by a non trivial friction force whose expression is derived from measurements on steady uniform flows. We show that the spreading of the mass…
We have studied the gravity driven flow of spherical shaped, millimetric sized granular material coated with aspherical, micron-sized, near frictionless lubricant particles. Experiments were performed on an inclined plane using two different sized particles for varying concentrations of the lubricant. The particle volumetric flow rate exhibits a non-monotonic behavior with increasing lubricant concentration. It shows an increase at lower lubricant concentration followed by a decrease at higher lubricant concentration. The lubricant particles adhere to the granular particle surface thereby redu…
We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle α with respect to the critical angle α_c. We find that the shear modulus of the system decreases with α, but reaches a finite value as αtends to α_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.
We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contr…
We studied the drag and lift forces acting on an inclined plate while it is dragged on the surface of a granular media, both in experiment and numerical simulation. In particular, we investigated the influence of the horizontal velocity of the plate and its angle of attack. We show that a steady wedge of grains is moved in front of the plow and that the lift and drag forces are proportional to the weight of this wedge. These constants of proportionality vary with the angle of attack but not (or only weakly) on the velocity. We found a universal effective friction law which accounts for the dep…
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials: assemblies of frictional spherical particles bonded by a small quantity of a wetting liquid, over a rough inclined plane. Our results show steady uniform flows for a wide range of parameters (the inclination angle and the mass flow-rate). A theoretical model, based on the Mohr-Coulomb yield criterion extended to inertial flows: $τ$ = $τ$c + $μ$(I)P, in which $τ$c…
The present paper reports a novel behavior involving regular polygons with n sides and filled to varying degrees with granular materials. These are comprised of a set of hollow polygons produced on a 3D printer, and a single larger hollow hexagon fabricated with wooden sides and clear Plexiglas faces. Empty or full polygons stop immediately at shallow ramp angles, and roll the full length of the ramp for steep ramp angles, approaching a terminal velocity. This is consistent with results previously reported by other investigators of rolling solid polygons and partially filled cylinders. In cont…
In this Letter, the 2-dimensional dense flow of polygonal particles on an incline with a flat frictional inferior boundary is analyzed by means of contact dynamics discrete element simulations, in order to develop boundary conditions for continuum models of dense granular flows. We show the evidence that the global slip phenomenon deviates significantly from simple sliding: a finite slip velocity is generally found for shear forces lower than the sliding threshold for particle-wall contacts. We determined simple scaling laws for the dependence of the slip velocity on shear rate, normal and she…
The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed where the flow is either highly energetic and strongly layered in depth for small inclinations, or non-uniform and oscillating for larger inclinations. For steady uniform flows, depth profiles of density, velocity and stress have been obtained using an improved coarse-graining method, which allows accurate statistics even at the base of the flo…
Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that it exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the angle of the slope. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 microns to 2 mm. The relative roughness corresponding to the m…
We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be…
We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring $h_s$ (the thickness at which the flow subsides) as a function of the plane inclination $θ$ on various surfaces. Measuring the surface velocity $u$ of the flow as a function of flow thickness $h$, we find that for sand and glass beads the Pouliquen flow rule $u/\sqrt{gh} \sim βh/h_s$ provides reasonable but not perfect collapse of…
Although a large number of astronomical craters are actually produced by the oblique impacts onto inclined surfaces, most of the laboratory experiments mimicking the impact cratering have been performed by the vertical impact onto a horizontal target surface. In previous studies on the effects of oblique impact and inclined terrain, only one of the impact angle $φ$ or target inclination angle $θ$ has been varied in the experiments. Therefore, we perform impact-cratering experiments by systematically varying both $φ$ and $θ$. A solid projectile of diameter $D_{\rm i}=6$~mm is impacted onto a sa…
The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $θ$. Three angles determine the phase diagram: $θ_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $θ_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $θ_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $θ_{r}<θ<θ_{max}$, three flow regime…
We formulate and solve a model problem of dispersion of dense granular materials in rapid shear flow down an incline. The effective dispersivity of the depth-averaged concentration of the dispersing powder is shown to vary as the Péclet number squared, as in classical Taylor--Aris dispersion of molecular solutes. An extensions to generic shear profiles is presented, and possible applications to industrial and geological granular flows are noted.
We study the flow of equal-volume binary granular mixtures of spheres and dumbbells with different aspect ratios down a rough inclined plane, using the discrete element method. We consider two types of mixtures -- in the first type the particles of the two species have equal volume but different aspect ratios (EV) and in the second type they have variable volumes and aspect ratios (VV). We also use mixtures of spheres of two different sizes (SS) with the same volume ratios as in the mixtures of the second type, as the base case. Based on the study of Guillard, Forterre and Pouliquen [\textit{J…
Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using discrete element method simulations, we show that segregation of a single particle intruder can be described in a unified manner across different flow configurations. A scaling relation for the net segregation force is obtained by measuring forces on an intruder particle in controlled-velocity flows where gravity and flow kinematics are varied independently. Th…
In a dry granular flow, size segregation behave differently for a mixture containing a few large beads with a size ratio (S) above 5 (Thomas, Phys.Rev.E 62,96(2000)). For moderate large S, large beads migrate to an intermediate depth in the bed: this is called intermediate segregation. For the largest S, large beads migrate to the bottom: this is called reverse segregation (in contrast with surface segregation). As the reversal and intermediate depth values depend on the bead fraction, this numerical study mainly uses a single large tracer. Small fractions are also computed showing the link be…
We present a new instability observed in rapid granular flows down rough inclined planes. For high inclinations and flow rates, the free surface of the flow experiences a regular deformation in the transverse direction. Measurements of the surface velocities imply that this instability is associated with the formation of longitudinal vortices in the granular flow. From the experimental observations, we propose a mechanism for the longitudinal vortex formation based on the concept of granular temperature.
Granular flow in a silo demonstrates multiple nonlocal rheological phenomena due to the finite size of grains. We solve the Nonlocal Granular Fluidity (NGF) continuum model in quasi-2D silo geometries and evaluate its ability to predict these nonlocal effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in arXiv:1411.5447, to produce full-field solutions. The implementation is validate…
Continuum modeling of size-segregation and flow in dense, bidisperse granular media: Accounting for segregation driven by both pressure gradients and shear-strain-rate gradients
Slow and dense granular flows often exhibit narrow shear bands, making them ill-suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field. We propose a set of testable constitutive assumptions, including rat…
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition between flowing and static components of the granular system. We apply this theory to several important granular problems: avalanche flow in deep and shallow inclined layers, rotating drums and shear granular flows between two plates. We carry out quantitative comparisons between the theory and experiment.
In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fra…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is used by most experimental and numerical studies to avoid sliding effects. Using DEM numerical simulations with side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-Bénard type of instability. In many aspects flows on a flat base…
We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation which describes the transition between flowing and static components of the granular system. This theory captures important phenomenology recently observed in experiments with granular flows on rough inclined planes (Daerr and Douady, Nature (London) v. 399, 241 (1999)): layer bistability, and transition from triangular avalanches propagating downhill at small inclination angles to balloon-shaped avalanches also propag…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the dynamics become intermittent over intermediate times, with strong temporal correlations between particle motions -- temporally heterogeneous dynamics. This intermittency is characterised through large scale structural events whereby the contact network periodically spans the system. A characteristic time scale associated with these processes increases as the s…
