We experimentally examined the history dependence of the rotation-induced granular deformation. As an initial state, we prepared a quasi-two-dimensional granular pile whose apex is at the rotational axis and its initial inclination is at the angle of repose. The rotation rate was increased from $0$ to $620$~(rpm) and then decreased back to $0$. During the rotation, deformation of the rotated granular pile was captured by a camera. From the acquired image data, granular friction coefficient $μ$ was measured as a function of the ratio between centrifugal force and gravity, $Γ$. To systematically evaluate the variation of $μ$ both in the increasing (spinning up) and decreasing (spinning down) rotation-rate regimes, surface profiles of the deformed granular piles were fitted to a model considering the force balance among gravity, friction, and centrifugal force at the surface. We found that $μ$ value grows in the increasing $Γ$ regime. However, when $Γ$ was reduced, $μ$ cannot recover its initial value. A part of the history-dependent behaviors of the rotated granular pile can be understood by the force balance model.
A granular media lattice gas (GMLG) model is used to study avalanches in a two-dimensional granular pile. We demonstrate the efficiency of the algorithm by showing that several features of the non-critical behaviour of real sandpile surfaces, such as the bounded outflow statistics or the finite-size effect of the time evolution of the pile mass, can be reproduced by this simulation approach.
Results on a generalized magnetically controlled ballistic deposition (MBD) model of granular piles are reported in order to search for the effect of "spin flip" probability q in building a granular pile. Two different regimes of spin cluster site distributions have been identified, a border line $q_c(βJ)$ where J is the interaction potential strength.
The formation of sandpiles is a subject if interest in the field of granular matter, but most experiments are unable to control the kinetic energy of the grains added to the apex of the growing pile. In this short article, we describe an opto-mechanical system to grow granular piles by adding sand from a fixed distance above the apex of the pile. To achieve that, we use a laser beam that detects the position of the apex and, as the pile grows, sends a feedback signal to a mechanical device able to control the height of the sand delivey system above the pile.
Although the gravity dependence of granular friction is crucial to understand various natural phenomena, its precise characterization is difficult. We propose a method to characterize granular friction under various gravity (body force) conditions controlled by centrifugal force; specifically, the deformation of a rotated granular pile was measured. To understand the mechanics governing the observed nontrivial deformation of this pile, we introduced an analytic model considering local force balance. The excellent agreement between the experimental data and theoretical model suggests that the d…
An experimental apparatus measuring free-surface deformation of a centrifuged granular pile is developed. By horizontally rotating a quasi two-dimensional granular pile whose apex is located at the vertical rotation axis, the resultant force of gravity and centrifuge yields the deformation of the granular pile. In this setup, centrifugal force depends on distance from the rotation axis whilst gravitational force is constant everywhere. Therefore, free-surface deformation by various centrifuge degrees can be systematically examined using this apparatus. In the system, a small unit consisting of…
We study the surface shape of two-dimensional piles using experiments and a continuum theory for surface flows of granular materials (the BCRE equations). We first obtain an analytical solution to the BCRE equations with a simple transformation and show that the surface shapes thereby predicted are in good agreement with the experimental results. By means of such an analytical solution, we find that the formation of the curved tails at the bottom of such piles depends not only on the properties of the granular materials but also on the drift velocity of the grains within the rolling layer.
As a fragile construction, a granular pile is very sensitive to minute external perturbations. In particular, it is now well established that a granular assembly is sensitive to variations of temperature. Such variations can produce localized rearrangements as well as global static avalanches inside a pile. In this review, we sum up the various observations that have been made concerning the effect of temperature on a granular assembly. In particular, we dwell on the way controlled variations of temperature have been employed to generate the compaction of a granular pile. After laying emphasis…
Nonlinear relaxation dynamics of a vertically-vibrated granular pile is experimentally studied. In the experiment, the flux and slope on the relaxing pile are measured by using a high-speed laser profiler. The relation of these quantities can be modeled by the nonlinear transport law assuming the uniform vibro-fluidization of an entire pile. The fitting parameter in this model is only the relaxation efficiency, which characterizes the energy conversion rate from vertical vibration into horizontal transport. We demonstrate that this value is a constant independent of experimental conditions. Th…
Using a specially designed experimental set up, we have studied the so-called continuous to intermittent flow transition in sand piles confined in a Hele-Shaw cell where the deposition height of the sand can be controlled. Through systematic measurements varying the height and the input flow, we have established, for the first time, how the size of the pile at which the transition takes place depends on the two parameters studied. The results obtained allows to explain, at least semi-quantitatively, the observations commonly reported in the literature, carried out in experiments where the depo…
We find the collapse of columns of granular rods to show range of behaviors that depends on particle aspect ratio (length $L$ to diameter $d$) and initial pile geometry (height/radius). For all aspect ratios $L/d$ below 24 there exists a critical height at $L/4$ below which the pile acts as a solid, maintaining its initial shape, and a second critical height at $3L/4$ above which the pile always collapses like an ordinary granular material. Separating the critical heights is a transition region in which the probability of collapse increases linearly from 0 to 1. This behavior is independent of…
We report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle; By contrast, for small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compacti…
We present a molecular dynamics study of the jamming/unjamming transition in two-dimensional granular piles with open boundaries. The grains are modeled by viscoelastic forces, Coulomb friction and resistance to rolling. Two models for the rolling resistance interaction were assessed: one considers a constant rolling friction coefficient, and the other one a strain dependent coefficient. The piles are grown on a finite size substrate and subsequently discharged through an orifice opened at the center of the substrate. Varying the orifice width and taking the final height of the pile after the …
Here we show that variations of temperature, even of a few degrees in amplitude, induce the ageing of a granular pile. In particular, we report measurements of physical properties of a granular heap submitted to thermal cycles. Namely, we focus on the evolution of the thermal linear-expansion coefficient and of the thermal conductivity of the pile with the number of cycles. The present contribution nicely supplements a recent article we published elsewhere [Phys. Rev. Lett. \textbf{101}, 148303 (2008)] and introduces a different and promising method to impose temperature cycles to a granular p…
We numerically study the static structure and the mechanical response of two-dimensional granular piles. The piles consist of polydisperse disks with and without friction. Special attention is paid for the rigid grain limit by examining the systems with various disk elasticities. It is shown that the static pile structure of frictionless disks becomes isostatic in the rigid limit, while the isostaticity of frictional pile depends on the pile forming procedure, but in the case of the infinite friction is effective, the structure becomes very close to isostatic in the rigid limit. The mechanical…
We study the avalanche dynamics of a pile of micrometer-sized silica grains in water-filled microfluidic drums. Contrary to what is expected for classical granular materials, avalanches do not stop at a finite angle of repose. After a first rapid phase during which the angle of the pile relaxes to an angle $θ\_c$, a creep regime is observed where the pile slowly flows until the free surface reaches the horizontal. This relaxation is logarithmic in time and strongly depends on the ratio between the weight of the grains and the thermal agitation (gravitational Péclet number). We propose a simple…
Assemblies of granular particles mechanically stable under their own weight contain arches. These are structural units identified as sets of mutually stable grains. It is generally assumed that these arches shield the weight above them and should bear most of the stress in the system. We test such hypothesis by studying the stress born by in-arch and out-of-arch grains. We show that, indeed, particles in arches withstand larger stresses. In particular, the isotropic stress tends to be larger for in-arch-grains whereas the anisotropic component is marginally distinguishable between the two type…
Granular flow dynamics on a vertically vibrated pile is studied by means of both laboratory experiments and numerical simulations. As already revealed, the depth-averaged velocity of a fully-fluidized granular pile under strong vibration, which is measured by a high-speed laser profiler in the experiment, can be explained by the nonlinear diffusion transport model proposed by our previous paper (Tsuji et al, Phys. Rev. Lett. 120, 128001 (2018)). In this paper, we report that a similar transport model can be applied to the relation between the surface velocity and slope in the experiment. These…
We investigate experimentally granular piles exhibiting steady surface flow. Below the surface flow, it has been believed exisitence of a `frozen' bulk region, but our results show absence of such a frozen bulk. We report here that even the particles in deep layers in the bulk exhibit very slow flow and that such motion can be detected at an arbitrary depth. The mean velocity of the creep motion decays exponentially with depth, and the characteristic decay length is approximately equal to the particle-size and independent of the flow rate. It is expected that the creep motion we have seeen is …
We use multi-speckle diffusive wave spectroscopy (MSDWS) to probe the micron-scale dynamics of a granular pile submitted to discrete gentle taps. The typical time-scale between plastic events is found to increase dramatically with the number of applied taps. Furthermore, this microscopic dynamics weakly depends on the solid fraction of the sample. This process is strongly analogous to the aging phenomenon observed in thermal glassy systems. We propose a heuristic model where this slowing down mechanism is associated with a slow evolution of the distribution of the contact forces between partic…
We study experimentally the relaxation towards mechanical equilibrium of a granular pile which has just experienced an avalanche and discuss it in the more general context of the granular jamming transition. Two coexisting dynamics are observed in the surface layer: a short time exponential decay consisting in rapid and independent moves of grains and intermittent bursts consisting in spatially correlated moves lasting for longer time. The competition of both dynamics results in long-lived intermittent transients, the total duration of which can late more than a thousand of seconds. We measure…
Sandpiles have become paradigmatic systems for granular flow studies in statistical physics. New directions of investigations are discussed here. Rather than varying the nature of the pile (sand, salt, rice,..) we have investigated changes in the boundary conditions. We have investigated experimentally and numerically sandpile structures on bases having a fractal perimeter. This type of perimeter induces the formation of a quite complex set of ridges and valleys. A screening effect of the valleys is observed and depends on the angle of repose. Binary granular systems have also been investigate…
The transition into a glassy state of the ensemble of static, mechanically stable configurations of a tapped granular pile is explored using extensive molecular dynamics simulations. We show that different horizontal sub-regions ("layers") along the height of the pile traverse this transition in a similar manner but at distinct tap intensities. We supplement the conventional approach based purely on properties of the static configurations with investigations of the grain-scale dynamics by which the tap energy is transmitted throughout the pile. We find that the effective energy that particles …
We study the avalanche dynamics of a pile of micron-sized silica grains in miniaturized rotating drums filled with water. Contrary to what is expected for classical granular materials, the avalanches do not stop at a finite angle of repose. Below an angle $θ$\_c, we observe a creep regime where the piles slowly flow until they become flat. In this regime, the relaxation is logarithmic in time and is slower when the ratio between the weight of the grains and the thermal agitation is increased. We propose a simple 1D model based on Kramer's escape rate to describe this flow.
We investigate the effects of lateral walls on the angle of movement and on the angle of repose of a granular pile. Our experimental results for beads immersed in water are similar to previous results obtained in air and to recent numerical simulations. All of these results, showing an increase of pile angles with a decreasing gap width, are explained by a model based on the redirection of stresses through the granular media. Two regimes are observed depending on the bead diameter. For large beads, the range of wall effects corresponds to a constant number of beads whereas it corresponds to a …
If a granular material is poured from above on a horizontal surface between two parallel, vertical plates, a sand heap grows in time. For small piles, the grains flow smoothly downhill, but after a critical pile size $X_c$, the flow becomes intermittent: sudden avalanches slide downhill from the apex to the base, followed by an "uphill front" that slowly climbs up, until a new downhill avalanche interrupts the process. By means of experiments controlling the distance between the apex of the sandpile and the container feeding it from above, we show that $X_c$ grows linearly with the input flux,…
The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference $δ$ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time $τ$ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when $δ$ is an integer part of $π$. Introduction of fluctuations of $δ$ supresses the singularities of $τ(δ)$ a…
An X-ray imaging technique is used to probe the stability of 3-dimensional granular packs in a slowly rotating drum. Well before the surface reaches the avalanche angle, we observe intermittent plastic events associated with collective rearrangements of the grains located in the vicinity of the free surface. The energy released by these discrete events grows as the system approaches the avalanche threshold. By testing various preparation methods, we show that the pre-avalanche dynamics is not solely controlled by the difference between the free surface inclination and the avalanche angle. As a…
Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modification…
We investigate experimentally the impact of heterogeneity on the capillary pressure hysteresis in fluid invasion of model porous media. We focus on `symmetric' heterogeneity, where the contact angles the fluid interface makes with the oil-wet ($θ_1$) and the water-wet ($θ_2$) beads add up to $π$. While enhanced heterogeneity is usually known to increase hysteresis phenomena, we find that hysteresis is greatly reduced when heterogeneities in wettability are introduced. On the contrary, geometric heterogeneity (like bi-disperse particle size) does not lead to such effect. We provide a qualitativ…
We report experimental results of the pattern developed by a mixture of two types of grains in a triangular rotating tumbler operating in the avalanche regime. At the centroid of the triangular tumbler an invariant zone appears where the grains do not move relative to the tumbler. We characterize this invariant zone by its normalized area, $A_i$, and its circularity index as a function of the normalized filling area $A$. We find a critical filling area so that only for $A>A_c$ invariant zones are obtained. These zones scale as $A_i\sim (A-A_c)^2$ near $A_c$. We have obtained a maximum in the c…
Model experiments are reported on the build-up of granular piles in two dimensions. These show that as the initial density of falling grains is increased, the resulting pile has decreasing final density and its coordination number approaches the low value predicted for the theoretical marginal rigidity state. This provides the first direct experimental evidence for this state of granular matter. We trace the decrease in the coordination number to the dynamics within an advancing yield front between the consolidated pile and the falling grains. We show that the front's size increases with initi…
We have investigated by rotating drum experiments the influence of a small amount of fine particles on the stability of a granular heap. The fine particles are shown to have a strong and ambivalent influence. For low fine particle content, the heap destabilizes by avalanches, and the fine particles tend to fluidize the heap. In contrast, for high fine particle content, they increase the cohesion of the heap, which destabilizes through stick-slip at the drum wall. We interpret and model the fluidification in the avalanching regime, which we show is independent of humidity, by granular lubricati…
We explore the compaction dynamics of a granular pile after a hard quench from a liquid into the glassy regime. First, we establish that the otherwise athermal granular pile during tapping exhibits annealing behavior comparable to glassy polymer or colloidal systems. Like those other systems, the pile undergoes a glass transition and "freezes" into different non-equilibrium glassy states at low agitation for different annealing speeds, starting from the same initial equilibrium state at high agitation. Then, we quench the system instantaneously from the highly-agitated state to below the glass…
When sand flows out of a funnel onto a surface, a three dimensional pile that is stabilized by friction grows taller as it spreads. Here we investigate an idealized two dimensional analogue: spreading of a pile of monodisperse oil droplets at a boundary. In our system the droplets are buoyant, adhesive, and in contrast to sand, here friction is negligible. The buoyant droplets are added to the pile one-at-a-time. As the aggregate grows, it reaches a critical height and the 2D pile spreads out across the barrier. We find that, while granularity is important, the growth process is reminiscent of…
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…
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…
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）
Origin of geometric cohesion in non-convex granular materials: interplay between interdigitation and rotational constraints enhancing frictional stability
Université de Montpellier, CNRS（蒙彼利埃大学）；Departamento de Ingeniería Civil y Ambiental, Facultad de Ingeniería, Universidad de los Andes（安第斯大学）；LMGC, Univ Montpellier, IMT Mines Ales, CNRS（蒙彼利埃大学）；Department of Civil, Geological, and Mining Engineering, Polytechnique Montréal（蒙特利尔高等学院）
Bulldozing an immersed granular material in a confined channel
University of Oxford（牛津大学）；The Australian National University（澳大利亚国立大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Bristol（布里斯托大学）；University of Cambridge（剑桥大学）；Swansea University（斯旺西大学）
We experimentally investigate how a long granular pile confined in a narrow channel destabilizes when it is inclined above the angle of repose. A uniform flow then develops, which is localized at the free surface. It first accelerates before reaching a steady uniform regime. During this process, an apparent erosion is observed and the thickness of the flowing layer increases. We precisely study the evolution of the vertical velocity profile in this transient regime. The measurements are compared with the prediction of a visco-plastic model [P. Jop, Y. Forterre and O. Pouliquen, Nature 441, 727…
A generalized so called magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called ''nip'', their interaction being described through a Hamiltonian. Results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or $-$) nip's clusters and clusters of holes (missing nips) ar…
We investigate the gravity driven rapid failure of a granular step composed of non-cohesive steel beads. The step is initially held together with electromagnets, and released when the current is switched off. We visualize the surface and the motion of the grains during the entire relaxation. The initial failure occurs at the surface and the subsequent flow is also confined to the surface as the step relaxes to its final state. The final shape of the surface is almost linear, depends on the initial angle of the step, and is not sensitive to the size of the grains. The average final slope of the…
Mössbauer spectroscopy is applied to study ultrasound vibration of a granular material. A pile of powder is placed onto the surface of piezo transducer vibrated with the frequency 12.68 MHz. The size of grains (1.3 $μ$m) is much smaller than the wavelength of ultrasound, but much larger than the vibration amplitude. Due to vibration a single line of the Mössbauer transmission spectrum is split into a comb structure with a period equal to the vibration frequency. This spectrum contains the information about fast and slow modes in granular dynamics. We developed a method which allows to measure …
We measure the torque acting on a rod rotated perpendicular to its axis in a granular bed, through which an upflow of gas is utilized to tune the hydrostatic loading between grains. At low rotation rates the torque is independent of speed, but scales quadratically with rod-length and linearly with depth; the proportionality approaches zero linearly as the upflow of gas is increased towards a critical value above which the grains are fluidized. At high rotation rates the torque exhibits quadratic rate- dependence and scales as the rod's length to the 4th power. The torque has no dependence on e…
We revisit the problem of the stress distribution in a frictional sandpile under gravity, equipped with a new numerical model of granular assemblies with both normal and tangential (frictional) inter-granular forces. Numerical simulations allow a determination of the spatial dependence of all the components of the stress field as a function of systems size, the coefficient of static friction and the frictional interaction with the bottom surface. Our study clearly demonstrates that interaction with the bottom surface plays a crucial role in the formation of a pressure dip under the apex of a g…
Compared to agile legged animals, wheeled and tracked vehicles often suffer large performance loss on granular surfaces like sand and gravel. Understanding the mechanics of legged locomotion on granular media can aid the development of legged robots with improved mobility on granular surfaces; however, no general force model yet exists for granular media to predict ground reaction forces during complex limb intrusions. Inspired by a recent study of sand-swimming, we develop a resistive force model in the vertical plane for legged locomotion on granular media. We divide an intruder of complex m…
The structure and stresses of static granular packs in cylindrical containers are studied using large-scale discrete element molecular dynamics simulations in three dimensions. We generate packings by both pouring and sedimentation and examine how the final state depends on the method of construction. The vertical stress becomes depth-independent for deep piles and we compare these stress depth-profiles to the classical Janssen theory. The majority of the tangential forces for particle-wall contacts are found to be close to the Coulomb failure criterion, in agreement with the theory of Janssen…
We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response displays two peaks which lie precisely on the downward lattice directions emanating from the point of application of the force. With increasing depth, the magnitude of the peaks decreases, and a central peak develops. On the bottom …
Cooperative events requiring anomalously large fluctuations are a defining characteristic for the onset of glassy relaxation across many materials. The importance of such intermittent events has been noted in systems as diverse as superconductors, metallic glasses, gels, colloids, and granular piles. Here, we show that prohibiting the attainment of new record-high energy fluctuations -- by explicitly imposing a ``lid'' on the fluctuation spectrum -- impedes further relaxation in the glassy phase. This lid allows us to directly measure the impact of record events on the evolving system in exten…
We performed computer simulations based on a two-dimensional Distinct Element Method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio $f$ of the magnetic dipole interaction and the gravitational force (\emph{interparticle force ratio}). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at $f_c \approx…
Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positio…
