A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency $\sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies $f$, a tail $\sim 1/f$ in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $τ$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.
We probe the rheology of weakly vibrated granular flows as function of flow rate, vibration strength and pressure by performing experiments in a vertically vibrated split-bottom shear cell. For slow flows, we establish the existence of a novel vibration dominated granular flow regime, where the driving stresses smoothly vanish as the driving rate is diminished. We distinguish three qualitatively different vibration dominated rheologies, most strikingly a regime where the shear stresses no longer are proportional to the pressure.
We experimentally probe the anisotropy of the fabric of weakly vibrated, flowing granular media. Depending on the driving parameters --- flow rate and vibration strength --- this anisotropy varies significantly. We show how the anisotropy collapses when plotted as function of the driving stresses, uncovering a direct link between stresses and anisotropy. Moreover, our data suggests that for small anisotropies, the shear stresses vanish. Anisotropy of the fabric of granular media thus plays a crucial role in determining the rheology of granular flows.
We show by using a Discrete Element Method that a bilayer of vibrated granular bidisperse spheres exhibits the striking feature that the horizontal velocity distribution of the top layer particles has a quasi-Gaussian shape, whereas that of the bottom layer is far from Gaussian. We examine in detail the relevance of all physical parameters (acceleration of the bottom plate, mass ratio, layer coverage). Moreover, a microscopic analysis of the trajectories and the collision statistics reveal how the mechanism of randomization.
We study experimentally the dynamics of a dense intruder sinking under gravity inside a vibrated 2D granular packing. The surrounding flow patterns are characterized and the falling trajectories are interpreted in terms of an effectivive friction coefficient related to the intruder mean descent velocity (flow rules). At higher confining pressures i.e. close to jamming, a transition to intermittent dynamics is evidenced and displays anomalous "on-off" blockade statistics. A systematic analysis of the flow rules, obtained for different intruder sizes, either in the flowing regime or averaged ove…
We present a new mechanism for the fluidization of a vibrated granular bed in the presence of interstitial air. We show that the air flow induced across the bed, as the gap in the bottom of the cell evolves, can fluidize the bed in a similar way as in gas-fluidized {\it static} beds. We use the model of Kroll to quantify the relevant variables suggested by the mechanism proposed. The relevance of the above fluidization for segregation phenomena is discussed.
We study number density distribution and the behavior of time correlation functions in the density of grains for a quasi-two dimensional system of vibrated grains. We study the system at various packing fractions, from low to high. At low densities we recover usual gas like behavior, reflected in a Poissonian statistics for the number density distribution. At higher densities we notice effects like formation of cages of the kind that are seen in glass transition.
A layer of granular material on a vertically vibrating sawtooth-shaped base exhibits horizontal flow whose speed and direction depend on the parameters specifying the system in a complex manner. Discrete-particle simulations reveal that the induced flow rate varies with height within the granular layer and oppositely directed flows can occur at different levels. The behavior of the overall flow is readily understood once this novel feature is taken into account.
Theoretical and experimental study of high-acceleration patterns in vibrated granular layers is presented. The order parameter model based on parametric Ginzburg-Landau equation is used to describe strongly nonlinear excitations including hexagons, interface between flat anti-phase domains and new localized objects, super-oscillons. The experiments confirmed the existence of super-oscillons and bound states of super-oscillons and interfaces. On the basis of order parameter model we predict analytically and confirm experimentally that the additional subharmonic driving results in controlled mot…
Using high-speed video and magnetic resonance imaging (MRI) we study the motion of a large sphere in a vertically vibrated bed of smaller grains. As previously reported we find a non-monotonic density dependence of the rise and sink time of the large sphere. We find that this density dependence is solely due to air drag. We investigate in detail how the motion of the intruder sphere is influenced by size of the background particles, initial vertical position in the bed, ambient pressure and convection. We explain our results in the framework of a simple model and find quantitative agreement in…
We establish that the rheological curve of dry granular media is non-monotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the non-monotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the non-monotonic flow curve governs the yielding behavior of granular media. Finally, we show that non-monotonic flow curves can be seen in at least two different flow geometries and for several granular materials.
Molecular dynamical (MD) simulations are performed to simulate two dimensional vibrofluidized granular materials in this work. Statistics on simulation results indicate that there exist shocks propagating upward in each vibrating cycle. Under certain driving parameters surface waves similar to Faraday instability in normal fluid coexist with internal waves. Relationship between the two kinds of waves is explored. Moreover simulation results indicate that periodically structured bottom can change the dispersion relationship and amplitude of surface waves.
We present an experimental study performed on a vibrated granular gas enclosed into a 2D rectangular cell. Experiments are realized in microgravity. High speed video recording and optical tracking allow to obtain the full kinematics (translation and rotation) of the particles. The inelastic parameters are retrieved from the experimental trajectories as well as the translational and rotational velocity distributions. We report that the experimental ratio of translational versus rotational temperature decreases to the density of the medium but increases with the driving velocity of the cell. The…
Large objects, immersed in a homogeneous granular system, migrate when subjected to vibrations. Under certain conditions large heavy objects rise and similar light ones sink to the bottom. This is called reverse buoyancy. We report an experimental study of this singular behavior, for a large sphere immersed in a deep granular bed. A simple mechanism is proposed to describe the motion of a sphere, inside a vertically vibrated granular system. When reverse buoyancy is observed, the measured vertical velocity of the immersed object, as a function of its density, shows a simple behavior. With a on…
We report experiments on the equipartition of kinetic energy between grains made of two different materials in a mixture of grains vibrated in 2 dimensions. In general, the two types of grains do not attain the same granular temperature, Tg = 1/2m v^2. However, the ratio of the two temperatures is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but is not sensitive to the inelasticity of grains. Also, this ratio is insensitive to compositional variables of the mixture such as the number fract…
Experiments and computer simulations are carried out to investigate ordering principles in a granular gas which phase separates under vibration. The densities of the dilute and the dense phase are found to follow a lever rule. A Maxwell construction is found to predict both the coexisting pressure and binodal densities remarkably well, despite the fact that the pressure-volume characteristic $P(v)$ is not an isotherm. Although the system is far from equilibrium and energy conservation is strongly violated, we derive the construction from the minimization of mechanical work and fluctuating part…
We report experimental studies of the effect of interstitial gas on mass-density-segregation in a vertically-vibrated mixture of equal-sized bronze and glass spheres. Sufficiently strong vibration in the presence of interstitial gas induces vertical segregation into sharply separated bronze and glass layers. We find that the segregated steady state (i.e., bronze or glass layer on top) is a sensitive function of gas pressure and viscosity, as well as vibration frequency and amplitude. In particular, we identify distinct regimes of behavior that characterize the change from bronze-on-top to glas…
We present a dynamic synchrotron X-ray imaging study of the effective temperature $T_{eff}$ in a vibrated granular medium. By tracking the directed motion and the fluctuation dynamics of the tracers inside, we obtained $T_{eff}$ of the system using Einstein relation. We found that as the system unjams with increasing vibration intensities $Γ$, the structural relaxation time $τ$ increases substantially which can be fitted by an Arrhenius law using $T_{eff}$. And the characteristic energy scale of structural relaxation yielded by the Arrhenius fitting is $E = 0.21 \pm 0.02$ $pd^3$, where $p$ is …
We study experimentally the collective motion of grains inside a U shaped tube undergoing vertical oscillations, and we develop a very simple quantitative model that captures relevant features of the observed behaviour. The height difference between the granular columns grows with time when the system is shaken at sufficiently low frequencies. The system exhibits two types of growth: exponentially divergent (type I) and exponentially saturating (type II), depending on the size of the grains. The type I growth can be quenched by removing the air whereas the type II behavior can occur in the abs…
We describe an experimental and computational investigation of the ordered and disordered phases of a vibrating thin, dense granular layer composed of identical metal spheres. We compare the results from spheres with different amounts of inelasticity and show that inelasticity has a strong effect on the phase diagram. We also report the melting of an ordered phase to a homogeneous disordered liquid phase at high vibration amplitude or at large inelasticities. Our results show that dissipation has a strong effect on ordering and that in this system ordered phases are absent entirely in highly i…
We report new patterns, consisting of coexistence of sub-harmonic/harmonic and asynchronous states [for example, a granular gas co-existing with (i) bouncing bed, (ii) undulatory subharmonic waves and (iii) Leidenfrost-like state], in experiments on vertically vibrated binary granular mixtures in a Heleshaw-type cell. Most experiments have been carried out with equimolar binary mixtures of glass and steel balls of same diameter by varying the total layer-height ($F$) for a range of shaking acceleration ($Γ$). All patterns as well as the related phase-diagram in the ($Γ, F$)-plane have been rep…
We investigate the spatial dependence of the density of vibrated granular beds, using simulations based on a hybrid Monte Carlo algorithm. We find that the initial consolidation is typically inhmogeneous, both in the presence of a constant shaking intensity and when the granular bed is submitted to `annealed shaking'. We also present a theoretical model which explains such inhomogeneous relaxation in terms of a `consolidation wave', in good qualitative agreement with our simulations. Our results are also in qualitative agreement with recent simulations.
The oscillatory force F_b^ac on the bottom of a rigid, vertically vibrated, grain filled column, reveals rich granular dynamics, even when the peak acceleration of the vibrations is signicantly less than the gravitational acceleration at the earth's surface. For loose packings or high frequencies, F_b^ac 's dynamics are dominated by grain motion. For moderate driving conditions in more compact samples, grain motion is virtually absent, but F_b^ac nevertheless exhibits strongly nonlinear and hysteretic behavior, evidencing a granular regime dominated by nontrivial force-network dynamics.
We describe experiments on monodisperse spherical particles in an annular cell geometry, vibrated from below and sheared from above. This system shows a freezing/melting transition such that under sufficient vibration a crystallized state is observed, which can be melted by sufficient shear. We characterize the hysteretic transition between these two states, and observe features reminiscent of both a jamming transition and critical phenomena.
When granular mixtures of different sizes are fluidized, each species spontaneously separates and condenses to form patterns. Although granular segregation has been extensively studied, the inability to directly observe the time evolution of the internal structure hinders the understanding of the mechanism of segregation dynamics driven by surface flow. In this study, we report rich band dynamics, including a self-replicating band, in a horizontally shaken granular mixture in a quasi-two-dimensional container where the granules formed steady surface waves. Direct observation of surface flow an…
We report experiments on the dynamics of vibrated particles constrained in a two-dimensional vertical container, motivated by the following question: how to get the most out of a given external vibration to maximize internal disorder (e.g. to blend particles) and agitation (e.g. to absorb vibrations)? Granular media are analogs to classical thermodynamic systems, where the injection of energy can be achieved by shaking them: fluidization arises by tuning either the amplitude or the frequency of the oscillations. Alternatively, we explore what happens when another feature, the container geometr…
We study statistical properties of vibrated granular monolayers using molecular dynamics simulations. We show that at high excitation strengths, the system is in a gas state, particle motion is isotropic, and the velocity distributions are Gaussian. As the vibration strength is lowered the system's dimensionality is reduced from three to two. Below a critical excitation strength, a gas-cluster phase occurs, and the velocity distribution becomes bimodal. In this phase, the system consists of clusters of immobile particles arranged in close-packed hexagonal arrays, and gas particles whose energy…
The critical phenomena associated to the liquid to solid transition of quasi-two-dimensional vibrated granular systems is studied using molecular dynamics simulations of the inelastic hard sphere model. The critical properties are associated to the fourfold bond-orientational order parameter $χ_4$, which measures the level of square crystallization of the system. Previous experimental results have shown that the transition of $χ_4$, when varying the vibration amplitude, can be either discontinuous or continuous, for two different values of the height of the box. Exploring the amplitude-height …
We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a non-static steady state via vertical shaking. The simulations explore a wide range of packing fractions, vertical accelerations and restitution coefficients, always staying below the crystallization limit. From the simulations we obtain the relevant Pair Distribution Functions (PDFs), and effective potentials for the interparticle interaction are extracted from these PDFs via the Ornstein-Zernike equation with the Percus-Yevick closure. The correlations in the granular structures origin…
Buoyancy-driven (thermal) convection in dilute granular media, fluidized by a vibrating base, is known to appear without the need of lateral boundaries in a restricted region of parameters (inelasticity, gravity, intensity of energy injection). We have recently discovered a second buoyancy-driven convection effect which occurs at any value of the parameters, provided that the impact of particles with the lateral walls is inelastic (Pontuale et al., Phys. Rev. Lett. 117, 098006 (2016)). It is understood that this novel convection effect is strictly correlated to the existence of perpendicular e…
We present a new mode of transport of spherical particles in a horizontally vibrated channel with sawtooth shaped side walls. The underlying driving mechanism is based on an interplay of directional energy injection transformed by the sidewall collisions and density dependent interparticle collisions. Experiments and matching numerics show that the average particle velocity reaches a maximum at 60% of the maximal filling density. Introducing a spatial phase shift between the channel boundaries increases the transport velocity by an order of magnitude.
We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corr…
The steady states of two vibrated granular gases separated by an adiabatic piston are investigated. The system exhibits a non-equilibrium phase transition with an spontaneous symmetry breaking. Even if the gases at both sides of the piston have the same number of particles and are mechanically identical, their steady volumes and temperatures can be rather different. The transition can be explained by a simple kinetic theory model expressing mechanical equilibrium and the energy balance occurring in the system. The model predictions are in good agreement with molecular dynamics simulation resul…
Granular materials present memory effects when submitted to tapping processes. These effects have been observed experimentally and are discussed here in the context of a general kind of model systems for compaction formulated at a mesoscopic level. The theoretical predictions qualitatively agree with the experimental results. As an example, a particular simple model is used for detailed calculations.
Granular materials are an important physical realization of active matter. In vibration-fluidized granular matter, both diffusion and self-propulsion derive from the same collisional forcing, unlike many other active systems where there is a clean separation between the origin of single-particle mobility and the coupling to noise. Here we present experimental studies of single-particle motion in a vibrated granular monolayer, along with theoretical analysis that compares grain motion at short and long time scales to the assumptions and predictions, respectively, of the active Brownian particle…
After some communications (EMAIL EXCHANGE) with the co-authors, this article has been withdrawn (for appropriate reason, please refer to the comments section).
Experimental results are presented for a vertically shaken granular layer. In the range of accelerations explored, the layer develops a convective motion in the form of one or more rolls. The velocity of the grains near the wall has been measured. It grows linearly with the acceleration, then the growing rate slows down. A rescaling with the amplitude of the wall velocity and the height of the granular layer makes all data collapse in a single curve. This can provide insights on the mechanism driving the motion.
We present experimental measurements on the spontaneous formation of compact spiral structures in vertically-vibrated granular chains. Under weak vibration, when the chain is quasi two-dimensional and self-avoiding, spiral structures emerge from generic initial configurations. We compare geometrical characteristics of the spiral with that of an ideal tight spiral. Globally, the spiral undergoes a slow rotation such that to keep itself wound, while internally, fast vibrational modes are excited along the backbone with transverse oscillations dominating over longitudinal ones. Spirals have an ex…
We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour similar to that of two-dimensional hard rectangular particles subject to thermal equilibrium fluctuations. However, due to dissipation, there is a much stronger tendency for particles to cluster into parallel arrangements in the granular system. These clusters behave as a polydisperse mixture of long life-time `superparticles', and some aspects of the system…
The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anti-correlation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the pl…
Observing and understanding the movement of an intruder through opaque dense suspensions such as quicksand remains a practical and conceptual challenge. Here we use an ultrasonic probe to investigate the dynamics of a steel ball sinking in a 3D dense glass bead packing saturated by water. We show that the frictional model developed for dry granular media can be used to describe the ball motion induced by horizontal vibration. From this rheology we infer the static friction coefficient and effective viscosity that decrease when increasing the vibration intensity. Our main finding is that the vi…
The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this work and previous studies is discussed.
Fast NMR imaging was used to measure the density profile of a three-dimensional granular medium fluidized by vertical vibrations of the container. For container acceleration much larger than gravity, the rise in center of mass of the granular medium is found to scale as (v0^alpha)/(N^beta) with alpha = 1.0 +/-0.2 and beta = 0.5 +/- 0.1, where v0 is the vibration velocity and N is the number of grains in the container. This value for alpha is significantly less than found previously for experiments and simulations in one dimension (alpha = 2) and two dimensions (alpha = 1.3-1.5).
We report an experimental study of the statistical properties of vibrated granular rings. In this system, a linked rod and bead metallic chain in the form of a ring is collisionally excited by a vertically oscillating plate. The dynamics are driven primarily by inelastic bead-plate collisions and are simultaneously constrained by the rings' physical connectedness. By imaging many instances of the ring configurations, we measure the ensemble averages and distributions of several physical characteristics on the scale of individual beads and composite ring. We study local properties such as inter…
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 simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A non-linear ratchet model with stick-slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed rec…
We experimentally study the velocity scaling of granular convection which is a possible mechanism of the regolith migration on the surface of small asteroids. In order to evaluate the contribution of granular convection to the regolith migration, the velocity of granular convection under the microgravity condition has to be revealed. Although it is hard to control the gravitational acceleration in laboratory experiments, scaling relations involving the gravitational effect can be evaluated by systematic experiments. Therefore, we perform such a systematic experiment of the vibration-induced gr…
We computationally study the frictional properties of sheared granular media subjected to harmonic vibration applied at the boundary. Such vibrations are thought to play an important role in weakening flows, yet the independent effects of amplitude, frequency, and pressure on the process have remained unclear. Based on a dimensional analysis and DEM simulations, we show that, in addition to a previously proposed criterion for peak acceleration that leads to breaking of contacts, weakening requires the absolute amplitude squared of the displacement is sufficiently large relative to the confinin…
We investigate hydrodynamic fluctuations in a 2D granular fluid excited by a vibrating base and in the presence of gravity, focusing on the transverse velocity modes. Since the system is inhomogeneous, we measure fluctuations in horizontal layers whose width is smaller than the characteristic hydrodynamic lengths: they can be considered as almost-homogeneous subsystems. The large time decay of autocorrelations of modes is exponential and compatible with vorticity diffusion due to shear viscosity, as in equilibrium fluids. The velocity structure factor, which strongly deviates from the equilibr…
A variant of the Direct Simulation Monte Carlo method is used to study the behavior of a granular gas, in two and three dimensions, under varying density, restitution coefficient, and inelasticity regimes, for realistic vibrating wall conditions. Our results agree quite well with recent experimental data. The role of the energy injection mechanism is discussed, as well as the behavior of state-functions, such as pressure, under realistic boundary conditions. Upon a density increase, we find signals of a clustering transition.
We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. As the compacity, $C$, of the mixture was increased, the evolution of three distinct phases was observed. We classify them as binary gas, segregation liquid and segregation crystal phases using macroscopic and microscopic measures. The binary gas to segregation liquid transition is consistent with a continuous phase transition and includes the characteristic feature of critical slowing down. At high compacities we observed an intriguing slow osci…
Rheology of dense vibrated granular flows: non-monotonic response controlled by granular temperature
Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides（巴黎萨克雷大学）；The Earth Observatory of Singapore, Nanyang Technological University（南洋理工大学新加坡地球观测中心）；Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli”（坎帕尼亚路易吉范维泰利大学数学与物理系）；Institute for Complex Systems CNR（CNR复杂系统研究所）；Department of Physics, University of Rome “La Sapienza”（罗马第一大学物理系）；INFN, Sezione Roma2（意大利国家核物理研究所罗马第二分部）；Department of Engineering, University of Campania “Luigi Vanvitelli”（坎帕尼亚路易吉范维泰利大学工程系）
We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical vibrations evolve to a dense, highly ordered, nematic state in which the long particle axes align with the vertical tube walls. We find that the orientational ordering process is reflected in a characteristic, steep rise in the local packing fraction. At any given height inside th…
The non-equilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301, 2004], which was announced to be a verification of the Fluctuation Relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such non equilibrium systems. We explain these results in terms of a two temperature Poisson process. Within this model, supported by independent Molecular Dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective tem…
Neicu and Kudrolli observed experimentally spontaneous formation of the long-range orientational order and large-scale vortices in a system of vibrated macroscopic rods. We propose a phenomenological theory of this phenomenon, based on a coupled system of equations for local rods density and tilt. The density evolution is described by modified Cahn-Hilliard equation, while the tilt is described by the Ginzburg-Landau type equation. Our analysis shows that, in accordance to the Cahn-Hilliard dynamics, the islands of the ordered phase appear spontaneously and grow due to coarsening. The generic …
We review recent developments in size separation in vibrated granular materials. Motivated by a need in industry to efficiently handle granular materials and a desire to make fundamental advances in non-equilibrium physics, experimental and theoretical investigations have shown size separation to be a complex phenomena. Large particles in a vibrated granular system invariably rise to the top. However, they may also sink to the bottom, or show other patterns depending on subtle variations in physical conditions. While size ratio is a dominant factor, particle specific properties such as density…
