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 equilibrium constant behavior, is well reproduced by an effective fluctuating hydrodynamics described by two noise terms: the first associated with vorticity diffusion and the second with the local energy exchange, which have internal and external character, respectively.
Liquid-crystalline ordering in vertically vibrated granular monolayers confined in annuli of different sizes is examined. The annuli consist of circular cavities with a central circular obstruction. In the absence of the central obstruction cylinders of low aspect-ratio exhibit tetratic order, except for the existence of four defects which restore the symmetry broken by the circular confinement. This behaviour is demanded by topology in systems with strong anchoring properties at the surface. By contrast, topology dictates that the annular geometry is compatible with a distorted tetratic phase…
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.
We analyse liquid-crystalline ordering in vertically vibrated monolayers of cylinders confined in a circular cavity. Short cylinders form tetratic arrangements with C$_4$ symmetry. This symmetry, which is incompatible with the geometry of the cavity, is restored by the presence of four point defects with total topological charge $+4$. Equilibrium Monte Carlo simulations predict the same structure. A new method to measure the elastic properties of the tetratic medium is developed which exploits the clear similarities between the vibrated dissipative system and the thermal equilibrium system. Ou…
We report the experimental findings of formation and motion of heap in granular materials in an inclined and vertically vibrated container. We show experimentally how the transport velocity of heap up container is related to the driving acceleration as well as the driving frequency of exciter. An analogous experiment was performed with a heap-shaped Plexiglas block. We propose that cohesion force resulted from pressure gradient in ambient gas plays a crucial role in enhancing and maintaining a heap, and ratchet effect causes the movement of the heap. An equation which governs the transport vel…
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…
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 study the dynamics of holes created in vertically vibrated dense suspensions and viscous Newtonian liquids. We find that all holes oscillate with the driving frequency, with a phase shift of $π/2$. In Newtonian liquids holes always close, while in suspensions holes may grow in time. We present a lubrication model for the closure of holes which is in good agreement with the experiments in Newtonian liquids. The growth rate of growing holes in suspensions is found to scale with the particle diameter over the suspending liquid viscosity. Comparing closing holes in Newtonian liquids to growing …
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…
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.
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…
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…
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…
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.
Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered micro-crystallites, time-periodic structures, and chaotic fluctuating patterns with complex dynamics. A model based on streaming flow gives a good quantitative account of the attractive part of the interaction.
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 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 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 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.
In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again. Depending on the experimental or numerical parameters, the energy bursts can occur either r…
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 describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a `collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety …
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…
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…
Molecular dynamics simulations are used to study fluidization of a vertically vibrated, three-dimensional shallow granular layer. As the container acceleration is increased above g, the granular temperature and root mean square particle displacement increase, gradually fluidizing the layer. For nearly elastic particles, or low shaking frequencies, or small layer depths, the end of the fluidization process is marked by an abrupt increase in the granular temperature and rms particle displacement. The layer is then fully fluidized since macroscopic, fluid-like phenomena such as convection rolls a…
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…
We report an experimental study on the transition between a disordered liquid-like state and a ordered solid-like one, in a collection of magnetically interacting macroscopic grains. A monolayer of magnetized particles is vibrated vertically at a moderate density. At high excitation a disordered, liquid-like state is observed. When the driving dimensionless acceleration $Γ$ is quasi-statically reduced, clusters of ordered grains grow below a critical value $Γ_{\rm c}$. These clusters have a well defined hexagonal and compact structure. If the driving is subsequently increased, these clusters r…
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 rev…
Grains inside a vertically vibrated box undergo a transition from a density inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition, and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor…
We report the observation of the homogenous nucleation of crystals in a dense layer of steel spheres confined between two horizontal plates vibrated vertically. Above a critical vibration amplitude, two-layer crystals with square symmetry were found to coexist in steady state with a surrounding granular liquid. By analogy to equilibrium hard sphere systems, the phase behavior can be explained through entropy maximization. However, dramatic non-equilibrium effects are present, including a significant difference in the granular temperatures of the two phases.
We have used an NMR technique to measure the short-time, three-dimensional displacement of grains in a system of mustard seeds vibrated vertically at 15g. The technique averages over a time interval in which the grains move ballistically, giving a direct measurement of the granular temperature profile. The dense, lower portion of the sample is well described by a recent hydrodynamic theory for inelastic hard spheres. Near the free upper surface the mean free path is longer than the particle diameter and the hydrodynamic description fails.
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 dynamics of a set of rods bouncing on a vertically vibrated plate is investigated using experiments, simulations, and theoretical analysis. The experiments and simulations are performed within an annulus to impose periodic boundary conditions. Rods tilted with respect to the vertical are observed to spontaneously develop a horizontal velocity depending on the acceleration of the plate. For high plate acceleration, the rods are observed to always move in the direction of tilt. However, the rods are also observed to move opposite to direction of tilt for a small range of plate acceleration a…
A partial monolayer of ~ 20000 uniform spherical steel beads, vibrated vertically on a flat plate, shows remarkable ordering transitions and cooperative behavior just below 1g maximum acceleration. We study the stability of a quiescent disordered or ``amorphous'' state formed when the acceleration is switched off in the excited ``gaseous'' state. The transition from the amorphous state back to the gaseous state upon increasing the plate's acceleration is generally subcritical: An external perturbation applied to one bead initiates a propagating front that produces a rapid transition. We measur…
We present simulations and a theoretical treatment of vertically vibrated granular media. The systems considered are confined in narrow quasi-two-dimensional and quasi-one-dimensional (column) geometries, where the vertical extension of the container is much larger than both horizontal lengths. The additional geometric constraint present in the column setup frustrates the convection state that is normally observed in wider geometries. This makes it possible to study collective oscillations of the grains with a characteristic frequency that is much lower than the frequency of energy injection. …
Vertically vibrated rod-shaped granular materials confined to quasi-2D containers self organize into distinct patterns. We find, consistent with theory and simulation, a density dependent isotropic-nematic transition. Along the walls, rods interact sterically to form a wetting layer. For high rod densities, complex patterns emerge as a result of competition between bulk and boundary alignment. A continuum elastic energy accounting for nematic distortion and local wall anchoring reproduces the structures seen experimentally.
We analyze a solenoidal motion in a vertically vibrated freely suspended thin smectic film. We demonstrate analytically that transverse oscillations of the film generate two-dimensional vortices in the plane of the film owing to hydrodynamic nonlinearity. An explicit expression for the vorticity of the in-plane film motion in terms of the film displacement is obtained. The air around the film is proven to play a crucial role, since it changes the dispersion relation of transverse oscillations and transmits viscous stresses to the film, modifying its bending motion. We propose possible experime…
We investigate the onset of the Faraday instability in a vertically vibrated wormlike micelle solution. In this strongly viscoelastic fluid, the critical acceleration and wavenumber are shown to present oscillations as a function of driving frequency and fluid height. This effect, unseen neither in simple fluids nor in previous experiments on polymeric fluids, is interpreted in terms of standing elastic waves between the disturbed surface and the container bottom. It is shown that the model of S. Kumar [Phys. Rev. E, {\bf 65}, 026305 (2002)] for a viscoelastic fluid accounts qualitatively for …
We present laboratory experiments of a vertically vibrated granular medium consisting of 1 mm diameter glass beads with embedded 8 mm diameter intruder glass beads. The experiments were performed in the laboratory as well as in a parabolic flight under reduced-gravity conditions (on Martian and Lunar gravity levels). We measured the mean rise velocity of the large glass beads and present its dependence on the fill height of the sample containers, the excitation acceleration, and the ambient gravity level. We find that the rise velocity scales in the same manner for all three gravity regimes an…
Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states thanks to energy injection mechanisms that take place throughout the system. These states can be stable even at high densities and inelasticities allowing for a detailed analysis of the hydrodynamic modes that govern the dynamics of granular fluids. Analyzing the decay of the time correlation functions it is shown that there is a crossover between a quasielastic regime in which energy evolves as a slow mode, to a inelastic regime, with energy slaved to the other conserved fi…
Rising motion of an obstacle in a vibrated granular medium is a classic problem of granular segregation, and called the Brazil nut (BN) effect. The controlling vibration parameters of the effect has been a long-standing problem. A simple possibility that the BN effect can be characterized solely by vibration velocity has recently been pointed out. The issue has become controversial before a long history of research, with only a few systems have provided for the simple possibility. Here, we investigate the rising motion of an obstacle in a vertically positioned one-layer granular bed under cont…
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…
One of the most noticeable collective motion of non-cohesive granular matter is clustering under certain conditions. In particular, when a quasi-two-dimensional monolayer of mono-disperse non-cohesive particles is vertically vibrated, a solid-liquid-like transition occurs when the driving amplitude exceeds a critical value. Here, the physical mechanism underlying particle clustering relies on the strong interactions mediated by grain collisions, rather than on grain-grain cohesive forces. In average, the solid cluster resembles a drop, with a striking circular shape. We experimentally investig…
We perform molecular dynamics simulations of model granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear wave…
Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2d fluidized granular experiment, with packing fractions $ϕ\in[10%,40%]$. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more comple…
