HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Stick-slip dynamics of an array of particles Farhang Radjai, Pierre Evesque, Daniel Bideau, S. Roux

Purpose - The purpose of this paper is to investigate the local feature of driven granular gases in event-driven molecular dynamic simulation, in order to achieve spatial profiles of local velocity distribution and granular temperature, and the local state with various coefficients of restitution.Design/methodology/approach - Event-driven molecular dynamic simulation is performed to study a vibro-fluidized granular gas system. Triangular-wave vibration is adopted in the simulation. The authors focus on the steady state of a driven granular gas.Findings - The simulation finds the local velocity distribution is asymmetric along vibration direction in this driven granular gas system, which agrees with the experimental results obtained in micro-gravity. A nonlinear spatial profile of the skewness of local velocity distribution in vibration direction is found in the simulation. Furthermore, it is found that the value of skewness increases with the system dissipation. It is also found that the two temperature components T+ and T- differ from each other. This shows breakdown of energy equipartition. The ratio between them drops exponentially along y direction in various coefficients of restitution. All results confirm that the bulk boundary effect relates to the dissipation properties of granular gases.Originality/value - This is the first MD simulation that investigates the bulk boundary effect to the local velocity distribution. The spatial profiles of the skewness of local velocity distribution are also investigated when changing the coefficient of restitution to study the influence of the system dissipative nature.

An event driven molecular dynamics simulation of granular gases in a rectangle container in the high frequency boundary vibration limit is performed. The local velocity distribution spatial profiles under various vibration velocities are presented. Two peaks of local velocity distribution in the marginal layers are observed. To quantify the spatial transformation of the local velocity distribution, we tit the major peak by a Gaussian function (with the mean xi and the standard deviation sigma). The results show that the fitting parameters of the major peaks, such as xi and sigma, can be well scaled by the vibration velocity.

A microgravity experimental study of vibrofluidized granular gas with intermediate number density is performed. Local velocity distributions are investigated, and are found to deviate measurably from a symmetric distribution for the velocity component in the direction of vibration due to the boundary heating mechanism. One generalized granular hydrodynamic theory (GSH) is used for a phenomenological model to describe this extended boundary effect by introducing additional variables to the two-peak distribution profile, which provides an account for the understanding of the bulk boundary effect.

We experimentally measure the local equation of state for two-dimensional horizontal fluidize granular gases confined in a rectangle box. Local equation of state can be seen as a local constitutive equation of temperature, pressure and the number density. Except the kinetic parts, the collision parts of the stress tensor are included. The diagonal components of the stress tensor are almost constant, which is consistent with the results from the simulation and hydrodynamic theory. Furthermore, the spacial profiles of the temperature and the number density are shown to be consistent with the experimental results of micro-gravity. Finally the local equations of state for different area fractions are found to have great discrepancies with the theoretical predictions no matter how the low or dense the density is.

The clustering behavior of a mono-disperse granular gas is experimentally studied in an asymmetric two-compartment setup. Unlike the random clustering in either compartment in the case of symmetric configuration when lowering the shaking strength to below a critical value, the directed clustering is observed, which corresponds to an imperfect pitchfork bifurcation. Numerical solutions of the flux equation using a modified simple flux function show qualitative agreements with the experimental results. The potential application of this asymmetric structure is discussed.

A 1d Boltzmann equation is introduced to describe the speed distribution function in granular gas system with local collision dissipation. It leads to introduce a new term, equivalent to an acceleration This term was always assumed to be 0, but it is not zero in general, even when the system is steady (i.e. when local mean flow equals 0). This shows that the flow (+ boundary) exerts a force on any extra steady particle (or plane) that drives it to the center. This result is analyzed, compared and interpreted using the Lagrangian & Eulerian view points of the mechanics; it demonstrates that classic view point of hydrodynamics does not hold anymore. The paper investigates different cases and gives experimental evidences of the features: it explains while local speed distribution f(v,r) of granular gas in a box subjected to vibration is non symmetric in the direction of vibration, while the system is stationary (mean local speed equals 0). Papers giving local experimental or simulated distributions are quoted, where two local pressures P+ = Sigma(v>0), (or v<0) (mv(2)) in + Ox and -Ox direction are different. It implies also introducing two local temperatures T-+/- in the +/- Ox vibration direction. These points are confirmed using 2d and 3d granular gas simulation. It should apply likely to get deeper understanding of different effects as the "granular Leidenfrost effect", the stoppage of vibrated-hourglass, some turbulent flow, and the granular-Maxwell-demon.

: This paper explains within simple arguments why the physics of granular gas has to be understood in a new way, different to the one proposed by P. Haff, and able to describe the energy delivered to it and dissipated by it. This requires to take into account the difference in the mean particle speed in the + and – ways of the excitation direction. These different means V + (= Σ mv + / Σ m ) and V - (= Σ mv - / Σ m ) exist mainly everywhere in the sample as shown in P&G 17 , 577 (2009) and P&G 18 , 1,(2010). In steady excitation, which imposes ( Σ m v + + Σ m v - ) =0, this generates the existence of a new force (cid:1) P + (cid:1) - (cid:1) P - (cid:1) , where P ± (= m Σ v ± ² ) are the mean kinetic pressures in the two ± directions , due to the fact that the “pressures” P ± on the two sides of a fixed plane are different. This new force was not taken into account; it is due to the speed asymmetry, combined with a particle-particle restitution coefficient e smaller than 1. In the scientific literature, everything is treated has one did want to deliver energy to the granular gas: the granular system at a local uniform temperature at the boundary, so that it cannot make any work (second principle of thermodynamics. It gets heat only from the boundary. If this was true, it would help mining excavation and treatment. This article tries to understand how we arrived there there. So the paper proposes a new writing of dissipation in granular fluid (liquid or

We present a micro-gravity experimental study of intermediate number density vibro-fluidized inelastic spheres in a rectangular container. Local velocity distributions are investigated, and are found to deviate measurably from a symmetric distribution for the velocity component of the vibrating direction when dividing particles along the vibration direction into several bins. This feature does not exist in the molecular gas. We further study the hydrodynamic profiles of pressures p and temperatures T in positive and negative components, such as p+y and p−y and T+y and T−y, in accordance with the sign of velocity components of the vibrating direction. Along vibration direction, granular media are found to be not only inhomogeneous and anisotropic, but also different greatly in positive and negative components. Energy equipartition breaks down in this case.

A 3-D molecular dynamics simulation of a bi-disperse vibro-fluidized granular gas in a cyclic three-compartment cell is performed. A cluster of particles is randomly found in one of the compartments. Lohse's flux model is modified to incorporate inelastic particle-boundary collisions. This model predicts that periodically there is clustering in each compartment. It is then found that if the model is further modified to incorporate Gaussian white noise, it correctly predicts the non-sequential clustering behavior confirming that there is no chaotic behavior.

The main topic of this paper (part 4) is the interpretation of data from extended simulations published in previous Poudres & Grains (see P&G 17, #1 to #18) concerning the dynamics of N equal-size spheres in a 3d rectangular cell excited along Oz in 0 gravity.(N=100, 500, 1000, 1200, 2000, 3000, 4000, 4500). Different Oz excitation kinds have been used (symmetric and non symmetric bi-parabolic, symmetric and non symmetric saw teeth, thermal wall). No rotation is included, dissipation is introduced via a restitution coefficient e= -V'n/Vn, where V'n and Vn are the relative ball speed along normal to ball centres after and before collision. It is proved that the local speed distribution along z is fundamentally dissymmetric in most part of the cell while the mean local speed is 0. This demonstrates the inability of a model based on a thermal bath (with a single local temperature) to describe this dissipative-granular-gas-system, even when assuming that this temperature varies in space. The other (1-3) parts sum up few results obtained in the very low density regime.

Recently, a tremendous amount of works has been performed to investigate properties of granular gas (see [Goldhirsch 2003] for a review). This problem is fundamental because it is a frontier of statistical mechanics when dissipation becomes dominant; hence it asks the problem of what dissipation changes in the behavior of a statistical ensemble of particles in interaction: within which limits can one use the analogue of thermodynamics concepts to describe the behavior of these systems?

The paper concerns the dynamics of N equal-size spheres in a 3d rectangular cell excited along Oz in Og gravity (N=100, 500, 1000, 1200, 2000, 3000, 4000, 4500). Due to collision the system of N balls is dissipative, and the problem is to understand the statistical mechanics of such a system, whatever the excitation. Here we will consider vibrating wall, in the z direction. Due to the absence of gravity, cells are denser in the center as soon as the particle number is such that dissipation becomes important. This occurs in normal condition of excitation as soon as the mean free path is smaller than the cell length. The main topic of this paper (§-V) is the interpretation of data obtained from these simulations. Different kinds of excitation have been used (symmetric and non symmetric biparabolic, symmetric and non symmetric saw teeth, thermal wall). No rotation is included, dissipation is introduced via a restitution coefficient e = -V l n/V n, where V 1 n and V n are the relative ball speed along normal to ball centres after and before collision. It is proved that the local speed distribution along β is fundamentally dissymmetric in most part of the cell while the mean local speed is 0. This demonstrates the inability of a model based on a thermal bath (with a single local temperature) to describe this dissipative granular gas system, even when assuming that this temperature varies in space. The results are coherent with simple mechanics principles which are described and discussed. We demonstrate these points using different local variations of distribution, such as the distribution of local speed Vz according to the position z in the cell for (a) a biparabolic excitation (sine) and ( b) thermal excitation: near edges (z=0, z=L) the distributions are not symmetric. The asymmetry is however weaker in sine than in sawteeth excitation. Also, the temperature for paticles in +z direction is different from those ones going in -z direction, what gives the asymmetry; and this asymetry varies with z. Besides we demonstrate the absence of propagating shock waves in such dense system with continuous excitation.

The effect of different possible kinds of motion of the exciting walls (cyclic, random, ...) is investigated on the dynamics of a granular dissipative gas. It is shown that the real distribution of speed of the wall which interact with the balls depend strongly on the real ball speed, due to a screening effect, so that the transfer of excitation from the walls to the cloud of particles may drastically depend on the ball speed itself. This makes the excitation quite non linear, with a change of efficiency law. This may explain the observation of a biphasic cloud when the mean free path of balls is slightly smaller than the cell size L, or may predict that the particles in the cloud is merely at rest as soon as the mean free path is smaller than L/10. It is obvious that the vibrating cell cannot be considered as a thermostat.

Experimental data from Maxwell's demon experiments on granular gas are revisited. It is shown that the transition nature changes from critical to sub-critical via a tri-critical point when frequency of vibration is increased continuously. So (i) the transition is not hyper-critical as asserted previously, but (ii) the fluctuations amplitude is spontaneously reinforced at the tri-critical point compared to the one at other frequencies. So, (iii) this analysis still contradicts a recent study which asserts that the bifurcation is always critical, and that fluctuations shall depend on the number of grains only. Beside, (iv) it is proposed a way to build an experiment, based on some modification of the "Maxwell's demon in granular gas" set up, which undergoes a hyper-critical bifurcation, with the use of some controlled feed-back of the flows. This last idea can be generalised and used in other domains where bifurcation theory applies, i.e. physics, chemistry, population dynamics, economy, to improve regulation, but generating hyper- fluctuations. Finally it is shown that the dynamical result is sensitive to the very-details of the regulation.

Clustering of shaken fluidized granular matter in connected compartments has been observed and studied in the laboratory. This clustering behavior in granular gas systems is related to the dissipative nature of granular system, and therefore shall not depend on gravity. This clustering phenomenon in compartmental configuration may provide a means for particle depletion and transportation in microgravity environment. In this work we propose different configurations for possible directed clustering in zero gravity. The related experiment has been planned for the Chinese satellite SJ-10.

Magnetic Resonance Imaging (MRI) technique was used to study the mixing and segregation processes of granular materials in a sophisticated tumbling blender (Turbula® mixer) using binary mixtures of sugar beads of different diameters d. Its motion generates mixtures with complex patterns. Effects of some parameters (beads diameter ratio, rotation speed, mixing time) were checked on segregation and mixing processes. We report in this paper, a qualitative and quantitative analysis of these phenomena. A segregation index S was defined to study the homogeneity and the kinetics of the mixing/segregation processes. When the ratio of bead diameters d max/ d min is approximately 1, mixing process is observed but segregation occurs as soon as d max/ d min is greater than 1.1.

We report on different experimental behaviours of granular dissipative matter excited by vibration as studied during the 43rd ESA campaign of Airbus A300-0g from CNES. The effect of g-jitter is quantified through the generation of a rattle effect. The French-European team's electromagnetic set-up is used, with 20Hz cam recording and high speed camera for a short duration (1s) during each parabola.

We present a micro-gravity experimental study of the statistical properties of intermediate number density vibro-fluidized inelastic spheres in a rectangular container. It is found that although when taking all the particles into account, the probability distributions of velocities both along and perpendicular to the vibration direction are exponential and symmetric, when dividing particles along the vibration direction into different bins, the local velocity distributions are found to deviate measurably from a symmetric distribution for the velocity component in the vibrating direction. The skewness analysis of the local distribution profiles for v(x) and v(y) shows that the local distribution of v(x) remains symmetric, however, the skewness of the distribution profile in v(y) changes nearly linear from positive to negative with skew = 0 near the center bin. This indicates a long range boundary effect of the asymmetry in v(y). We further studied the hydrodynamic profiles granular pressure p(x) and p(y), and temperature T-x and T-y in positive and negative components such as p(x)(+) and p(x)(-), and T-x(+) and T-x(-), in accordance with the sign of velocity components. The profiles for the two components are found different along the y direction. Along vibration direction granular medium is found inhomogeneous and anisotropic not only in the particle number densities, but also in v(y), p(y) and T-y. This suggests new hydrodynamical modeling is needed for such vibro-fluidized granular systems.

The problem of Maxwell's demon in granular gas is revisited in the case of a mixture of two particle species. The phase space is found to be 2d. Existence of cyclic orbits, with periodic segregation, is demonstrated by investigating the case of 2 kinds of particles with identical parameters but different masses. At large excitation equi-partition shall be obtained, but convergence towards the steady state is found in spiral. The spiral convergence is imposed due to the rule of kinetic-energy transfer between the two species. It results that the most probable scenario is that the steady state breaks into cyclic orbit at lower amplitude of vibration below a bifurcation threshold. The nature of the bifurcation is not known; it can be critical, subcritical, hypercritical or can exhibit a tri-critical point as varying the control parameters. No conclusion is obtained at very low vibration amplitude: it is guessed two scenarii under further cooling which generates Maxwell's demon and segregation..