Cluster growth in two- and three-dimensional granular gases

Visual analysis of density and velocity profiles in dense 3D granular gases

Granular multiparticle ensembles are of interest from fundamental statistical viewpoints as well as for the understanding of collective processes in industry and in nature. Extraction of physical data from optical observations of three-dimensional (3D) granular ensembles poses considerable problems. Particle-based tracking is possible only at low volume fractions, not in clusters. We apply shadow-based and feature-tracking methods to analyze the dynamics of granular gases in a container with vibrating side walls under microgravity. In order to validate the reliability of these optical analysis methods, we perform numerical simulations of ensembles similar to the experiment. The simulation output is graphically rendered to mimic the experimentally obtained images. We validate the output of the optical analysis methods on the basis of this ground truth information. This approach provides insight in two interconnected problems: the confirmation of the accuracy of the simulations and the test of the applicability of the visual analysis. The proposed approach can be used for further investigations of dynamical properties of such media, including the granular Leidenfrost effect, granular cooling, and gas-clustering transitions.

Cluster-Induced Deagglomeration in Dilute Gravity-Driven Gas-Solid Flows of Cohesive Grains

Clustering is often presumed to lead to enhanced agglomeration between cohesive grains due to the reduced relative velocities of particles within a cluster. Our discrete-particle simulations on gravity-driven, gas-solid flows of cohesive grains exhibit the opposite trend, revealing a new mechanism we coin "cluster-induced deagglomeration." Specifically, we examine relatively dilute gas-solid flows and isolate agglomerates of cohesive origin from overall heterogeneities in the system, i.e., agglomerates of cohesive origin and clusters of hydrodynamic origin. We observe enhanced clustering with an increasing system size (as is the norm for noncohesive systems) as well as reduced agglomeration. The reduced agglomeration is traced to the increased collisional impact velocities of particles at the surface of a cluster; i.e., higher levels of clustering lead to larger relative velocities between the clustered and nonclustered regions, thereby serving as an additional source of granular temperature. This physical picture is further evidenced by a theoretical model based on a balance between the generation and breakage rates of agglomerates. Finally, cluster-induced deagglomeration also provides an explanation for a surprising saturation of agglomeration levels in gravity-driven, gas-solid systems with increasing levels of cohesion, as opposed to the monotonically increasing behavior seen in free-evolving or driven granular systems in the absence of gravity. Namely, higher cohesion leads to more energy dissipation, which is associated with competing effects: enhanced agglomeration and enhanced clustering, the latter of which results in more cluster-induced deagglomeration.

An instrument for studying granular media in low-gravity environment

A new experimental facility has been designed and constructed to study driven granular media in a low-gravity environment. This versatile instrument, fully automatized, with a modular design based on several interchangeable experimental cells, allows us to investigate research topics ranging from dilute to dense regimes of granular media such as granular gas, segregation, convection, sound propagation, jamming, and rheology-all without the disturbance by gravitational stresses active on Earth. Here, we present the main parameters, protocols, and performance characteristics of the instrument. The current scientific objectives are then briefly described and, as a proof of concept, some first selected results obtained in low gravity during parabolic flight campaigns are presented.

Dimension dependence of clustering dynamics in models of ballistic aggregation and freely cooling granular gas

Via event-driven molecular dynamics simulations we study kinetics of clustering in assemblies of inelastic particles in various space dimensions. We consider two models, viz., the ballistic aggregation model (BAM) and the freely cooling granular gas model (GGM), for each of which we quantify the time dependence of kinetic energy and average mass of clusters (that form due to inelastic collisions). These quantities, for both the models, exhibit power-law behavior, at least in the long time limit. For the BAM, corresponding exponents exhibit strong dimension dependence and follow a hyperscaling relation. In addition, in the high packing fraction limit the behavior of these quantities become consistent with a scaling theory that predicts an inverse relation between energy and mass. On the other hand, in the case of the GGM we do not find any evidence for such a picture. In this case, even though the energy decay, irrespective of packing fraction, matches quantitatively with that for the high packing fraction picture of the BAM, it is inversely proportional to the growth of mass only in one dimension, and the growth appears to be rather insensitive to the choice of the dimension, unlike the BAM.

Early-stage aggregation in three-dimensional charged granular gas

Neutral grains made of the same dielectric material can attain considerable charges due to collisions and generate long-range interactions. We perform molecular dynamic simulations in three dimensions for a dilute, freely cooling granular gas of viscoelastic particles that exchange charges during collisions. As compared to the case of clustering of viscoelastic particles solely due to dissipation, we find that the electrostatic interactions due to collisional charging alter the characteristic size, morphology, and growth rate of the clusters. The average cluster size grows with time as a power law, whose exponent is relatively larger in the charged gas than the neutral case. The growth of the average cluster size is found to be independent of the ratio of characteristic Coulomb to kinetic energy, or equivalently, of the typical Bjerrum length. However, this ratio alters the crossover time of the growth. Both simulations and mean-field calculations based on Smoluchowski's equation suggest that a suppression of particle diffusion due to the electrostatic interactions helps in the aggregation process.

Shock propagation in locally driven granular systems

We study shock propagation in a system of initially stationary hard spheres that is driven by a continuous injection of particles at the origin. The disturbance created by the injection of energy spreads radially outward through collisions between particles. Using scaling arguments, we determine the exponent characterizing the power-law growth of this disturbance in all dimensions. The scaling functions describing the various physical quantities are determined using large-scale event-driven simulations in two and three dimensions for both elastic and inelastic systems. The results are shown to describe well the data from two different experiments on granular systems that are similarly driven.

Declustering in a granular gas as a finite-size effect

The existence of dense clusters has been shown to be a transient phenomenon for realistic models of granular collisions, where the coefficient of restitution depends on the impact velocity. We report direct numerical simulations that elucidate the conditions for the disappearance of structures. We find that upon cluster formation the granular temperature and the convective kinetic energy couple and both follow Haff's law. Furthermore, we show that clusters will eventually dissolve in all finite-size systems. We find the strong power law t'∝L(12) for the dependency of the declustering time on system size. Our results imply that only in systems close to the initial critical system size both clustering and declustering transitions are observable.

Structural characterization of submerged granular packings

We consider the impact of the effective gravitational acceleration on microstructural properties of granular packings through experimental studies of spherical granular materials saturated within fluids of varying density. We characterize the local organization of spheres in terms of contact connectivity, distribution of the Delaunay free volumes, and the shape factor (parameter of nonsphericity) of the Voronoï polygons. The shape factor gives a clear physical picture of the competition between less and more ordered domains of particles in experimentally obtained packings. As the effective gravity increases, the probability distribution of the shape factor becomes narrower and more localized around the lowest values of the shape factor corresponding to regular hexagon. It is found that curves of the pore distributions are asymmetric with a long tail on the right-hand side, which progressively reduces while the effective gravity gets stronger for lower densities of interstitial fluid. We show that the distribution of local areas (Voronoï cells) broadens with decreasing value of the effective gravity due to the formation of lose structures such as large pores and chainlike structures (arches or bridges). Our results should be particularly helpful in testing the newly developed simulation techniques involving liquid-related forces associated with immersed granular particles.

Energy decay in three-dimensional freely cooling granular gas

The kinetic energy of a freely cooling granular gas decreases as a power law t(-θ) at large times t. Two theoretical conjectures exist for the exponent θ. One based on ballistic aggregation of compact spherical aggregates predicts θ=2d/(d+2) in d dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts θ=d/2 when 2≤d≤4. We do extensive simulations in three dimensions to find that while θ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description.

How dynamical clustering triggers Maxwell's demon in microgravity

In microgravity, the gathering of granular material can be achieved by a dynamical clustering whose existence depends on the geometry of the cell that contains the particles and the energy that is injected into the system. By compartmentalizing the cell in several subcells of smaller volume, local clustering is triggered and the so formed dense regions act as stable traps. In this paper, molecular dynamics simulations were performed in order to reproduce the phenomenon and to analyze the formation and the stability of such traps. Depending on the total number N of particles present in the whole system, several clustering modes are encountered and a corresponding bifurcation diagram is presented. Moreover, an iterative model based on the measured particle flux F as well as a theoretical model giving the asymptotical steady states are used to validate our results. The obtained results are promising and can provide ways to manipulate grains in microgravity.

Clustering of inelastic soft spheres in homogeneous turbulence

In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.

Shock propagation in granular flow subjected to an external impact

We analyze a recent experiment [Boudet, Cassagne, and Kellay, Phys. Rev. Lett. 103, 224501 (2009)] in which the shock created by the impact of a steel ball on a flowing monolayer of glass beads is studied quantitatively. We argue that radial momentum is conserved in the process and hence show that in two dimensions the shock radius increases in time t as a power law t{1/3}. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction and are shown to compare well at intermediate times. At long times the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to the accumulation of particles at the shock front and propose a simple hard sphere model that incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.

Molecular-dynamics simulation of clustering processes in sea-ice floes

In seasonally ice-covered seas and along the margins of perennial ice pack, i.e., in regions with medium ice concentrations, the ice cover typically consists of separate floes interacting with each other by inelastic collisions. In this paper, hitherto unexplored analogies between this type of ice cover and two-dimensional granular gases are used to formulate a model of ice dynamics at the floe level. The model consists of (i) momentum equations for floe motion between collisions, formulated in the form of a Stokes-flow problem, with floe-size-dependent time constant and equilibrium velocity, and (ii) a hard-disk collision model. The numerical algorithm developed is suitable for simulating particle-laden flow of N disk-shaped floes with arbitrary size distributions. The model is applied to study clustering phenomena in sea ice with power-law floe-size distribution. In particular, the influence of the average ice concentration A on the formation and characteristics of clusters is analyzed in detail. The results show the existence of two regimes, at low and high ice concentrations, differing in terms of the exponents of the cluster-size distribution and of the size of the largest cluster.

Phase transitions in vibrated granular systems in microgravity

We numerically investigated various dynamical behaviors of a vibrated granular gas in microgravity. Using the parameters of an earlier Mini-Texus 5 experiment, three-dimensional simulations, based on molecular dynamics, efficiently reproduce experimental results. Using Kolmogorov-Smirnov tests, four dynamical regimes have been distinguished: gaseous state, partial clustering, complete clustering, and bouncing aggregates. Different grain radii and densities have been considered in order to describe a complete (r,η)-phase diagram. The latter exhibits rich features such as phase transitions and triple points. Our work emphasizes the complexity of diluted granular systems and opens fundamental perspectives.

Dynamical collision network in granular gases

We address the problem of recollisions in cooling granular gases. To this aim, we dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an event driven simulation of inelastic hard disks from time 0 until time t . The network is decomposed into its k -core structure: particles in a core of index k have collided at least k times with other particles in the same core. The difference between cores k+1 and k is the so-called k -shell, and the set of all shells is a complete and nonoverlapping decomposition of the system. Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e., a t{-2} energy decay, is unstable toward a strongly inhomogeneous phase with clusters and vortices, where energy decays as t{-1} . The clear transition between those two phases appears in the evolution of the k -shells structure in the collision network. In the homogeneous state the k -shell structure evolves as in a growing network with a fixed number of vertices and randomly added links: the shell distribution is strongly peaked around the most populated shell, which has an index k{max} approximately 0.9(d) with (d) the average number of collisions experienced by a particle. During the final nonhomogeneous state a growing fraction of collisions is concentrated in small, almost closed, communities of particles: k{max} is no more linear in (d) and the distribution of shells becomes extremely large developing a power-law tail approximately k{-3} for high shell indexes. We conclude proposing a simple algorithm to build a correlated random network that reproduces, with few essential ingredients, the whole observed phenomenology, including the t{-1} energy decay. It consists of two kinds of collisions (links): single random collisions with any other particle and long chains of recollisions with only previously encountered particles. The algorithm disregards the exact spatial arrangement of clusters, suggesting that the observed stringlike structures are not essential to determine the statistics of recollisions and the energy decay.

Simulation study of granular compaction dynamics under vertical tapping

We study, by numerical simulation, the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. Shaking is modeled by a series of vertical expansion of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by rho(t)=rho{infinity}-DeltarhoE{alpha}[-(ttau){alpha}], where E{alpha} denotes the Mittag-Leffler function of order 0<alpha<1 . The parameter tau is found to decay with tapping intensity Gamma according to a power law tau proportional, variantGamma{-gamma}, where parameter gamma is almost independent on the material properties of grains. Also, an expression for the grain mobility during the compaction process has been obtained. We characterize the local organization of disks in terms of contact connectivity and distribution of the Delaunay "free" volumes. Our analysis at microscopic scale provides evidence that compaction is mainly due to a decrease of the number of the largest pores. An interpretation of the memory effects observed for a discontinuous shift in tapping intensity Gamma is provided by the analysis of the time evolution of connectivity numbers and volume distribution of pores.

Shock wave propagation in vibrofluidized granular materials

Shock wave formation and propagation in vertically vibrated quasi-two-dimensional granular materials are studied by digital high speed photography. Steep density and temperature wave fronts form at the bottom of the granular layer when the layer collides with vibrating plate. Then the fronts propagate upwards through the layer. The temperature front is always in the transition region between the upward and downward granular flows. The effects of driving parameters and particle number on the shock are also explored.