Onset of thermal convection in a horizontal layer of granular gas

Pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres

We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted so that the particles do not levitate over the grid, resulting in quasi-two-dimensional dynamics. We show that the behavior of diffusion and correlations in this system is particularly rich. Noticeably as well (and related to the complex dynamical behavior), a variety of phases appear, with important peculiarities with respect to analogous setups. We observe gas, liquid, glass, and hexagonal crystal phases. Most notably, we show that the melting of the hexagonal crystal occurs in coexistence with a liquid phase. This strikingly differs from the corresponding transition in a purely two-dimensional systems of air-fluidized disks, for which no phase coexistence has been reported in the literature.

Zero-gravity thermal convection in granular gases

Previous experimental and theoretical evidence has shown that convective flow may appear in granular fluids if subjected to a thermal gradient and gravity (Rayleigh-Bénard-type convection). In contrast to this, we present here evidence of gravity-free thermal convection in a granular gas, with no presence of external thermal gradients either. Convection is here maintained steady by internal gradients due to dissipation and thermal sources at the same temperature. The granular gas is composed by identical disks and is enclosed in a rectangular region. Our results are obtained by means of an event-driven algorithm for inelastic hard disks.

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.

Phase-coexisting patterns, horizontal segregation, and controlled convection in vertically vibrated binary granular mixtures

We report patterns consisting of coexistence of synchronous and asynchronous states [for example, a granular gas co-existing with (i) bouncing bed, (ii) undulatory subharmonic waves, and (iii) Leidenfrost-like states] in experiments on vertically vibrated binary granular mixtures in a Hele-Shaw 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 reproduced via molecular dynamics simulations of the same system. The segregation of heavier and lighter particles along the horizontal direction is shown to be the progenitor of such phase-coexisting patterns as confirmed in both experiment and simulation. At strong shaking we uncover a partial convection state in which a pair of convection rolls is found to coexist with a Leidenfrost-like state. The crucial role of the relative number density of two species on controlling the buoyancy-driven granular convection is demonstrated. The onset of horizontal segregation can be explained in terms of an anisotropic diffusion tensor.

Viscorotational shear instability of Keplerian granular flows

The linear stability of viscous Keplerian flow around a gravitating center is studied using the rheological granular fluid model. The linear rheological instability triggered by the interplay of the shear rheology and Keplerian differential rotation of incompressible dense granular fluids is found. Instability sets in in granular fluids, where the viscosity parameter grows faster than the square of the local shear rate (strain rate) at constant pressure. Found instability can play a crucial role in the dynamics of dense planetary rings and granular flows in protoplanetary disks.

Noise induces rare events in granular media

The granular Leidenfrost effect [B. Meerson, et al., Phys. Rev. Lett. 91, 024301 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.024301; P. Eshuis et al., Phys. Rev. Lett. 95, 258001 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.258001] is the levitation of a mass of granular matter when a wall below the grains is vibrated, giving rise to a hot granular gas below the cluster. We find by simulation that for a range of parameters the system is bistable: the levitated cluster can occasionally break and give rise to two clusters and a hot granular gas above and below. We use techniques from the theory of rare events to compute the mean transition time for breaking to occur. This requires the introduction of a two-component reaction coordinate.

Thermal Convection in Granular Gases with Dissipative Lateral Walls

We consider a granular gas under the action of gravity, fluidized by a vibrating base. We show that a horizontal temperature gradient, here induced by limiting dissipative lateral walls (DLW), leads always to a granular thermal convection (DLW TC) that is essentially different from ordinary bulk-buoyancy-driven convection (BBD TC). In an experiment where BBD TC is inhibited, by reducing gravity with an inclined plane, we always observe a DLW TC cell next to each lateral wall. Such a cell squeezes towards the nearest wall as the gravity and/or the number of grains increase. Molecular dynamics simulations reproduce the experimental results and indicate that at large gravity or number of grains the DLW TC is barely detectable.

Pattern transition, microstructure, and dynamics in a two-dimensional vibrofluidized granular bed

Experiments are conducted in a two-dimensional monolayer vibrofluidized bed of glass beads, with a goal to understand the transition scenario and the underlying microstructure and dynamics in different patterned states. At small shaking accelerations (Γ=Aω^{2}/g<1, where A and ω=2πf are the amplitude and angular frequency of shaking and g is the gravitational acceleration), the particles remain attached to the base of the vibrating container; this is known as the solid bed (SB). With increasing Γ (at large enough shaking amplitude A/d) and/or with increasing A/d (at large enough Γ), the sequence of transitions/bifurcations unfolds as follows: SB ("solid bed") to BB ("bouncing bed") to LS ("Leidenfrost state") to "2-roll convection" to "1-roll convection" and finally to a gas-like state. For a given length of the container, the coarsening of multiple convection rolls leading to the genesis of a "single-roll" structure (dubbed the multiroll transition) and its subsequent transition to a granular gas are two findings of this work. We show that the critical shaking intensity (Γ_{BB}^{LS}) for the BB→LS transition has a power-law dependence on the particle loading (F=h_{0}/d, where h_{0} is the number of particle layers at rest and d is the particle diameter) and the shaking amplitude (A/d). The characteristics of BB and LS states are studied by calculating (i) the coarse-grained density and temperature profiles and (ii) the pair correlation function. It is shown that while the contact network of particles in the BB state represents a hexagonal-packed structure, the contact network within the "floating cluster" of the LS resembles a liquid-like state. An unsteadiness of the Leidenfrost state has been uncovered wherein the interface (between the floating cluster and the dilute collisional layer underneath) and the top of the bed are found to oscillate sinusoidally, with the oscillation frequency closely matching the frequency of external shaking. Therefore, the granular Leidenfrost state is a period-1 wave as is the case for the BB state.

Hydrodynamics of a vibrated granular monolayer

We investigate the long-standing puzzle of phase separation in a granular monolayer vibrated from below. Although this system is three dimensional, an interesting dynamics occurs mostly in the horizontal plane, perpendicular to the direction of vibration. Experiments [Olafsen and Urbach, Phys. Rev. Lett. 81, 4369 (1998)] demonstrated that for a high amplitude of vibration the system is in the gaslike phase, but when the amplitude becomes smaller than a certain threshold, a phase separation occurs: A solidlike dense condensate of particles forms in the center of the system, surrounded by particles in the gaslike phase. We explain theoretically the experimentally observed coexistence of dilute and dense phases, employing Navier-Stokes granular hydrodynamics. We show that the phase separation is associated with a negative compressibility of granular gas.

Onset of convection in strongly shaken granular matter

Strongly vertically shaken granular matter can display a density inversion: A high-density cluster of beads is elevated by a dilute gaslike layer of fast beads underneath ("granular Leidenfrost effect"). For even stronger shaking the granular Leidenfrost state becomes unstable and granular convection rolls emerge. This transition resembles the classical onset of convection in fluid heated from below at some critical Rayleigh number. The same transition is seen in molecular dynamics (MD) simulations of the shaken granular material. The critical shaking strength for the onset of granular convection can be calculated from a linear stability analysis of a hydrodynamiclike model of the granular flow. Experiment, MD simulations, and theory quantitatively agree.

Exploring the limits of granular hydrodynamics: a horizontal array of inelastic particles

The limits of granular hydrodynamics are explored in the context of the one-dimensional granular system introduced by Du, Li, and Kadanoff [Phys. Rev. Lett. 74, 1268 (1995)]. The density profile of the characteristic steady state, in which a single particle commutes between the driving wall and a dense cluster, is well captured by a hydrodynamic description provided that the finite size of the particles is incorporated. The temperature, however, is not well described: since all energy exchange is located at the border of the cluster, it is precisely for this quantity that the continuum approach breaks down.

van der Waals-like phase-separation instability of a driven granular gas in three dimensions

We show that the van der Waals-like phase-separation instability of a driven granular gas at zero gravity, previously investigated in two-dimensional settings, persists in three dimensions. We consider a monodisperse granular gas driven by a thermal wall of a three-dimensional rectangular container at zero gravity. The basic steady state of this system, as described by granular hydrodynamic equations, involves a denser and colder layer of granulate located at the wall opposite to the driving wall. When the inelastic energy loss is sufficiently high, the driven granular gas exhibits, in some range of average densities, negative compressibility in the directions parallel to the driving wall. When the lateral dimensions of the container are sufficiently large, the negative compressibility causes spontaneous symmetry breaking of the basic steady state and a phase separation instability. Event-driven molecular dynamics simulations confirm and complement our theoretical predictions.

Friction and convection in a vertically vibrated granular system

The effect of friction in the thermal convection instability of granular fluids is studied by means of molecular dynamics simulations. It is found that the transitions between different convective states (zero, one, and two rolls) are primarily governed by the average energy loss per collisions and not by the friction and restitution coefficients separately, and can be roughly described in terms of a single effective restitution coefficient. The average energy loss per collisions, for a fixed value of the restitution coefficient, shows a maximum for a friction coefficient kappa approximately 0.3. The presence of this maximum manifests itself as a reentrant behavior in the transition lines in parameter space when the value of the friction coefficient is increased beyond 0.3.

Convection in vibrated annular granular beds

The response to vibration of a granular bed, consisting of a standard cylindrical geometry but with the addition of a dissipative cylindrical inner wall, has been investigated both experimentally (using positron emission particle tracking) and numerically (using hard sphere molecular dynamics simulation). The packing fraction profiles and granular temperature distributions (in both vertical and horizontal directions) were determined as a function of height and distance from the axis. The two sets of results were in reasonable agreement. The molecular dynamics simulations were used to explore the behavior of the granular bed in the inner wall-outer wall coefficient of restitution phase space. It was observed that one could control the direction of the toroidal convection rolls by manipulating the relative dissipation at the inner and outer walls via the coefficients of restitution, and with several layers of grains it was seen that double convection rolls could also be formed, a result that was subsequently confirmed experimentally.

Thermal convection in monodisperse and bidisperse granular gases: a simulation study

We present results of a simulation study of inelastic hard disks vibrated in a vertical container. An event-driven molecular dynamics method is developed for studying the onset of convection. Varying the relevant parameters (inelasticity, number of layers at rest, intensity of the gravity) we are able to obtain a qualitative agreement of our results with recent hydrodynamical predictions. Increasing the inelasticity, a first continuous transition from the absence of convection to one convective roll is observed, followed by a discontinuous transition to two convective rolls, with hysteretic behavior. At fixed inelasticity and increasing gravity, a transition from no convection to one roll can be evidenced. If the gravity is further increased, the roll is eventually suppressed. Increasing the number of monolayers the system eventually localizes mostly at the bottom of the box: in this case multiple convective rolls as well as surface waves appear. We analyze the density and temperature fields and study the existence of symmetry breaking in these fields in the direction perpendicular to the injection of energy. We also study a binary mixture of grains with different properties (inelasticity or diameters). The effect of changing the properties of one of the components is analyzed, together with density, temperature, and temperature ratio fields. Finally, the presence of a low fraction of quasielastic impurities is shown to determine a sharp transition between convective and nonconvective steady states.

Role of friction in pattern formation in oscillated granular layers

Particles in granular flows are often modeled as frictionless (smooth) inelastic spheres; however, there exist no frictionless grains, just as there are no elastic grains. Our molecular dynamics simulations reveal that friction is essential for realistic modeling of vertically oscillated granular layers: simulations of frictionless particles yield patterns with an onset at a container acceleration about 30% smaller than that observed in experiments and simulations with friction. More importantly, even though square and hexagonal patterns form for a wide range of the oscillation parameters in experiments and in our simulations of frictional inelastic particles, only stripe patterns form in the simulations without friction, even if the inelasticity is increased to obtain as much dissipation as in frictional particles. We also consider the effect of particle friction on the shock wave that forms each time the granular layer strikes the container. While a shock wave still forms for frictionless particles, the spatial and temporal dependence of the hydrodynamic fields differ for the cases with and without friction.

Giant fluctuations at a granular phase separation threshold

We investigate a phase separation instability that occurs in a system of nearly elastically colliding hard spheres driven by a thermal wall. If the aspect ratio of the confining box exceeds a threshold value, granular hydrostatics predict phase separation: the formation of a high-density region coexisting with a low-density region along the wall that is opposite to the thermal wall. Event-driven molecular dynamics simulations confirm this prediction. The theoretical bifurcation curve agrees with the simulations quantitatively well below and well above the threshold. However, in a wide region of aspect ratios around the threshold, the system is dominated by fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of the origin of the giant fluctuations are discussed.