Are Brazil nuts attractive?

Microscopic structure and dynamics study of granular segregation mechanism by cyclic shear

Granular mixtures with size difference can segregate upon shaking or shear. However, the quantitative study of this process remains difficult because it can be influenced by many mechanisms. Conflicting results on similar experimental systems are frequently obtained when the experimental conditions are not well controlled, which is mainly due to the fact that many mechanisms can be at work simultaneously. Moreover, it is often that macroscopic or empirical measures, which lack microscopic physical bases, are used to explain the experimental findings and therefore cannot provide an accurate and complete depiction of the overall process. Here, we carry out a detailed and systematic microscopic structure and dynamics study of a cyclically sheared granular system with rigorously controlled experimental conditions. We find that both convection and arching effect play important roles in the segregation process in our system, and we can quantitatively identify their respective contributions.

Depletion forces in athermally sheared mixtures of frictionless disks and rods in two dimensions

We carry out numerical simulations to study the behavior of an athermal mixture of frictionless circular disks and elongated rods in two dimensions, under three different types of global linear deformation at a finite strain rate: (i) simple shearing, (ii) pure shearing, and (iii) isotropic compression. We find that the fluctuations induced by such deformations lead to depletion forces that cause rods to group in parallel oriented clusters for the cases of simple and pure shear, but not for isotropic compression. For simple shearing, we find that as the fraction of rods increases, this clustering increases, leading to an increase in the average rate of rotation of the rods, and a decrease in the magnitude of their nematic ordering.

Asymmetric and long range interactions in shaken granular media

We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, the amplitude, and the packing density of grains. We determine the local density and kinetic energy profiles of granular particles along the axis of the dimer to find no gradients in the density fields and additive gradients in the kinetic energies.

Casimir effect between pinned particles in two-dimensional jammed systems

The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.

Granular core phenomenon induced by convection in a vertically vibrated cylindrical container

A mixture of 13X molecular sieve (13XMS) particles and glass particles with identical diameters is placed in a cylindrical container. Under vertical vibration, heavier glass particles tend to cluster and are wrapped inside the convection of 13XMS particles, resulting in the granular core phenomenon. The vibration frequency f strongly influences particle convection and particle cluster modes. By contrast, the effect of the dimensionless acceleration amplitude Γ can be neglected. For different f ranges, the granular core is classified as center-type and ring-type cores. For the center-type core, heavy particles are distributed as an approximate zeroth-order Bessel function of the first kind in the radial direction and an exponential function in the height direction. For the ring-type core, the concentration of heavy particles follows the power-series function in the radial direction. A granular transport model is then established based on heavy-particle movements under steady state to analyze the effect of vibration parameters and granular convection on density segregation.

Clustering-Induced Attraction in Granular Mixtures of Rods and Spheres

Depletion-induced aggregation of rods enhanced by clustering is observed to produce a novel model of attractive pairs of rods separated by a line of spheres in a quasi-2D, vertically-shaken, granular gas of rods and spheres. We show that the stability of these peculiar granular aggregates increases as a function of shaking intensity. Velocity distributions of spheres inside and outside of a pair of rods trapping a line of spheres show a clear suppression of the momentum acquired by the trapped spheres. The condensed phase formed between the rods is caused by a clustering instability of the trapped spheres, enhanced by a vertical guidance produced by the confining rods. The liberated area corresponding to direct excluded-volume pairs and indirect depletion-aggregated pairs is measured as a function of time. The stability of rod pairs mediated by spheres reveals an attraction comparable in strength to the one purely induced by depletion forces.

Granular segregation driven by particle interactions

We report the results of an experimental study of particle-particle interactions in a horizontally shaken granular layer that undergoes a second order phase transition from a binary gas to a segregation liquid as the packing fraction C is increased. By focusing on the behavior of individual particles, the effect of C is studied on (1) the process of cluster formation, (2) cluster dynamics, and (3) cluster destruction. The outcomes indicate that the segregation is driven by two mechanisms: attraction between particles with the same properties and random motion with a characteristic length that is inversely proportional to C. All clusters investigated are found to be transient and the probability distribution functions of the separation times display a power law tail, indicating that the splitting probability decreases with time.

Convecting particle diffusion in a binary particle system under vertical vibration

We studied the separation behaviour of binary granular particles in a vertically vibrated container. The final separation of the binary particle system exhibited the Brazil-Nut (BN) effect, though it was not complete. Particle convection occurred, and four different typical convection modes were observed when the frequency f changed from 20 Hz to 80 Hz at constant dimensionless acceleration Γ = 4πAf(2)/g. However, when Γ changed from 2 to 4 at constant f, the system's convection mode stayed almost the same. In our experiments, one type of particle generally moved much faster than the other, so the former was termed the 'convecting' particle, and the latter was termed the 'non-convecting' particle. To study the separation results qualitatively, we divided the system into vertical layers and calculated the mass distribution of the binary particles along the z axis. The results showed that when f increased at constant Γ or Γ decreased at constant f, the convecting particles, usually the smaller and lighter ones, distributed less to the top side and more to the bottom side of the container. Finally, to explain the experimental results, we derived a mass conservation equation for the convecting particles considering simultaneous convection and diffusion. The equation described the experimental results well. We also analysed the effects of f, Γ, diameter ratio, density ratio, etc., on the final separation results.

Flow-mediated coupling on projectiles falling within a superlight granular medium

Interesting collective motion emerges when several heavy intruder disks fall in a loose packed, quasi-two-dimensional granular bed of extremely light grains [F. Pacheco-Vázquez and J. C. Ruiz-Suárez, Nat. Commun. 1, 123 (2010)]. In particular, when two disks impact side by side, they initially repel and then they attract each other until they finally stop. Here we perform experiments and discrete-element soft-particle simulations to determine the range of action and the origin of these attractive and repulsive flow-mediated forces. We find that (1) the drag force on the disks fluctuate with a characteristic length linked to force chains that build up and break; (2) the repulsive force is present when the separation of the intruder disks is less than 6 times the size of the grains of the granular bed, which is the size of an aperture that allows a continuous discharge flow from a container; (3) the attractive force has a range of action between 5 and 6 times the size of the intruder disks; and (4) attraction exists only when intruders move faster than 1 m/s. These results suggest that repulsion originates from jamming of grains between intruders, and it supports the idea that attraction could be due to a "granular pressure" drop in the region between intruders caused by a high flow velocity of grains: a Bernoulli-like effect. However, our results do not rule out other mechanisms of interaction, like fluctuation-induced forces.

Long-range interactions in randomly driven granular fluids

We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles immersed in such a fluidized bed of fine particles leads to the confinement of the fluctuation spectrum of the hydrodynamic fields, which results in effective long-range interactions between the intruders. The analytical predictions are in agreement with the results of discrete element method simulations. By changing the shape and orientation of the intruders, we address how the effective force is affected by small changes in the boundary conditions.

Nonadditivity of fluctuation-induced forces in fluidized granular media

We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.

Horizontal segregation of mono-layer granules coordinated by vertical motion

We experimentally investigate the segregation of a binary mixture of spherical beads confined between two horizontal vertically vibrating plates. The two kinds of beads are of equal diameter and mass but have different restitution coefficients. Segregation occurs in particular ranges of vibration amplitude and frequency. We find that the collisions between beads at an angle to the horizontal plane induce an effective horizontal repulsive force. When one or both bead types bounce up and down in synchronization, the effective repulsive force between the two types of beads is likely to be larger than that found within a single bead type, resulting in the mixture segregating. Non-horizontal collisions also play a role in stabilizing the segregation state by transferring the horizontal kinetic energy back into vertical motion.

Cooperative dynamics in the penetration of a group of intruders in a granular medium

An object moving in a fluid experiences a drag force that depends on its velocity, shape and the properties of the medium. From this simplest case to the motion of a flock of birds or a school of fish, the drag forces and the hydrodynamic interactions determine the full dynamics of the system. Similar drag forces appear when a single projectile impacts and moves through a granular medium, and this case is well studied in the literature. On the other hand, the case in which a group of intruders impact a granular material has never been considered. Here, we study the simultaneous penetration of several intruders in a very low-density granular medium. We find that the intruders move through it in a collective way, following a cooperative dynamics, whose complexity resembles flocking phenomena in living systems or the movement of reptiles in sand, wherein changes in drag are exploited to efficiently move or propel.

Rise of a Brazil nut: a transition line

Using molecular dynamics we study the behavior of a large particle immersed in a bed of smaller ones. The system is bidimensional, consisting of many rough inelastic hard disks of equal size plus a larger one: the intruder. All possible parameters of the system are kept fixed except for two dimensionless parameters determining the frequency and amplitude of the vibrating base. A systematic exploration of this parameter space leads to determining a transition line separating a zone in which the Brazil nut effect is observed and one in which it is not. The results strongly suggest that, in the region of the parameter space in which the study is made, there is a minimum amplitude and a maximum frequency for the Brazil nut effect to take place. These results compare well with isolated results from other authors.

Segregation induced by inelasticity in a vibrofluidized granular mixture

We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species, where most dissipative particles submerge in the less dissipative ones. The segregation occurs even if one type of the particles is elastic. In order to have a complete description of the system, we study the structure of the fluid at microscopic scale (few particle diameters). The density and temperature pair distribution functions show strong enhancements with respect to the equilibrium ones at the same density. In particular, there is an increase in the probability that the more inelastic particles group together in pairs (microsegregation). Microscopically the segregation is buoyancy driven, by the appearance of a dense and cold region around the more inelastic particles.

Interaction between intruders in vibrated granular beds

Two neutrally buoyant intruder particles in a granular bed fluidized by vertical, sinusoidal vibration are known to interact with each other over a range of about five intruder diameters. Using molecular dynamics simulations, we investigate in detail the spatial and temporal nature of this interaction. We show that the force of attraction between intruders can be calculated from the local density and kinetic energy using a simple equation of state. Moreover, the interaction can be changed from attractive to repulsive by reducing the coefficient of restitution between the intruders and host particles, one of the key results of this work.

Intruder clustering in three-dimensional granular beds

We present results of computer simulations for neutrally buoyant intruders in a vertically vibrated three-dimensional granular bed of smaller host particles. Under sinusoidal excitation, pairs of intruders interact over a distance of several intruder diameters; a group of intruders forms a cluster. The strength of the interaction grows as the number of intruders is increased. We show that the tendency to cluster may be manipulated through the use of nonsinusoidal excitation, which allows partial mixing. Finally, we investigate the effects of walls on the clustering of intruders.

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.

Dynamically induced effective interaction in periodically driven granular mixtures

We show that a granular mixture subject to horizontal oscillations can be reduced to a monodisperse system of particles interacting via an effective interaction. This interaction is attractive at short distances and strongly anisotropic, and its features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, which takes into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.

Fluctuation-induced casimir forces in granular fluids

We numerically investigate the behavior of driven noncohesive granular media and find that two fixed large intruder particles, immersed in a sea of small particles, experience, in addition to a short-range depletion force, a long-range repulsive force. The observed long-range interaction is fluctuation-induced and we propose a mechanism similar to the Casimir effect that generates it: The hydrodynamic fluctuations are geometrically confined between the intruders, producing an unbalanced renormalized pressure. An estimation based on computing the possible Fourier modes explains the repulsive force and is in qualitative agreement with the simulations.

Segregation of large granules from close-packed cluster of small granules due to buoyancy

Segregation of large granules in a vibrofluidized granular bed with inhomogeneous granular number density distribution is studied by an event-driven algorithm. Simulation results show that the mean vertical position of large granules decreases with the increase of the density ration of the large granules to the small ones. This conclusion is consistent with the explanation that the net pressure due to the small surrounding particle impacts balances the large granular weight, and indict that the upward movement of the large granules is driven by the buoyancy. The values of temperature, density, and pressure of the systems are also computed by changing the conditions such as heating temperature on the bottom and restitution coefficient of particles. These results indicate that the segregation of large granules also happen in the systems with density inversion or even close-packed cluster of particles floating on a low-density fluid, due to the buoyancy. An equation of state is proposed to explain the buoyancy.

Granular species segregation under vertical tapping: effects of size, density, friction, and shaking amplitude

We present extensive molecular dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both the Brazil nut effect (larger particles on the top, BN) and the reverse Brazil nut effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive "segregation diagram" and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency.

Size segregation in granular media induced by phase transition

In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for a hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism that gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from the Brazil nut to the reverse Brazil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps.