Variational approach to hard sphere segregation under gravity

Extremely Non-Auxetic Behavior of a Typical Auxetic Microstructure Due to Its Material Properties

The re-entrant honeycomb microstructure is one of the most famous, typical examples of an auxetic structure. The re-entrant geometries also include other members as, among others, the star re-entrant geometries with various symmetries. In this paper, we focus on one of them, having a 6-fold symmetry axis. The investigated systems consist of binary hard discs (two-dimensional particles with two slightly different sizes, interacting through infinitely repulsive pairwise potential), from which different structures, based on the mentioned geometry, were formed. To study the elastic properties of the systems, computer simulations using the Monte Carlo method in isobaric-isothermal ensemble with varying shape of the periodic box were performed. The results show that all the considered systems are isotropic and not auxetic-their Poisson's ratio is positive in each case. Moreover, Poisson's ratios of the majority of examined structures tend to +1 with increasing pressure, which is the upper limit for two-dimensional isotropic media, thus they can be recognized as the ideal non-auxetics in appropriate thermodynamic conditions. The results obtained contradict the common belief that the unique properties of metamaterials result solely from their microstructure and indicate that the material itself can be crucial.

Extreme Poisson’s Ratios of Honeycomb, Re-Entrant, and Zig-Zag Crystals of Binary Hard Discs

Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. In contrast to equidiameter HD, which crystallize into a homogeneous solid which is elastically isotropic due to its six-fold symmetry axis, the systems studied in this work contain artificial patterns and can be either isotropic or anisotropic. It turns out that the symmetry of the patterns obtained by the appropriate arrangement of two types of discs strongly influences their elastic properties. The Poisson’s ratio (PR) of each of the considered structures was studied in two aspects: (a) its dependence on the external isotropic pressure and (b) in the function of the direction angle, in which the deformation of the system takes place, since some of the structures are anisotropic. In order to accomplish the latter, the general analytic formula for the orientational dependence of PR in 2D systems was used. The PR analysis at extremely high pressures has shown that for the vast majority of the considered structures it is approximately direction independent (isotropic) and tends to the upper limit for isotropic 2D systems, which is equal to +1. This is in contrast to systems of equidiameter discs for which it tends to 0.13, i.e., a value almost eight times smaller.

Particle segregation in a sedimenting bidisperse soft sphere system

We study the sedimentation process of a binary colloidal soft sphere system where significant overlaps of the particles are possible. We employ estimates of the equation of states in the small and large pressure limit in order to predict the final states of the sedimentation process. Furthermore, Brownian dynamics simulations were performed in order to confirm the predictions and to explore the dynamics of the sedimentation. We observe that the segregation process due to gravity usually consists of multiple steps. Instead of single particles moving upwards or downwards we usually observe that first local segregation occurs, then clusters consisting of particles of one species are formed that finally sink towards their equilibrium position within the final sedimentation profile. The possible final states include complex phases like a phase consisting of large particles on the top and the bottom of the system with small particles in between. We also observe metastable network-like structures.

Spiral trajectory in the horizontal Brazil nut effect

An intruder to a group of identical beads contained in a circular plate which is subjected to a circular vibration will trace approximately a cyclic spiral. The trajectory is a result of both migration and rotation. The intruder migrates in the radial direction while rotating with a constant speed with respect to the center of mass of the whole group of beads. The rotation velocity is due to friction between the beads and the container wall and determined by the vibration amplitude and the number of beads. The migration direction is dependent on the size ratio and mass ratio of the intruder to the background beads. The migration speed is constant for the outward migration, but decreases gradually when the intruder migrates toward the center of mass of the whole cluster for the inward case.

Density-driven segregation in vertically vibrated binary granular mixtures

Segregation in vertically vibrated binary granular mixtures with the same size is studied experimentally. The partially segregated state occurring in this system is observed carefully. We find that the characteristic of the partially segregated state is that the lighter particles tend to rise and form a pure layer on the top of the system while the heavier particles and some of the lighter ones stay at the bottom and form a mixed layer. The ratio of the thickness of the pure top layer to that of the whole system can be taken as an order parameter, which describes the degree of the segregation quantitatively and is useful in the investigation of the system. By use of it, we find that the segregation state is only dependent on the density ratio of the two kinds of particles. The dependent of the segregation on the vibration frequency is also studied by use of this order parameter, and finally, two typical phase diagrams are given.

Mechanisms in the size segregation of a binary granular mixture

A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

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.

A horizontal Brazil-nut effect and its reverse

Transport effects in a monolayer consisting of a binary granular mixture, confined in a horizontally vibrating circular dish, are studied experimentally and compared with a reduced theoretical model. Depending on the ratio of the particles' material density and size, migration of the larger particles occurs either towards the boundary or to the center of the circular container. These directed motions show similarities to the Brazil-nut effect and its reverse form.

Separation of binary granular mixtures under vibration and differential magnetic levitation force

The application of both a strong magnetic field and a magnetic field gradient to a diamagnetic or paramagnetic material can produce a vertical force that acts in concert with the force of gravity. We consider a binary granular mixture in which the two components have different magnetic susceptibilities and therefore experience different effective forces of gravity when subjected to an inhomogeneous magnetic field. Under vertical vibration, such a mixture may rapidly separate into regions almost pure in the two components. We investigate the conditions for this behavior, studying the speed and completeness of separation as a function of differential effective gravity and the frequency and amplitude of vibration. The influence of the cohesive magnetic dipole-dipole interactions on the separation process is also investigated. In our studies insight is gained through the use of a molecular dynamics simulation model.

Are Brazil nuts attractive?

We present event-driven simulation results for single and multiple intruders in a vertically vibrated granular bed. Under our vibratory conditions, the mean vertical position of a single intruder is governed primarily by a buoyancylike effect. Multiple intruders also exhibit buoyancy governed behavior; however, multiple neutrally buoyant intruders cluster spontaneously and undergo horizontal segregation. These effects can be understood by considering the dynamics of two neutrally buoyant intruders. We have measured an attractive force between such intruders which has a range of five intruder diameters, and we provide a mechanistic explanation for the origins of this force.

Segregation in fluidized versus tapped packs

We compare the predictions of two different statistical mechanics approaches, corresponding to different physical measurements, proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). In particular we analytically solve at a mean field level the partition function of a simple hard sphere lattice model under gravity and focus on the phenomenon of size segregation. We find that the two approaches lead to similar results and seem to coincide in the limit of very low shaking amplitude. However, they give different predictions of the crossovers from Brazil nut effect to reverse Brazil nut effect with respect to the shaking amplitude, which could be detected experimentally.

Air-driven Brazil nut effect

A large heavy object may rise to the top of a bed of smaller particles under the influence of vertical vibration, the "Brazil nut effect." Recently it has been noted that interstitial air can influence the Brazil nut rise time. Here we report that the air movement induced by vertical vibration produces a very strong Brazil nut effect for fine granular beds. We use a porous-bottomed box to investigate the mechanism responsible for this effect and to demonstrate that it is related to the piling of fine beds, first reported by Chladni and studied by Faraday. Both effects are due to the strong interaction of the fine particles with the air, as it is forced through the bed by the vibration.

Reversing the Brazil-nut effect: competition between percolation and condensation

We report on experiments on vertically shaken binary granular mixtures, which separate into their components due to the external excitation. This well-known phenomenon, where large particles rise to the top of the mixture, is called the Brazil-nut effect. Recent theoretical findings predict also a reverse Brazil-nut effect, where large particles sink to the bottom of the container. We choose spherical beads of various diameters and materials in order to observe the transition from Brazil-nut effect to its reverse form. The direction of demixing depends sensitively on the external excitation, so that it is possible to switch between both effects for a given mass density ratio.