Segregation in binary mixtures under gravity

Statistics of a two-dimensional immersed granular gas magnetically forced in volume

We present an experimental study of the dynamics of a set of magnets within a fluid in which a remote torque applied by a vertical oscillating magnetic field transfers angular momentum to individual magnets. This system differs from previous experimental studies of granular gas where the energy is injected by vibrating the boundaries. Here, we do not observe any cluster formation, orientational correlation and equipartition of the energy. The magnets' linear velocity distributions are stretched exponentials, similar to three-dimensional boundary-forced dry granular gas systems, but the exponent does not depend on the number of magnets. The value of the exponent of the stretched exponential distributions is close to the value of 3/2 previously derived theoretically. Our results also show that the conversion rate of angular momentum into linear momentum during the collisions controls the dynamics of this homogenously forced granular gas. We report the differences among this homogeneously forced granular gas, ideal gas, and nonequilibrium boundary-forced dissipative granular gas.

Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.

Lift force acting on an intruder in dense, granular shear flows

We report a lift force model for intruders in dense, granular shear flows. Our derivation is based on the thermal buoyancy model of Trujillo and Hermann [Physica A 330, 519 (2003)10.1016/S0378-4371(03)00621-6], but it takes into account both granular temperature and pressure differences in the derivation of the net buoyancy force acting on the intruder. In a second step, the model is extended to take into account also density differences between the intruder and the bed particles. The model predicts very well the rising and sinking of intruders, the lift force acting on intruders as determined by discrete element model simulations, and the neutral-buoyancy limit of intruders in shear flows. Phenomenologically, we observe a cooling upon the introduction of an intruder into the system. This cooling effect increases with intruder size and explains the sinking of large intruders. On the other hand, the introduction of small to midsized intruders, i.e., up to four times the bed particle size, leads to a reduction in the granular pressure compared to the hydrostatic pressure, which in turn causes the rising of small to midsized intruders.

Accurate buoyancy and drag force models to predict particle segregation in vibrofluidized beds

The segregation of large intruders in an agitated granular system is of high practical relevance, yet the accurate modeling of the segregation (lift) force is challenging as a general formulation of a granular equivalent of a buoyancy force remains elusive. Here, we critically assess the validity of a granular buoyancy model using a generalization of the Archimedean formulation that has been proposed very recently for chute flows. The first model system studied is a convection-free vibrated system, allowing us to calculate the buoyancy force through three different approaches, i.e., a generalization of the Archimedean formulation, the spring force of a virtual spring, and through the granular pressure field. The buoyancy forces obtained through these three approaches agree very well, providing strong evidence for the validity of the generalization of the Archimedean formulation of the buoyancy force which only requires an expression for the solid fraction of the intruder, hence allowing for a computationally less demanding calculation of the buoyancy force as coarse graining is avoided. In a second step, convection is introduced as a further complication to the granular system. In such a system, the lift force is composed of granular buoyancy and a drag force. Using a drag model for the slow-velocity regime, the lift force, directly measured through a virtual spring, can be predicted accurately by adding a granular drag force to the generalization of the Archimedean formulation of the granular buoyancy. The developed lift force model allows us to rationalize the dependence of the lift force on the density of the bed particles and the intruder diameter, the independence of the lift force on the intruder diameter, and the independence of the lift force on the intruder density and the vibration strength (once a critical value is exceeded).

Experimental investigation of segregation of granular mixtures during heap formation

The present study is on segregation of granular mixtures during heap formation in a quasi two-dimensional rectangular bin where binary mixture of a specified composition is poured intermittently into the auxiliary hopper and then allowed to pass through the gap (k = 10 mm) between the divider and the plate and finally settle on to the heap. The profiles of number fraction of big particles are plotted along the flow directions to study the segregation phenomena for surface profile. It shows that larger particles travel more distance and smaller particles settle near the pouring point for all cases studied.

Velocity Distribution of a Homogeneously Cooling Granular Gas

In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity of the particles decreases after the driving is shut off. Moreover, it predicts that the rescaled particle velocity distribution will approach a stationary state with overpopulated high-velocity tails as compared to the Maxwell-Boltzmann distribution. While this fundamental theoretical result was reproduced by numerical simulations, an experimental confirmation is still missing. Using a microgravity experiment that allows the spatially homogeneous excitation of spheres via magnetic fields, we confirm the theoretically predicted exponential decay of the tails of the velocity distribution.

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component i to be approximately proportional to 2σ_{i}+〈σ〉, where σ_{i} is the diameter of the disk and 〈σ〉 is the mean diameter.

Stress partition and microstructure in size-segregating granular flows

When a granular mixture involving grains of different sizes is shaken, sheared, mixed, or left to flow, grains tend to separate by sizes in a process known as size segregation. In this study, we explore the size segregation mechanism in granular chute flows in terms of the pressure distribution and granular microstructure. Therefore, two-dimensional discrete numerical simulations of bidisperse granular chute flows are systematically analyzed. Based on the theoretical models of J. M. N. T. Gray and A. R. Thornton [Proc. R. Soc. A 461, 1447] and K. M. Hill and D. S. Tan [J. Fluid Mech. 756, 54 (2014)], we explore the stress partition in the phases of small and large grains, discriminating between contact stresses and kinetic stresses. Our results support both gravity-induced and shear-gradient-induced segregation mechanisms. However, we show that the contact stress partition is extremely sensitive to the definition of the partial stress tensors and, more specifically, to the way mixed contacts (i.e., involving a small grain and a large grain) are handled, making conclusions on gravity-induced segregation uncertain. By contrast, the computation of the partial kinetic stress tensors is robust. The kinetic pressure partition exhibits a deviation from continuum mixture theory of a significantly higher amplitude than the contact pressure and displays a clear dependence on the flow dynamics. Finally, using a simple approximation for the contact partial stress tensors, we investigate how the contact stress partition relates to the flow microstructure and suggest that the latter may provide an interesting proxy for studying gravity-induced segregation.

Shear-induced segregation of particles by material density

Recently, shear rate gradients and associated gradients in velocity fluctuations (e.g., granular temperatures or kinetic stresses) have been shown to drive segregation of different-sized particles in a manner that reverses at relatively high solids fractions (〈f〉>0.50). Here we investigate these effects in mixtures of particles differing in material density through computational and theoretical studies of particles sheared in a vertical chute where we vary the solids fraction from 〈f〉=0.2 to 0.6. We find that in sparse flows, 〈f〉=0.2 to 0.4, the heavier (denser) particles segregate to lower shear rates similarly to the heavier (larger) particles in mixtures of particles differing only in size. However, there is no segregation reversal at high f in mixtures of particles differing in density. At all solids fractions, heavier (denser) particles segregate to regions of lower shear rates and lower granular temperatures, in contrast with segregation of different-sized particles at high f, where the heavier (larger) particles segregate to the region of higher shear rates. Kinetic theory predicts well the segregation for both types of systems at low f but breaks down at higher f's. Our recently proposed mixture theory for high f granular mixtures captures the segregation trends well via the independent partitioning of kinetic and contact stresses between the two species. In light of these results, we discuss possible directions forward for a model framework that encompasses segregation effects more broadly in these systems.

Hydrodynamic granular segregation induced by boundary heating and shear

Segregation induced by a thermal gradient of an impurity in a driven low-density granular gas is studied. The system is enclosed between two parallel walls from which we input thermal energy to the gas. We study here steady states occurring when the inelastic cooling is exactly balanced by some external energy input (stochastic force or viscous heating), resulting in a uniform heat flux. A segregation criterion based on Navier-Stokes granular hydrodynamics is written in terms of the tracer diffusion transport coefficients, whose dependence on the parameters of the system (masses, sizes, and coefficients of restitution) is explicitly determined from a solution of the inelastic Boltzmann equation. The theoretical predictions are validated by means of Monte Carlo and molecular dynamics simulations, showing that Navier-Stokes hydrodynamics produces accurate segregation criteria even under strong shearing and/or inelasticity.

Characterization of a Vortex Shaking Method for Aerosolizing Fibers

Generation of well-dispersed, well-characterized fibers is important in toxicology studies. A vortex-tube shaking method is investigated using glass fibers to characterize the generated aerosol. Controlling parameters that were studied included initial batch amounts of glass fibers, preparation of the powder (e.g., preshaking), humidity, and airflow rate. Total fiber number concentrations and aerodynamic size distributions were typically measured. The aerosol concentration is only stable for short times (t < 10 min) and then falls precipitously, with concomitant changes in the aerosol aerodynamic size distribution; the plateau concentration and its duration both increase with batch size. Preshaking enhances the initial aerosol concentration and enables the aerosolization of longer fibers. Higher humidity strongly affects the particle size distribution and the number concentration, resulting in a smaller modal diameter and a higher number concentration. Running the vortex shaker at higher flow rates (Q > 0.3 lpm), yields an aerosol with a particle size distribution representative of the batch powder; running the vortex shaker at a lower aerosol flow rate (Q ~ 0.1 lpm) only aerosolizes the shorter fibers. These results have implications for the use of the vortex shaker as a standard aerosol generator.

Thermal segregation of intruders in the Fourier state of a granular gas

A low density binary mixture of granular gases is considered within the Boltzmann kinetic theory. One component, the intruders, is taken to be dilute with respect to the other, and thermal segregation of the two species is described for a special solution to the Boltzmann equation. This solution has a macroscopic hydrodynamic representation with a constant temperature gradient and is referred to as the Fourier state. The thermal diffusion factor characterizing conditions for segregation is calculated without the usual restriction to Navier-Stokes hydrodynamics. Integral equations for the coefficients in this hydrodynamic description are calculated approximately within a Sonine polynomial expansion. Molecular dynamics simulations are reported, confirming the existence of this idealized Fourier state. Good agreement is found for the predicted and simulated thermal diffusion coefficient, while only qualitative agreement is found for the temperature ratio.

Segregation of an intruder in a heated granular dense gas

A recent segregation criterion [Phys. Rev. E 78, 020301(R) (2008)] based on the thermal diffusion factor Λ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of Λ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of the intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo method to get the kinetic diffusion coefficient D(0). The comparison between theory and simulation shows that the second Sonine approximation to D(0) yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE-RBNE transition, the kinetic theory results for the factor Λ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.

Phase transitions in shear-induced segregation of granular materials

We computationally study shear-induced segregation of different-sized particles in vertical chute flow. We find that, for low solid fractions, large particles segregate toward regions of low shear rates where the granular temperature (velocity variance) is low. As the solid fraction increases, this trend reverses, and large particles segregate toward regions of high shear rates and temperatures. We find that this is a global phenomenon: local segregation trends reverse at high system solid fractions even where local solid fractions are small. The reversal corresponds to the growth of a single enduring cluster of 30%-60% of the particles that we propose changes the segregation dynamics.

Clustering in rapid granular flows of binary and continuous particle size distributions

The dynamic clustering phenomenon in two-dimensional simple shear flows has been investigated using molecular dynamic simulations of systems containing binary and continuous size distributions of equal-material-density particles. Particular attention has been paid to two questions: (1) Does the presence of size nonuniformities serve to enhance or attenuate the presence of clusters? (2) Do particles of a given size preferentially segregate within the clusters? With respect to the first question, the prominence of clustered regions increases with increasing deviation from the monodisperse limit in the case of both binary and continuous size distributions. With respect to the second question, the larger particles of both binary and continuous size distributions are consistently observed to segregate within the transient clustered regions. Further investigation of granular temperatures within the clustered and dilute regions reveals that this segregation is consistent with previously observed temperature-driven segregation in steady-state systems; large particles favor the lower-temperature (clustered) regions. Moreover, observation of clustering length scales suggests that large particles may favor the center of the clustered regions, where granular temperatures are expected to reach a minimum.

Segregation by thermal diffusion in moderately dense granular mixtures

A theory based on a solution of the inelastic Enskog equation that goes beyond the weak dissipation limit is used to determine the thermal diffusion factor of a binary granular mixture under gravity. The Enskog equation that aims to describe moderate densities neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, the thermal diffusion factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, composition, density and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail in the tracer limit case, showing that the phase diagrams depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis, which is based on a preliminary short report of the author (Phys. Rev. E 78, 020301(R) (2008)), extends previous theoretical results derived in the dilute limit case.

Mass transport of impurities in a moderately dense granular gas

Transport coefficients associated with the mass flux of impurities immersed in a moderately dense granular gas of hard disks or spheres described by the inelastic Enskog equation are obtained by means of the Chapman-Enskog expansion. The transport coefficients are determined as the solutions of a set of coupled linear integral equations recently derived for polydisperse granular mixtures [Garzó, Phys. Rev. E 76, 031304 (2007)]. With the objective of obtaining theoretical expressions for the transport coefficients that are sufficiently accurate for highly inelastic collisions, we solve the above integral equations by using the second Sonine approximation. As a complementary route, we numerically solve by means of the direct simulation Monte Carlo method (DSMC) the inelastic Enskog equation to get the kinetic diffusion coefficient D0 for two and three dimensions. We have observed in all our simulations that the disagreement, for arbitrarily large inelasticity, in the values of both solutions (DSMC and second Sonine approximation) is less than 4%. Moreover, we show that the second Sonine approximation to D0 yields a dramatic improvement (up to 50%) over the first Sonine approximation for impurity particles lighter than the surrounding gas and in the range of large inelasticity. The results reported in this paper are of direct application in important problems in granular flows, such as segregation driven by gravity and a thermal gradient. We analyze here the segregation criteria that result from our theoretical expressions of the transport coefficients.

Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid

A segregation criterion based on the inelastic Enskog kinetic equation is derived to show the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the different parameters of the system. In contrast to previous theoretical attempts, the approach is not limited to the near-elastic case, takes into account the influence of both thermal gradients and gravity, and applies for moderate densities. The form of the phase diagrams for the BNE-RBNE transition depends sensitively on the value of gravity relative to the thermal gradient, so that it is possible to switch between both states for given values of the mass and size ratios, the coefficients of restitution, and the solid volume fraction. In particular, the influence of collisional dissipation on segregation becomes more important when the thermal gradient dominates over gravity than in the opposite limit. The present analysis extends previous results derived in the dilute limit case and is consistent with the findings of some recent experimental results.

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.

Species segregation in one-dimensional granular-system simulations

We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10 pi L/N epsilon , where N is the total number of particles, L the spatial extent of the system and epsilon the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless N epsilon<or= 10 pi . Species segregation, driven by the frictional force occurs as a result of the strong temperature gradients within clusters which pushes the light particles towards the clusters' edges and the heavy particles towards the center. Segregation within clusters is complete at the time of inelastic collapse.

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.

Hydrodynamic profiles for an impurity in an open vibrated granular gas

The hydrodynamic state of an impurity immersed in a low density granular gas is analyzed. Explicit expressions for the temperature and density fields of the impurity in terms of the hydrodynamic fields of the gas are derived. It is shown that the ratio between the temperatures of the two components, measuring the departure from the energy equipartition, only depends on the mechanical properties of the particles, being therefore constant in the bulk of the system. This ratio plays an important role in determining the density profile of the intruder and its position with respect to the gas, since it determines the sign of the pressure diffusion coefficient. The theoretical predictions are compared with molecular dynamics simulation results for the particular case of the steady state of an open vibrated granular system in the absence of macroscopic fluxes, and a satisfactory agreement is found.

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.

Reversing the Brazil nut effect

We propose a lattice model for studying the Brazil Nut Effect (BNE), i.e. the phase segregation occurring when a granular material is vertically shaked. The model considers the tap intensity and the mobility mu of the grains as the main physical parameters. Different mobilities for different grain species lead to segregation (BNE) patterns, reverse segregation (RBNE) patterns, "sandwhich" layered structures or vertical domains. A phase diagram (decompaction chi, mobility difference between both species Delta mu) is obtained in which the different phases are emphasized. In a narrow region of the diagram, different phases coexist. It is shown that the BNE segregation could be reversed by increasing the tap intensity or the characteristics of the grains. Numerical results are compared with earlier experimental works.

Energy partition and segregation for an intruder in a vibrated granular system under gravity

The difference of temperatures between an impurity and the surrounding gas in an open vibrated granular system is studied. It is shown that, in spite of the high inhomogeneity of the state, the temperature ratio remains constant in the bulk of the system. The lack of energy equipartition is associated to the change of sign of the pressure diffusion coefficient for the impurity at certain values of the parameters of the system, leading to a segregation criterium. The theoretical predictions are consistent with previous experimental results, and also in agreement with molecular dynamics simulation results reported in this Letter.

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 theory for particle size segregation in shallow granular free-surface flows

Granular materials composed of a mixture of grain sizes are notoriously prone to segregation during shaking or transport. In this paper, a binary mixture theory is used to formulate a model for kinetic sieving of large and small particles in thin, rapidly flowing avalanches, which occur in many industrial and geophysical free-surface flows. The model is based on a simple percolation idea, in which the small particles preferentially fall into underlying void space and lever large particles upwards. Exact steady-state solutions have been constructed for general steady uniform velocity fields, as well as time-dependent solutions for plug-flow, that exploit the decoupling of material columns in the avalanche. All the solutions indicate the development of concentration shocks, which are frequently observed in experiments. A shock-capturing numerical algorithm is formulated to solve general problems and is used to investigate segregation in flows with weak shear.

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.

Sensitivity of granular segregation of mixtures in quasi-two-dimensional fluidized layers

Size segregation is studied using a quasi-two-dimensional rotating cylinder system for mixtures of different size, near-spherical particles. Flow occurs only in a thin surface layer, whereas the remaining particles rotate as a fixed bed. In most of the systems studied, the measured radial weight fraction profiles in the bed show significant double segregation (a core of small particles as well as a thin layer of small particles at the periphery). The profiles are found to be sensitively dependent on the surface roughness of the particles in the mixture, and double segregation reduces with particle roughness. Double segregation is also sensitive to cylinder diameter and no double segregation is observed for the smaller diameter cylinders used. The system, however, shows two unexpected scalings: (i). the scaled profiles are nearly the same for different cylinder diameters, when the cylinder diameter to the cylinder length ratio is the same, and (ii). the profiles obtained are found to be insensitive to the size of the large particles in the mixture but depend strongly on the size of the small particles.

Two-dimensional inclined chute flows: transverse motion and segregation

We present an experimental study of two-dimensional dense inclined chute flows consisting of both monodisperse and bidisperse disks. We analyzed the trajectories of the particles within the flow in a steady regime. (i) In monodisperse flows, particles are arranged in layers that are in motion relative to one another, and it is found that the particles have a nonzero probability of being transferred to adjacent layers. We measured the mean time spent by a particle in a given layer. This residence time is found to decrease with increasing layer height. The particle transfer between layers can be interpreted as transverse motion of a diffusive nature. The diffusion coefficient associated with each layer increases linearly with the layer height. (ii) In polydisperse flows consisting of a small percentage (less than 1%) of small disks among large ones, the small particles have a net downward motion on which a fluctuating behavior is superimposed. At short times, the small particle motion can be described as a biased Brownian motion. The ratio of the characteristic time of diffusion to that of convection is found to increase with the layer height, indicating that the segregation process is more efficient in the upper layers of the flow. At longer times, the transverse motion of the small particles seems to differ greatly from a classical biased Brownian motion.