Individual constituent balance equations are often used to derive expressions for species-specific segregation velocities in flows of dense granular mixtures. We propose a semiempirical expression for the interspecies momentum exchange in density-bidisperse granular flows as an extension of ideas from kinetic theory and compare it to a previous viscous drag approach that is analogous to particles settling in a fluid. The proposed model expands the range of the granular kinetic theory from short-duration binary collisions to the multiple enduring contacts characteristic of dense shear flows and incorporates the effects of particle friction, concentration ratio, and local flow conditions. The segregation velocities derived from the momentum balance equation using both interspecies drag models match the downward and upward segregation velocities of heavy and light particles obtained from DEM simulations through the flowing layer depth for different density ratios and constituent concentrations in confined shear flows. Predictions of the kinetic theory inspired approach are additionally compared to results from free surface heap flow simulations, and, again, a close match is observed.
Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due to the opposing effects of the two segregation mechanisms. Using discrete element method (DEM) simulations of combined size and density segregation we show that the segregation velocity is well described by a model that depends linearly on the local shear rate and quadratically on the species concentration. Concentration profiles predicted by incorporating th…
Reverse segregation and self-organization in inclined chute flows of bidisperse granular mixtures
Sandia National Laboratories（桑迪亚国家实验室）；Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室计算科学与工程中心）；School of Math, Science, and Engineering, Central New Mexico Community College（新墨西哥中部社区学院数理工程学院）
Continuum modeling of size-segregation and flow in dense, bidisperse granular media: Accounting for segregation driven by both pressure gradients and shear-strain-rate gradients
We present numerical evidence for an additional discontinuous transition inside the jammed regime for an asymmetric bidisperse granular packing upon compression. This additional transition line separates jammed states with networks of predominantly large particles from jammed networks formed by both large and small particles, and the transition is indicated by a discontinuity in the number of particles contributing to the jammed network. The additional transition line emerges from the curves of jamming transitions and terminates in an end-point where the discontinuity vanishes. The additional …
While convective flows are implicated in many granular segregation processes, the associated particle-scale rearrangements are not well understood. A three-dimensional bidisperse mixture segregates under steady shear, but the cyclically driven system either remains mixed or segregates slowly. Individual grain motion shows no signs of particle-scale segregation dynamics that precede bulk segregation. Instead, we find that the transition from non-segregating to segregating flow is accompanied by significantly less reversible particle trajectories, and the emergence of a convective flow field.
Liquid foam flows in a Hele-Shaw cell were investigated. The plug flow obtained for a monodisperse foam is strongly perturbed in the presence of bubbles whose size is larger than the average bubble size by an order of magnitude at least. The large bubbles migrate faster than the mean flow above a velocity threshold which depends on its size. We evidence experimentally this new instability and, in case of a single large bubble, we compare the large bubble velocity with the prediction deduced from scaling arguments. In case of a bidisperse foam, an attractive interaction between large bubbles in…
Discrete element method is conducted to investigate the bidisperse dense granular flow having big and small grains in a two dimensional hopper. A half-circular dynamical force arch is observed above the outlet and Beverloo's law is verified to describe the relationship between flow rate and outlet size. The bidisperse flow can reach the maximum flow rate when a small fraction of big grains is added into the monodisperse flow with only small grains. The distributions of contact force, packing fraction and grain velocity indicate that the flow properties in the hopper are closely related to the …
We experimentally study particle scale dynamics during segregation of a bidisperse mixture under oscillatory shear. Large and small particles show an underlying asymmetry that is dependent on the local particle concentration, with small particles segregating faster in regions of many large particles and large particles segregating slower in regions of many small particles. We quantify the asymmetry on bulk and particle scales, and capture it theoretically. This gives new physical insight into segregation and reveals a similarity with sedimentation, traffic flow and particle diffusion.
Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate that the collisional diffusion is essentially independent of overburden pressure. Because the rate of segregation diminishes with overburden pressure, the tendency for particles to segregate weakens relative to the re-mixing of particles due to collisional diffusion as the overburden pressure increases. Using a continuum approach that includes a pressure depen…
Using simulations and a virtual-spring-based approach, we measure the segregation force, Fseg, over a range of size-bidisperse mixture concentrations, particle size ratios, and shear rates to develop a model for Fseg that extends its applicability from the well-studied non-interacting intruders regime to finite-concentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the single intruder assumption applies and provides an accurate description of the pressure partitioning between species.
We study the bulk properties of isotropic bidisperse granular mixtures using discrete element simulations. The focus is on the influence of the size (radius) ratio of the two constituents and volume fraction on the mixture properties. We show that the effective bulk modulus of a dense granular (base) assembly can be enhanced by up to 20% by substituting as little as 5% of its volume with smaller sized particles. Particles of similar sizes barely affect the macroscopic properties of the mixture. On the other extreme, when a huge number of fine particles are included, most of them lie in the voi…
Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating drums -- which suggest that the dynamics of systems at intermediate and high density might be amenable to a statistical mechanics approach.
The size-segregation of granular materials, a process colloquially known as the Brazil Nut Effect, has generally been thought to proceed faster the greater the size difference of the particles. We experimentally investigate sheared bidisperse granular materials as a function of the size ratio of the two species, and find that the mixing rate at low confining pressure behaves as expected from percolation-based arguments. However, we also observe an anomalous effect for the re-segregation rates, wherein particles of both dissimilar and similar sizes segregate more slowly than intermediate partic…
Using Brownian dynamics simulations we perform a systematic investigation of the shear-induced migration of colloidal particles subject to Poiseuille flow in both cylindrical and planar geometry. We find that adding an attractive component to the interparticle interaction enhances the migration effect, consistent with recent simulation studies of platelet suspensions. Monodisperse, bidisperse and polydisperse systems are studied over a range of shear rates, considering both steady states and the transient dynamics arising from the onset of flow. For bidisperse and polydisperse systems size seg…
The segregation and the phase inversion are investigated through a simple granular system which consists of only two inelastic hard spheres in a square box with an energy source. With the variation of the coefficient of restitution, the mass ratio between two spheres or the box size, we show that two types of segregated states and crossover between them are realized in such a small simple system.
We study the granular segregation in a tapered rotating drum by means of simulations. In this geometry, both radial and axial segregation appear, the strength of which depends on the filling fraction. We study the effect of the drum's tapering angle on the segregation speed and show that, coherently with several recent studies, the axial segregation is due to the combined effect of the radial segregation and the shape of the drum. We show that the axial segregation behaves in a way analogous to the one found in chute flows, and corresponds to previous theories for shallow gravity driven surfac…
We present an X-ray tomography study of the segregation mechanisms of tracer particles in a three-dimensional cyclically sheared bi-disperse granular medium. Big tracers are dragged by convection to rise to the top surface and then remain trapped there due to the small downward convection cross-section, which leads to segregation. Additionally, we also find that the local structural up-down asymmetry due to arching effect around big tracers will induce the tracers to have a net upward displacement against its smaller neighbors, which is another mechanism for segregation.
Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of …
We present a continuum approach to model segregation of size-bidisperse granular materials in unsteady bounded heap flow as a prototype for modeling segregation in other time varying flows. In experiments, a periodically modulated feed rate produces stratified segregation like that which occurs due to intermittent avalanching, except with greater layer-uniformity and higher average feed rates. Using an advection-diffusion-segregation equation and characterizing transient changes in deposition and erosion after a feed rate change, we model stratification for varying feed rates and periods. Feed…
Granular segregation is an important mechanism for industrial processes aiming at mixing grains. Additionally, it plays a pivotal role in determining the kinematics of geophysical flows. Because of segregation, the grainsize distribution varies in space and time. Additional complications arise from the presence of comminution, where new particles are created, enhancing segregation. This has a feedback on the comminution process, as particles change their local neighbourhood. Simultaneously, particles are generally undergoing remixing, further complicating the segregation and comminution proces…
Discrete particle simulation methods have been used to study axial segregation in a horizontal rotating cylinder that is partially filled with a mixture of two different kinds of granular particles. Under suitable conditions segregation was found to occur, with the particles separating into a series of bands perpendicular to the axis. In certain cases the band structure exhibited time-dependent behavior, including band formation, merging and motion along the axis, all corresponding to phenomena that arise experimentally. In order to examine how the many parameters specifying the problem affect…
A novel process is described that produces horizontal size segregation in a vertically vibrated layer of granular material. The behavior is a consequence of two distinct phenomena that are unique to excited granular media: vibration which causes the larger particles to rise to the top of the layer, and a vibrating base with a sawtooth surface profile which can produce stratified flows in opposite directions at different heights within the layer. The result of combining these effects is that large and small particles are horizontally driven in opposite directions. The observations reported here…
Discrete particle simulations are used to model segregation in granular mixtures of three different particle species in a horizontal rotating drum. Axial band formation is observed, with medium-size particles tending to be located between alternating bands of big and small particles. Partial radial segregation also appears; it precedes the axial segregation and is characterized by an inner core region richer in small particles. Axial bands are seen to merge during the long simulation runs, leading to a coarsening of the band pattern; the relocation of particles involved in one such merging eve…
Starting from the hydrodynamic equations of binary granular mixtures, we derive an evolution equation for the relative velocity of the intruders, which is shown to be coupled to the inertia of the smaller particles. The onset of Brazil-nut segregation is explained as a competition between the buoyancy and geometric forces: the Archimedean buoyancy force, a buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other-one tensile in nature, due to the size-difference. We show that inelastic dissipation strongly affects…
We measure stability of two-dimensional granular mixtures in a rotating drum and relate grain configurations to stability. For our system, the smaller but smoother grains cluster near the center of the drum, while the larger, rougher grains remain near the outer edge. One consequence of the size segregation is that the smaller grains heavily influence the stability of the heap. We find that the maximum angle of stability is a non-linear function of composition, changing particularly rapidly when small grains are first added to a homogeneous pile of large grains. We conclude that the grain conf…
We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. An order parameter for the segregated structures is defined and the effect of the variation of the combined filling fraction, $C$, of the mixture on the observed pattern formation is systematically studied. The surprising result is that there is a critical event associated with the onset of the pattern, at $C=0.647\pm0.049$, which has the characteristics of a second order phase transition, including critical slowing down.
The phenomena of radial and axial segregation in a horizontal rotating cylinder containing a mixture of granular particles of two different species have been modeled using discrete particle simulation. Space-time plots and detailed imagery provide a comprehensive description of what occurs in the system. As is the case experimentally, the nature of the segregation depends on the parameters defining the problem; the radial component of the segregation may be transient or long-lasting, and the axial component may or may not develop. Simulations displaying the different kinds of behavior are desc…
We investigate axial segregation of binary mixtures in a laterally shaken horizontal channel formed by ratchet-like sidewalls that appear as concatenated trapeziums when not offset axially. Grain mixtures shaken in such a channel are observed to segregate in two stages: they first separate rapidly into two vertically arranged layers and, then, these layers move axially in opposite directions, segregating the two species. Here, we conduct experiments to study the influence on the segregation process of various parameters: the size ratio of grains, the shaking frequency and the channel's geometr…
We report experimental studies of the effect of interstitial gas on mass-density-segregation in a vertically-vibrated mixture of equal-sized bronze and glass spheres. Sufficiently strong vibration in the presence of interstitial gas induces vertical segregation into sharply separated bronze and glass layers. We find that the segregated steady state (i.e., bronze or glass layer on top) is a sensitive function of gas pressure and viscosity, as well as vibration frequency and amplitude. In particular, we identify distinct regimes of behavior that characterize the change from bronze-on-top to glas…
When granular mixtures of different sizes are fluidized, each species spontaneously separates and condenses to form patterns. Although granular segregation has been extensively studied, the inability to directly observe the time evolution of the internal structure hinders the understanding of the mechanism of segregation dynamics driven by surface flow. In this study, we report rich band dynamics, including a self-replicating band, in a horizontally shaken granular mixture in a quasi-two-dimensional container where the granules formed steady surface waves. Direct observation of surface flow an…
This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains diff…
We report new patterns, consisting of coexistence of sub-harmonic/harmonic and asynchronous states [for example, a granular gas co-existing with (i) bouncing bed, (ii) undulatory subharmonic waves and (iii) Leidenfrost-like state], in experiments on vertically vibrated binary granular mixtures in a Heleshaw-type 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 rep…
Segregation and mixing of granular mixtures during heap formation have important consequences in industry and agriculture. This research investigates three different final particle configurations of bi-disperse granular mixtures -- stratified, segregated and mixed -- during filling of quasi-two dimensional silos. We consider a larger number and relatively wider range of control parameters than previous studies, including particle size ratio, flow rate, system size and heap rise velocity. The boundary between stratified and unstratified states is primarily controlled by the two-dimensional flow…
Processes of mixing and segregation in a packed bed of granular material stirred by a periodically moving rectangular bar are simulated by the discrete element method (DEM). Influence of mechanical properties of the particle material (dynamic friction coefficient, density, elastic modulus) on the segregation intensity is researched. Dynamic friction coefficient was found to have the most noticeable influence to the segregation intensity.
The intruder segregation dependence on size and density is investigated in the framework of a hydrodynamic theoretical model for vibrated granular media. We propose a segregation mechanism based on the difference of densities between different regions of the granular system, which give origin to a buoyant force that acts on the intruder. From the analytic solution of the segregation velocity we can analyze the transition from the upward to downward intruder's movement.
We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. The setup allows to control the humidity level from 5 % to 100 %RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approximately 2000 polymer spheres become highly charged at low humidity levels (<30 %RH), but acquire almost no charge for humidity levels above 80 %RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latte…
We study the effect of fluids on the angle of repose and the segregation of granular matter poured into a silo. The experiments are conducted in two regimes where: (i) the volume fraction of the fluid is small and it forms liquid bridges between particles, and (ii) the particles are completely immersed in the fluid. The data is obtained by imaging the pile formed inside a quasi-two dimensional silo through the transparent glass side walls. In the first series of experiments, the angle of repose is observed to increase sharply with the volume fraction of the fluid and then saturates at a value …
While granular segregation in partially filled containers has been studied extensively, granular dynamics in densely filled spheres is not fully understood. Here, surface band segregation and granular convection are reported in a rotating sphere of highly compacted glass beads. Distinct from Rayleigh-Benard convection, granular convection has a butterfly-shaped structure with vortexes of alternating layers of small/large beads, which is stable and independent of the sphere size. Two concentric interfaces at the zero tangential/norm flux are discovered, which divide the sphere into three layers…
