Stratification, segregation, and mixing of granular materials in quasi-two-dimensional bounded heaps

Effect of Particle Shape on the Flow of an Hourglass

The flow rate of a granulate out of a cylindrical container is studied as a function of particle shape for flat and elongated ellipsoids experimentally and numerically. We find a nonmonotonic dependence of the flow rate on the grain aspect ratio a/b. Starting from spheres the flow rate grows and has two maxima around the aspect ratios of a/b≈0.6 (lentil-like ellipsoids) and a/b≈1.5 (ricelike ellipsoids) reaching a flow rate increase of about 15% for lentils compared to spheres. For even more anisometric shapes (a/b=0.25 and a/b=4) the flow rate drops. Our results reveal two contributing factors to the nonmonotonic nature of the flow rate: both the packing fraction and the particle velocity through the orifice are nonmonotonic functions of the grain shape. Thus, particles with slightly nonspherical shapes not only form a better packing in the silo but also move faster through the orifice than spheres. We also show that the resistance of the granulate against shearing increases with aspect ratio for both elongated and flat particles; thus change in the effective friction of the granulate due to changing particle shape does not coincide with the trend in the flow rate.

Numerical measurement of flow fluctuations to quantify cohesion in granular materials

The flow of cohesive granular materials in a two-dimensional rotating drum is investigated using discrete element method simulations. Contacts between particles are modeled based on the widely used model of the spring-dashpot and Coulomb's friction law. A simplified model of intermediate range attraction between grains (i.e., cohesion) has been used in order to reproduce the flow of electrostatic or wet granular materials. Granular flow is generated by means of a rotating drum and the effect of the rotation speed, the friction between the grains, and the cohesion are studied. Significantly different flow behaviors are observed when cohesion is added. Plug flow appears in the rotating drum for a wide range of rotation speeds when cohesion becomes sufficiently strong. We propose a measurement of surface flow fluctuations to quantify the strength of cohesion, inspired by the previous observation of plug flow. Then, we make use of the results to include the effect of cohesion into a theoretical flow model. A good agreement is obtained between theory and numerical measurements of the granular bed's dynamic angle of repose, which allows us to propose a method for estimating the microscopic cohesion between grains based on the measurement of surface fluctuations.

A brief review of (multi-scale) modelling approaches to segregation

Segregation in dense granular flows is a large problem in many areas of industry and the natural environment. In the last few years an advection-diffusion style framework has been shown to capture segregation in many geometries. Here, we review the different ways such a framework has been obtained by different authors, compare the forms and make recommendations for the best form to use. Finally, we briefly outline some of the remaining open-questions.

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.

Pattern formation in a fully three-dimensional segregating granular flow

Segregation patterns of size-bidisperse particle mixtures in a fully three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using both experiments and a continuum model. Pattern formation results from the interaction of size segregation with chaotic regions and nonmixing islands of the flow. Specifically, large particles in the flowing surface layer are preferentially deposited in nonmixing islands despite the effects of collisional diffusion and chaotic transport. The protocol-dependent structure of the unstable manifolds of the flow surrounding the nonmixing islands provides further insight into why certain segregation patterns are more robust than others.

Modeling Segregation in Granular Flows

Accurate continuum models of flow and segregation of dense granular flows are now possible. This is the result of extensive comparisons, over the last several years, of computer simulations of increasing accuracy and scale, experiments, and continuum models, in a variety of flows and for a variety of mixtures. Computer simulations-discrete element methods (DEM)-yield remarkably detailed views of granular flow and segregation. Conti-nuum models, however, offer the best possibility for parametric studies of outcomes in what could be a prohibitively large space resulting from the competition between three distinct driving mechanisms: advection, diffusion, and segregation. We present a continuum transport equation-based framework, informed by phenomenological constitutive equations, that accurately predicts segregation in many settings, both industrial and natural. Three-way comparisons among experiments, DEM, and theory are offered wherever possible to validate the approach. In addition to the flows and mixtures described here, many straightforward extensions of the framework appear possible.

Diffusion of size bidisperse spheres in dense granular shear flow

Diffusion is an important particle behavior in granular flow. Although granular diffusion has been studied for decades, the diffusion of size bidisperse particles has not been well understood. In this paper, discrete element method simulations with the Lees-Edwards boundary condition are performed to quantify the relation between the diffusion coefficient (D) and flow parameters for size bidisperse spheres in dense granular flow. The influences of the shear rate (γ[over ̇]), the solids fraction (f), and the diameter ratio (D_{LS}) of particles on diffusion are studied. The effects of the friction coefficient (μ) and the restitution coefficient (e) are also investigated. The results indicate that while small particles diffuse faster than large particles in a binary system the volume weighted average diffusion coefficient is proportional to the shear rate and the square of the volume weighted average particle diameter, d^{2}, and it is inversely proportional to the solids fraction. The quantified relation is given as D=k_{d}γ[over ̇]d^{2}, where k_{d}=0.0186/f, and this relation is not sensitive to the diameter ratio for D_{LS}≤3. The diffusion coefficient is not sensitive to the friction coefficient except for the extreme condition where μ<0.1, and it is also not sensitive to the restitution coefficient between 0.3 and 0.9.

Continuum modelling of segregating tridisperse granular chute flow

Segregation and mixing of size multidisperse granular materials remain challenging problems in many industrial applications. In this paper, we apply a continuum-based model that captures the effects of segregation, diffusion and advection for size tridisperse granular flow in quasi-two-dimensional chute flow. The model uses the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The predictions from the model are consistent with experimentally validated discrete element method (DEM) simulations over a wide range of flow conditions and particle sizes. The degree of segregation depends on the Péclet number, Pe, defined as the ratio of the segregation rate to the diffusion rate, the relative segregation strength κ_ij between particle species i and j, and a characteristic length L, which is determined by the strength of segregation between smallest and largest particles. A parametric study of particle size, κ_ij , Pe and L demonstrates how particle segregation patterns depend on the interplay of advection, segregation and diffusion. Finally, the segregation pattern is also affected by the velocity profile and the degree of basal slip at the chute surface. The model is applicable to different flow geometries, and should be easily adapted to segregation driven by other particle properties such as density and shape.

Transient response in granular quasi-two-dimensional bounded heap flow

We study the transition between steady flows of noncohesive granular materials in quasi-two-dimensional bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing particles that propagates downstream over the rising free surface with a wedge front velocity inversely proportional to the square root of time. An additional longer duration transient process continues after the wedge front reaches the downstream wall. The entire transition is well modeled as a moving boundary problem with a diffusionlike equation derived from local mass balance and a local relation between the flux and the surface slope.

Micromechanical Origin of Particle Size Segregation

We computationally study the micromechanics of shear-induced size segregation and propose distinct migration mechanisms for individual large and small particles. While small particles percolate through voids without enduring contacts, large particles climb under shear through their crowded neighborhoods with anisotropic contact network. Particle rotation associated with shear is necessary for the upward migration of large particles. Segregation of large particles can be suppressed with inadequate friction, or with no rotation; increasing interparticle friction promotes the migration of large particles, but has little effect on the percolation of small particles.

Binary mixtures of disks and elongated particles: Texture and mechanical properties

We analyze the shear strength and microstructure of binary granular mixtures consisting of disks and elongated particles by varying systematically both the mixture ratio and degree of homogeneity (from homogeneous to fully segregated). The contact dynamics method is used for numerical simulations with rigid particles interacting by frictional contacts. A counterintuitive finding of this work is that the shear strength, packing fraction, and, at the microscopic scale, the fabric, force, and friction anisotropies of the contact network are all nearly independent of the degree of homogeneity. In other words, homogeneous mixtures have the same strength properties as segregated packings of the two particle shapes. In contrast, the shear strength increases with the proportion of elongated particles correlatively with the increase of the corresponding force and fabric anisotropies. By a detailed analysis of the contact network topology, we show that various contact types contribute differently to force transmission and friction mobilization.

Modelling density segregation in flowing bidisperse granular materials

Preventing segregation in flowing granular mixtures is an ongoing challenge for industrial processes that involve the handling of bulk solids. A recent continuum-based modelling approach accurately predicts spatial concentration fields in a variety of flow geometries for mixtures varying in particle size. This approach captures the interplay between advection, diffusion and segregation using kinematic information obtained from experiments and/or discrete element method (DEM) simulations combined with an empirically determined relation for the segregation velocity. Here, we extend the model to include density-driven segregation, thereby validating the approach for the two important cases of practical interest. DEM simulations of density bidisperse flows of mono-sized particles in a quasi-two-dimensional-bounded heap were performed to determine the dependence of the density-driven segregation velocity on local shear rate and particle concentration. The model yields theoretical predictions of segregation patterns that quantitatively match the DEM simulations over a range of density ratios and flow rates. Matching experiments reproduce the segregation patterns and quantitative segregation profiles obtained in both the simulations and the model, thereby demonstrating that the modelling approach captures the essential physics of density-driven segregation in granular heap flow.

Shear-Rate-Independent Diffusion in Granular Flows

We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.

Symmetrically periodic segregation in a vertically vibrated binary granular bed

Periodic segregation behaviors in fine mixtures of copper and alumina particles, including both percolation and eruption stages, are experimentally investigated by varying the ambient air pressure and vibrational acceleration. For the cases with moderate air pressure, the heaping profile of the granular bed keeps symmetrical in the whole periodic segregation. The symmetrical shape of the upper surface of the granular bed in the eruption stage, which resembles a miniature volcanic eruption, could be described by the Mogi model that illuminates the genuine volcanic eruption in the geography. When the air pressure increases, an asymmetrical heaping profile is observed in the eruption stage of periodic segregation. With using the image processing technique, we estimate a relative height difference between the copper and the alumina particles as the order parameter to quantitatively characterize the evolution of periodic segregation. Both eruption and percolation time, extracted from the order parameter, are plotted as a function of the vibration strength. Finally, we briefly discuss the air effect on the granular segregation behaviors.

Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps

Quasi-two-dimensional bounded heap flow is a useful model for many granular flows in industry and nature. It belongs to a family of free surface flows—inclined chute flow, rotating tumbler flow and unbounded heap flow—but differs from the others in that uniform deposition of particles onto the static bed results in the uniform rise of the heap. The kinematics, however, are only partially understood. We performed discrete element method simulations to study granular flows in quasi-two-dimensional bounded heaps. The experimentally validated computational results show a universal functional form for the streamwise velocity profile for both monodisperse and bidisperse systems when velocities and coordinates are scaled by the local surface velocity and the local flowing layer thickness. This holds true regardless of streamwise location, feed rate, particle size distribution and, most surprisingly, the local particle concentration for bidisperse flows. The local surface velocity decreases linearly in the streamwise direction, while the flowing layer thickness remains nearly constant; both quantities depending only on local flow rate and local mean particle diameter. Additionally, the velocity profile normal to the overall flow, which is important in understanding segregation, can be predicted analytically from the streamwise velocity and matches the simulation results.