Coarsening of axial segregation patterns of slurries in a horizontally rotating drum

Effects of size polydispersity on segregation of spherical particles in rotating drum

To get insight into the segregation process of a polydisperse granular materials flow, we numerically investigated the migration process of particles in a rotating drum operating in the rolling regime by means of the discrete element method. Particle migration is analyzed through the variation of the proportion of particles in different zones where the flow property is characterized. The proportion of particles in different zones of the drum shows to increase in the center of the flow radially and axially where a higher concentration of small particles is observed, while its decreases in other zones with a higher concentration of larger particles. Interestingly, we find that the migration process of particles leads to radial and axial segregation which is caused by a combination between the exerted fluctuation forces on particles and its surrounding pressure gradient.

Self-Induced Rayleigh-Taylor Instability in Segregating Dry Granular Flows

Dry-granular material flowing on rough inclines can experience a self-induced Rayleigh-Taylor (RT) instability followed by the spontaneous emergence of convection cells. For this to happen, particles are different in size and density; the larger particles are denser but still segregate toward the surface. When the flow is initially made of two layers of particles (dense particles above), a RT instability develops during the flow. When the flow is initially made of one homogeneous layer mixture, the granular segregation leads to the formation of an unstable layer of large, dense particles at the surface, that subsequently destabilizes in a RT plume pattern. The unstable density gradient has been only induced by the motion of the granular matter. This self-induced Rayleigh-Taylor instability and the two-layer RT instability are studied using two different methods: experiments and simulations. At last, contrary to the usual fluid behavior where the RT instability relaxes into two superimposed stable layers of fluid, the granular flow evolves to a pattern of alternated bands corresponding to recirculation cells analogous to Rayleigh-Bénard convection cells where segregation sustains the convective motion.

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.

Magnetic resonance imaging of granular materials

Magnetic Resonance Imaging (MRI) has become one of the most important tools to screen humans in medicine; virtually every modern hospital is equipped with a Nuclear Magnetic Resonance (NMR) tomograph. The potential of NMR in 3D imaging tasks is by far greater, but there is only "a handful" of MRI studies of particulate matter. The method is expensive, time-consuming, and requires a deep understanding of pulse sequences, signal acquisition, and processing. We give a short introduction into the physical principles of this imaging technique, describe its advantages and limitations for the screening of granular matter, and present a number of examples of different application purposes, from the exploration of granular packing, via the detection of flow and particle diffusion, to real dynamic measurements. Probably, X-ray computed tomography is preferable in most applications, but fast imaging of single slices with modern MRI techniques is unmatched, and the additional opportunity to retrieve spatially resolved flow and diffusion profiles without particle tracking is a unique feature.

Segregation of granular mixtures in a spherical tumbler

Segregation of polydisperse granular materials in rotating containers is a ubiquitous but still not satisfactorily understood phenomenon. This study describes axial segregation of bidisperse granular mixtures of glass beads in a spherical container, rotating about its horizontal axis. Depending on the filling fraction of the mixer and on the composition of the mixture, qualitatively different spontaneously formed patterns are observed. For technical applications, the well-localized segregated bands allow a convenient separation of individual components of the mixtures. It is particularly surprising that the initial compositions of the granular mixtures have a fundamental influence on the location of the segregated bands. This evidences a collective pattern forming mechanism. The spontaneous formation of these bands cannot simply be traced back to individual particle dynamics. Existing models for segregation in spherical mixers are critically examined and extensions are suggested.

Molecular dynamics simulation: a tool for exploration and discovery using simple models

Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome is not always a foregone conclusion. The present survey focuses on several simple model systems that exhibit surprisingly rich emergent behavior, all studied by molecular dynamics (MD) simulation.The examples are taken from the disparate fields of fluid dynamics, granular matter and supramolecular self-assembly. In studies of fluids modeled at the detailed microscopic level using discrete particles, the simulations demonstrate that complex hydrodynamic phenomena in rotating and convecting fluids—the Taylor–Couette and Rayleigh–Bénard instabilities—cannot only be observed within the limited length and time scales accessible to MD, but even allow quantitative agreement to be achieved. Simulation of highly counter-intuitive segregation phenomena in granular mixtures, again using MD methods, but now augmented by forces producing damping and friction, leads to results that resemble experimentally observed axial and radial segregation in the case of a rotating cylinder and to a novel form of horizontal segregation in a vertically vibrated layer. Finally, when modeling self-assembly processes analogous to the formation of the polyhedral shells that package spherical viruses, simulation of suitably shaped particles reveals the ability to produce complete, error-free assembly and leads to the important general observation that reversible growth steps contribute to the high yield. While there are limitations to the MD approach, both computational and conceptual, the results offer a tantalizing hint of the kinds of phenomena that can be explored and what might be discovered when sufficient resources are brought to bear on a problem.

Structural characterization of submerged granular packings

We consider the impact of the effective gravitational acceleration on microstructural properties of granular packings through experimental studies of spherical granular materials saturated within fluids of varying density. We characterize the local organization of spheres in terms of contact connectivity, distribution of the Delaunay free volumes, and the shape factor (parameter of nonsphericity) of the Voronoï polygons. The shape factor gives a clear physical picture of the competition between less and more ordered domains of particles in experimentally obtained packings. As the effective gravity increases, the probability distribution of the shape factor becomes narrower and more localized around the lowest values of the shape factor corresponding to regular hexagon. It is found that curves of the pore distributions are asymmetric with a long tail on the right-hand side, which progressively reduces while the effective gravity gets stronger for lower densities of interstitial fluid. We show that the distribution of local areas (Voronoï cells) broadens with decreasing value of the effective gravity due to the formation of lose structures such as large pores and chainlike structures (arches or bridges). Our results should be particularly helpful in testing the newly developed simulation techniques involving liquid-related forces associated with immersed granular particles.

Effects of grain shape on packing and dilatancy of sheared granular materials

A granular material exposed to shear shows a variety of unique phenomena: Reynolds dilatancy, positional order and orientational order effects may compete in the shear zone. We study granular packing consisting of macroscopic prolate, oblate and spherical grains and compare their behaviour. X-ray tomography is used to determine the particle positions and orientations in a cylindrical split bottom shear cell. Packing densities and the arrangements of individual particles in the shear zone are evaluated. For anisometric particles, we observe the competition of two opposite effects. On the one hand, the sheared granules are dilated, on the other hand the particles reorient and align with respect to the streamlines. Even though aligned cylinders in principle may achieve higher packing densities, this alignment compensates for the effect of dilatancy only partially. The complex rearrangements lead to a depression of the surface above the well oriented region while neighbouring parts still show the effect of dilation in the form of heaps. For grains with isotropic shapes, the surface remains rather flat. Perfect monodisperse spheres crystallize in the shear zone, whereby positional order partially overcompensates dilatancy effects. However, even slight deviations from the ideal monodisperse sphere shape inhibit crystallization.

Transitions between multiple attractors in a granular experiment

We report on a granular experiment that produces multiple quasiperiodic pattern solutions in a rotating flat container filled with a bidisperse mixture of grains. The observed dynamics show a pronounced spatiotemporally periodic drift of segregated patterns. In the course of long experiment durations, the system switches between different states that appear to be stable oscillatory solutions over many periods. In the long-term limit, the system does not tend toward a stationary state. The results complement and extend previous observations in cylindrical geometries, and represent a challenge for modeling and theoretical description.

Segregation in horizontal rotating cylinders using magnetic resonance imaging

The dynamics of granular materials, particularly radial and axial segregation in horizontal rotating cylinders containing large and small particles, is studied by Magnetic Resonance Imaging (MRI). Stationary three-dimensional (3D) images and real-time two-dimensional (2D) structural images showing radial segregation, band formation, and band merging are reported. Quantitative local particle concentrations are measured in a noninvasive manner from the different magnetic resonance responses of the seeds throughout segregation. Data are acquired with sufficiently high temporal (300 ms for 2D images) and spatial resolutions (0.94 mm cubic voxels), to give insights into the underlying mechanisms of both radial and axial segregation. In particular, the increasing rate of the local particle concentration during radial segregation is quantified. Particle migration is observed in the bulk material of the 75% and 82% full cylinders during both radial and axial segregation, showing that this region beneath the avalanche layer does not behave as a solid body. We also provide direct experimental evidence to support recent numerical simulations of band merging.

Diffusive and subdiffusive axial transport of granular material in rotating mixers

The segregation of granular mixtures in rotating cylinders into axial bands is not well understood so far. Abnormal diffusion of the grains has been proposed to play an important role in that process. We measure axial diffusion in binary mixtures, completely embedded in water, by means of nuclear magnetic imaging (magnetic resonance imaging). It is found that the small size particles in a radially segregated structure undergo normal (Fickian) axial diffusion, whereas an initial pulse of the large species shows subdiffusive behavior. An interpretation within a model for the particle dynamics is given. The diffusion of small particles occurs in the axial kernel, whereas particles of the large species migrate on the free surface of the granular bed.

Axial and radial segregation of granular mixtures in a rotating spherical container

We report the formation of axial segregation patterns of bidisperse granular mixtures of glass beads in a spherical container which is rotated about a central axis. When the rotation axis is horizontal, three distinct segregation bands are formed for a broad range of geometrical and dynamical parameters. We find two distinct regimes: at low fill levels the small size beads of the mixture are collected at the poles and the large size beads in a central band. At high fill levels the pole regions are occupied by large beads, while the small beads form the central band. The critical fill level for this structural transition decreases with increasing container size. For a container with 37 mm inner diameter, containing a mixture of 0.5 and 1.5 mm beads, the transition occurs between 40% and 50% fill level. When the rotation axis is tilted, the band positions are shifted and two-band structures are formed with the smaller particles at the lower pole. In our experiments the granulate is submersed in water; this allows NMR imaging of the complete three-dimensional band structures. We compare the observed segregation structures to those in cylindrical mixers and propose a model for the qualitative explanation of the pattern formation process.

Axial band scaling for bidisperse mixtures in granular tumblers

Axial banding in rotating tumblers has been experimentally observed, but the dependence of band formation on the relative concentration of the bidisperse particles has not been thoroughly examined. We consider axial band formation and coarsening for dry and liquid granular systems of bidisperse mixtures of glass beads where the small particle volume fraction ranges from 10% to 90% in half-filled tumblers for several rotation rates. Single bands form for small particle volume fractions as low as 10% and as high as 90%, usually near the end walls. Band formation along the entire length of the tumbler is less likely at very low or very high volume fractions. After many rotations the segregation pattern coarsens, and for small particle volume fractions of 50% and greater, the coarsening is logarithmic. For very low or very high small particle volume fractions, the rate of coarsening is either not logarithmic or coarsening does not occur within the duration of the experiment (600 rotations). When bands form, the width of the band for either the small or large particles scales with the tumbler diameter.

Bundle dynamics of interacting polar rods

We use a probabilistic model of microtubule interaction via molecular motors to study microtubule bundle interaction. Our model indicates that initially disordered systems of interacting polar rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results show a long term attraction and coalescing of bundles indicating a clear coarsening in the system; Microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale.

Simulated three-component granular segregation in a rotating drum

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 event is examined. Overall, the behavior is similar to experiment and represents a generalization of what occurs in the simpler two-component mixture.

Influences of the interstitial liquid on segregation patterns of granular slurries in a rotating drum

Granular mixtures immersed in a liquid (slurries) show segregation dynamics which are quantitatively and qualitatively different from those of dry systems. The principal mechanisms of the segregation dynamics in slurries, as well as the relevant material parameters that must be taken into account in a dynamic description are not sufficiently understood so far. We investigate experimentally the influence of the viscosity of the interstitial liquid on the coarsening of axial segregation patterns in a horizontally rotating mixer. It is found that not only the characteristic time scales but also fundamental structural features of these patterns are influenced by the viscous properties of the liquid component.

Radial and axial segregation of granular matter in a rotating cylinder: a simulation study

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 described and the particle dynamics associated with the axially segregated state examined. The importance of an appropriate choice of interaction for representing the effective friction force is demonstrated.