Session G20: Granular Flows: Mixing and Separation

Segregating photoelastic particles in free-surface granular flows.

We present results from a novel experimental set-up creating 2D avalanches of photoelastic discs. Two distinct hoppers supply either monodisperse or bidisperse particles at adjustable flow-rates into a 2 meter long, narrow acrylic chute inclined at 20\textdegree . For 20--40 seconds the avalanche maintains a steady-state that accelerates and thins downstream. The chute basal roughness is variable, allowing for different flow profiles. Using a set of polarizers and a high-speed camera, we visualize and quantify the forces due to dynamic interactions between the discs using photoelastic theory. Velocity and density profiles are derived from particle tracking at different distances from the discharge point and are coarse-grained to obtain continuous fields. With the access to both force information and dynamical properties via particle-tracking, we can experimentally validate existing mu(I) and non-local rheologies. As an extension, we probe the effect of granular segregation in bimodal mixtures by using the two separate inflow hoppers. We derive the state of segregation along the avalanche channel and measure the segregation velocities of each species. This provides insight in, and a unique validation of, the fundamental physical processes that drive segregation in avalanching geometries.   

Mixing and non-mixing behavior of three-dimensional granular flows in a spherical tumbler

We consider mixing of granular materials in the simplest three-dimensional (3D) flow geometry possible, that of a half-filled spherical tumbler rotated by less than $90^{\circ}$ alternately about two perpendicular horizontal axes, as a prototype to investigate mixing under the competing influences of both stretching (during flow) and cutting \& shuffling (upon changing the axis of rotation). In experiments, x-ray visualization of a tracer reveals persistent non-mixing regions, which have properties that are surprisingly consistent with predictions of a continuum model simulation and an idealized model based on the mathematics of piecewise isometries in which an object is cut, rearranged, and then reassembled into the same shape. Tracer particles are designed to either stay near the tumbler wall, which maps the properties of the outermost shell of the sphere, or, in contrast, to fully explore the 3D volume of the tumbler under the influence of collisional diffusion. The 3D trajectories indicate that mixing is enhanced when the particle travels across radial shells. Thus, 3D mixing can be predicted by models sampling 2D surfaces over a range of radii.   

The impact of flow rheology on both density and size segregations

Shear induced segregation is a problem of considerable import both industrially and academically. As a granular material is sheared, the bed dilates and heavier (or smaller) particles typically move perpendicular to the mean flow. In the present work, we perform a computational study -- based on the Discrete Element Method -- of the flow in a simple boundary-driven planar shear cell. We show a direct connection between density/size segregation with granular rheology that has the potential to spur a substantial jump in our understanding of both fields and lead to a transformation in the way that particle flow research is conducted.~ Our results exhibit a behavior transition in segregation which mimics how the effective friction coefficient changes with changing flow rheology.~ Moreover, by recasting a segregation model in terms of rheologically-relevant dimensionless groups, we establish a novel expression which is able to collapse results for a wide range of conditions for both density and size segregation.~ Ultimately, these expressions can have a profound impact on both the study of granular flow/ mixing as well as industrial practice.   

Forces on a segregating particle

Size segregation in flowing granular materials is not well understood at the particle level. In this study, we perform a series of 3D Discrete Element Method (DEM) simulations to measure the segregation force on a single spherical test particle tethered to a spring in the vertical direction in a shearing bed of particles with gravity acting perpendicular to the shear. The test particle is the same size or larger than the bed particles. At equilibrium, the downward spring force and test particle weight are offset by the upward buoyancy-like force and a size ratio dependent force. We find that the buoyancy-like force depends on the bed particle density and the Voronoi volume occupied by the test particle. By changing the density of the test particle with the particle size ratio such that the buoyancy force matches the test particle weight, we show that the upward size segregation force is a quadratic function of the particle size ratio. Based on this, we report an expression for the net force on a single particle as the sum of a size ratio dependent force, a buoyancy-like force, and the weight of the particle.   

Activity induced phase transition in mixtures of active and passive agents

Collective behaviors of self-propelling agents are ubiquitous in nature that produces interesting patterns. The objective of this study is to investigate the phase transition in mixtures of active and inert agents suspended in a liquid. A modified version of the Vicsek Model has been used (see Mahapatra et al., Physical Review E (2017), 062610), where the particles are modeled as soft disks with finite mass, confined in a square domain. The particles are required to align their local motion to their immediate neighborhood, similar to the Vicsek model. We identified the transition from disorganized thermal-like motion to an organized vortical motion. We analyzed the nature of the transition by using different order parameters. Furthermore the switching between the phases has been investigated via artificial nucleation of randomly picked active agents spanning the entire domain. Finally the motivation for this phase transition has been explained via average dissipation and the mean square displacement (MSD) of the agents.   

Mixing on a spherical shell by cutting and shuffling with non-orthogonal rotation axes

We examine a dynamical system that models the mixing of granular material in a half-filled spherical tumbler rotated about two horizontal alternating axes by using the machinery of cutting and shuffling through piecewise-isometries (PWI). Previous restrictions on how the domain is cut and shuffled are relaxed to allow non-orthogonal axes of rotation. Mixing is not only dependent on the amount of rotation used to induce mixing, but also on the relative orientation of the rotation axes. Well mixed regions within the PWI, which have a high density of cuts, typically interact with the periodic cutting boundary for both rotation axes. However, there are parameter combinations where the two rotations cut distinctly separate regions. The three-parameter space (a rotation about each axis and the relative orientation of the axes) is rich with detailed mixing features such as fractal boundaries and elliptic-like non-mixing regions.   

Crystallization of sheared hard spheres at 64.5\% volume fraction

A classic experiment by G.D. Scott $(\it {Nature}$ ${\bf 188}$, 908, 1960) showed that pouring balls into a rigid container filled the volume to an upper limit of 64\% of the container volume, which is well below the 74\% volume fraction filled by spheres in a hexagonal close packed (HCP) or face center cubic (FCC) lattice. Subsequent experiments have confirmed a ``random closed packed" (RCP) fraction of about 64\%. However, the physics of the RCP limit has remained a mystery. Our experiment on a cubical box filled with 49400 weakly sheared glass spheres reveals a first order phase transition from a disordered to an ordered state at a volume fraction of 64.5\%. The ordered state consists of crystallites of mixed FCC and HCP symmetry that coexist with the amorphous bulk. The transition is initiated by {\it homogeneous} nucleation: in the shearing process small crystallites with about ten or fewer spheres dissolve, while larger crystallites grow. A movie illustrates the crystallization process.   

Influence of adhesion on random loose packings of binary micro-particle mixtures

Binary adhesive packings of microspheres with certain size ratios are investigated via a 3D discrete-element method specially developed with adhesive contact mechanics. We found a novel phenomenon that the packing fraction of the binary adhesive mixtures decreases monotonically with the increase of the amount of small components. It was further divulged that this behavior results from the competition between a geometrical filling effect and an adhesion effect. The positive geometrical filling effect only depends on the size ratio, while a dimensionless adhesion parameter $Ad$ is employed to characterize the negative adhesion effect, which comes to its maximum at $Ad \approx 10$. Structural properties, including contact network, partial coordination number, radial distribution function and angular distribution function, are analyzed in order to give a better understanding of such adhesive binary packings.   

Dynamics and pattern transition in a two-dimensional vibrofluidized granular bed

Experiments are conducted in a two-dimensional monolayer vibrofluidized bed of glass beads, with an aim to study the dynamics and the transition scenario in different patterned states. At small shaking accelerations ($\Gamma=A\omega^2/g<1$, where $A$ and $\omega= 2\pi f $ are the amplitude and angular frequency of shaking and $g$ is the gravitational acceleration), the particles remain attached to the base of the vibrating container; this is known as the solid bed (SB). With increasing $\Gamma$ (at large enough shaking amplitude $A/d$) and/or with increasing $A/d$ (at large enough $\Gamma$), the sequence of transitions/bifurcations unfolds as follows: SB (“solid bed”) to BB (“bouncing bed”) to LS (“Leidenfrost state”) to “2-roll convection” to “1-roll convection” and finally to a gas-like state. For a given length of the container, the coarsening of multiple convection rolls leading to the genesis of a “single-roll” structure (dubbed the "multiroll transition") and its subsequent transition to a granular gas are two findings of this work. We show that the critical shaking intensity $\Gamma_{BB}^{LS}$ for the $BB \rightarrow LS$ transition has a power-law dependence on the particle loading ($F$) and the shaking amplitude ($A/d$).