Isolating segregation mechanisms in a split-bottom cell

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).

Size segregation of irregular granular materials captured by time-resolved 3D imaging

When opening a box of mixed nuts, a common experience is to find the largest nuts at the top. This well-known effect is the result of size-segregation where differently sized ‘particles’ sort themselves into distinct layers when shaken, vibrated or sheared. Colloquially this is known as the ‘Brazil-nut effect’. While there have been many studies into the phenomena, difficulties observing granular materials mean that we still know relatively little about the process by which irregular larger particles (the Brazil nuts) reach the top. Here, for the first time, we capture the complex dynamics of Brazil nut motion within a sheared nut mixture through time-lapse X-ray Computed Tomography (CT). We have found that the Brazil nuts do not start to rise until they have first rotated sufficiently towards the vertical axis and then ultimately return to a flat orientation when they reach the surface. We also consider why certain Brazil nuts do not rise through the pack. This study highlights the important role of particle shape and orientation in segregation. Further, this ability to track the motion in 3D will pave the way for new experimental studies of segregating mixtures and will open the door to even more realistic simulations and powerful predictive models. Understanding the effect of size and shape on segregation has implications far beyond food products including various anti-mixing behaviors critical to many industries such as pharmaceuticals and mining.

Exploring shear-induced segregation in controlled-velocity granular flows

Particle segregation in geophysical and industrial granular flows is typically driven by gravity and shear. While gravity-induced segregation is relatively well understood, shear-induced segregation is not. In particular, what controls segregation in the absence of gravity and the interplay between shearand gravity-driven segregation remain unclear. Here, we explore the shear-induced segregation force on an intruder particle in controlled-velocity granular flows where the shear profile is systematically varied. The shear-induced segregation force is found to be proportional to the shear rate gradient, which effectively pushes the large intruder from lower to higher shear rate regions. A scaling law is developed for the segregation force that is accurate over a wide range of overburden pressures and shear rates, and hence inertial numbers.

Nonlocal Effects in Inhomogeneous Flows of Soft Athermal Disks

We numerically investigate nonlocal effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave-number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with nonlocal constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.

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.

Effect of pressure on segregation in granular shear flows

The effect of confining pressure (overburden) on segregation of granular material is studied in discrete element method (DEM) simulations of horizontal planar shear flow. To mitigate changes to the shear rate due to the changing overburden, a linear with depth variation in the streamwise velocity component is imposed using a simple feedback scheme. Under these conditions, both the rate of segregation and the ultimate degree of segregation in size bidisperse and density bidisperse granular flows decrease with increasing overburden pressure and scale with the overburden pressure normalized by the lithostatic pressure of the particle bed. At overburdens greater than approximately 20 times the lithostatic pressure at the bottom of the bed, the density segregation rate is zero while the size segregation rate is small but nonzero, suggesting that different physical mechanisms drive the two types of segregation. The segregation rate scales close to linearly with the inertial number for both size bidisperse and density bidisperse mixtures under various flow conditions, leading to a proposed pressure dependence term for existing segregation velocity correlations. Surprisingly, particle stiffness has only a minor effect on segregation, although it significantly affects the packing density.

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.

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.

Nonadditivity of fluctuation-induced forces in fluidized granular media

We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.

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.

Shear-driven segregation of dense granular mixtures in a split-bottom cell

Shear-driven segregation of dense granular mixtures has been associated with a number of interesting pattern formation problems. We use experimental and computational split-bottom cells to isolate segregation effects associated with shear gradients from those associated with gravity. We find the effect of shear gradients much less dramatic than initial observations of segregation suggest. While a segregation pattern emerges in a circular split-bottom cell that appears coincident with the shear gradient, we find the pattern is orthogonal to the active segregation flux. We measure a toroidal convection roll that, in conjunction with gravity-driven segregation, is likely responsible for the dramatic horizontal segregation pattern. On the other hand, computational results from a parallel split-bottom cell indicate a subtle segregation flux associated with the shear gradient. The nature of the driving mechanism is unknown. A current predictive form of kinetic theory based on binary collisions dominating the particle dynamics predicts segregation in the opposite direction from observed trends. This indicates the direction of shear-driven segregation depends on the nature of the flow itself, collisional or frictional.

Shear zone refraction and deflection in layered granular materials

Refraction and deflection of shear zones in layered granular materials were studied experimentally and numerically. We show that (i) according to a recent theoretical prediction [T. Unger, Phys. Rev. Lett. 98, 018301 (2007)] shear zones refract in layered systems in analogy with light refraction, (ii) zone refraction obeys Snell's law known from geometric optics, and (iii) under natural pressure conditions (i.e., in the presence of gravity) the zone can also be deflected by the interface, so that the deformation of the high friction material is avoided.

Segregation pattern competition in a thin rotating drum

Results are presented of an experimental investigation into patterned size segregation of binary granular mixtures in a thin rotating drum that is half full. It is observed that streaks of small particles are formed within regions of large ones where the integer number of streaks is fixed over a range of rotation rate of the drum. Different patterns form in adjacent parameter ranges and the dynamics associated with the exchange between neighboring states is analyzed using angular spatiotemporal diagrams. These help to reveal properties of the merging mechanism for streaks of small particles. We report experimental evidence that the merging of streaks is mediated by the movement of a surplus material in a direction opposite to that of the rotation of the drum. The excess material is distributed throughout the pattern and the extra streak eventually disappears.