Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session H15: Granular Flows: Mixing, Segregation and Separation (5:45pm  6:30pm CST)Interactive On Demand

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H15.00001: Unifying Gravity and Kinematicsinduced Segregation Forces in Dense Granular Flows Lu Jing, Julio M. Ottino, Richard M. Lueptow, Paul B. Umbanhowar Particle size segregation is common in many natural and industrial processes involving flowing granular materials. Complex, and even contradictory, segregation phenomena have been observed depending on boundary conditions and forcing. For example, larger particles rise against gravity and toward low shear regions in free surface flows down inclines, but migrate laterally to high shear regions in a silo. Despite recent progress in modeling granular segregation, a universal description remains elusive. We develop a unified scaling for the segregation force on intruder particles consisting of two parts: a gravityinduced pressure gradient term (buoyancylike but modified by the particle size ratio) and a shear rate gradient term that pushes larger (smaller) intruders toward regions of higher (lower) shear rate. The scaling is obtained by measuring segregation forces on intruder particles in velocitycontrolled flows, and then validated (without refitting) in other flow geometries, including walldriven flows, inclined walldriven flows, vertical silo flows, and free surface flows down inclines. Comparing the segregation force to the intruder weight predicts the segregation direction in various flow configurations. [Preview Abstract] 

H15.00002: Size segregation theory for binary granular mixtures based on forces on a single large particle Anurag Tripathi, Alok Kumar, Mohit Nema, Devang Khakhar The segregation force acting on a few large size intruder particles in a flowing granular medium is measured using DEM simulations without any restriction on the motion of the intruder particle. Accurate measurement of the net upward force causing the segregation of large particles of same density is done by accounting for the drag force on the large size intruder particles. This net upward force, measured for dilute concentrations of the large intruder particles, is corrected for higher concentrations of the large particles. This theoretical formulation yields a segregation flux which is similar to empirical size segregation flux based approaches used in literature. Specifically, we find a cubic dependence on the large particle concentration and a linear dependence on shear rate. The theory also suggests dependency on other flow variables which are not captured in the currently used empirical approaches. The predictions of the concentration and the velocity field using this approach for steady, fully developed chute flow of binary mixtures for a wide range of compositions and inclinations match very well with the DEM simulations for the two different size ratios considered in this study. [Preview Abstract] 

H15.00003: A theory for densitydriven segregation in flowing ternary granular mixtures Vishnu Sahu, Shivani Agrawal, Anurag Triphati We consider the case of ternary granular mixture of spherical particles of same size and different density, in a dense gravitydriven flow over a rough inclined plane. A continuum model for predicting steady state concentration profiles is presented using the segregation forces acting on the particles. The buoyancy force acting on the particle is given by Archimedes principle with an effective volume associated with the particle while the drag force is given by a modified Stoke’s law. The flow and segregation process are intercoupled and require the concentration profiles to be computed using an iterative method. The theoretical predictions from the momentum balance equations along with a mixture rheological model and current density segregation model are compared with DEM simulations. The steady state concentration profiles predicted are in good agreement with the DEM simulations results for a variety of compositions over a range of different inclination angles for different density ratios. [Preview Abstract] 

H15.00004: Attraction and repulsion between two large particles in a granular flow. Nathalie Fraysse, Umberto D'Ortona, Nathalie Thomas The interaction between particles immersed in a fluid has been studied for long. Its rich phenomenology includes for example the draftingkissingtumbling behavior. For nonNewtonian fluids, other complex phenomena occur like oblique settling of two particles or locking at a defined distance. In a granular flow made of small particles (diameter d), a few large particles (diameter D), or intruders, locate near the bottom of the flow for D/d \textgreater 5 (Thomas PRE 2000). Here we present a DEM study of the interaction between two large intruders flowing near the bottom of a granular flow down an incline. Initially, the intruders (D$=$10d) are placed obliquely at a distance 2D in flows of increasing thickness H$=$7d up to 30d. In some simulations, two perpendicular virtual springs are also added between the intruders to measure the interaction forces. For all thicknesses, intruders align with the flow. A transition occurs between thin flows H\textless 8d where intruders attract each other and are almost in contact, an intermediate regime 9d\textless H\textless 16d where they lock on at a specific distance that increases with H, and thick flows H\textgreater 16d where intruders repel each other. This transition also depends on D and slightly on the incline slope. When several intruders flow altogether, they organize into trains. [Preview Abstract] 

H15.00005: Segregation modeling for particles varying in both size and density Yifei Duan, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow Granular materials tend to segregate by particle size and density when sheared. In particle mixtures varying in size or density alone, small particles sink (driven by percolation) and light particles rise (driven by buoyancy). However, when the constituent species vary from each other in both size and density, which particles will rise or sink is difficult to predict. In particular, modeling 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 find that the local segregation velocity is well described by a model that depends linearly on local shear rate and quadratically on species concentration. Concentration fields predicted by including this segregation model in a continuum transport equation match DEM simulation results well for different combinations of particle size and density ratios. Surprisingly, the direction of segregation for a range of mixtures of large, heavy and small, light particles depends on the local species concentration. [Preview Abstract] 

H15.00006: Predicting Granular Segregation of Species with Overlapping Size Distributions Song Gao, Julio Ottino, Paul Umbanhowar, Richard Lueptow Segregation of two sizepolydisperse particle species with overlapping size distributions can occur in practical systems. A continuum approach can be extended to model segregation of two species with overlapping size distributions that matches discrete element method simulation results. Since size dispersity of the two species does not affect the degree of species segregation significantly, the local species concentration can be accurately modeled as a mixture of two sizemonodisperse species using a simpler bidisperse model, even with substantial overlap of the two species distributions. However, for broad size distributions the local average particle size can be influenced by size dispersity in some regions of the flow. The segregation length scale characterizing the tendency for the two species to segregate, which can be measured for mixtures of two polydisperse species, closely follows the value associated with the mean diameters of the two species. While based on quasitwodimensional bounded heap flow, our findings should also directly apply to a wide range of other dense granular flow geometries, including rotating tumblers, conical chutes, wedgeshaped heaps, confined shear, and more complicated geometries such as hoppers. [Preview Abstract] 

H15.00007: Connecting 3D granular segregation patterns to piecewise isometries Thomas Lynn, Mengqi Yu, Julio Ottino, Richard Lueptow, Paul Umbanhowar One of the simplest 3D systems for mixing granular materials is a halffilled spherical tumbler repeatedly rotated about one horizontal axis and then another. Despite its simplicity, complex flow structures appear, including nonmixing islands, chaotic mixing regions, and barriers to transport, each sensitive to the amount of rotation about each axis. For sizedisperse granular material, larger particles segregate to the surface of the thin flowing layer and the tumbler periphery. For certain rotation pairs, large particles either accumulate in and around nonmixing islands due to weak axial drift or remain trapped in isolated mixing (chaotic) regions. The complex dynamics that create barriers to transport are explored using a continuum model and particle simulations. Going further, an approximation of the system in the limit of an infinitely thin flowing layer offers new insight into barriers to transport even in the absence of segregation. By treating the infinitely thin flowing layer system as a sequence of cutandshuffle actions, the tumbler `flow' can be mathematically described as a piecewise isometry (PWI). The PWI dynamics can be split into invariant subsets and nonmixing islands corresponding to chaotic regions and segregation regions in the tumbler, respectively. [Preview Abstract] 

H15.00008: Segregation Modeling in Modulated Granular Heap Flow Richard M. Lueptow, Zhekai Deng, Hongyi Xiao, Julio M. Ottino, Paul B. Umbanhowar Although granular segregation has been investigated extensively for steady flows under various operating conditions and geometries, segregation in unsteady granular flows has not been explored in detail. We focus here on stratification in unsteady sizebidisperse bounded heap flow. Previous experiments have shown that periodically alternating between high and low feed rates of particles falling onto the heap results in regular stratified layers of large and small particles. We model this stratification in a bounded heap using an advectiondiffusion equation with an added segregation term. Simply repeatedly switching the model from a low volume flow rate to a high volume flow rate instantaneously along the entire length of the flowing layer results in stratification patterns similar to those observed in experiments. A flow kinematics model that describes the downstreammoving front of particles after a change in the flow rate provides higher fidelity and displays some of the underlying physics how the stratified pattern forms. [Preview Abstract] 

H15.00009: Predicting nonspherical particle segregation in dense granular flows Ryan P Jones, Julio M Ottino, Paul B Umbanhowar, Richard M Lueptow Segregation, or demixing, of sheared sizedisperse mixtures of noncohesive spherical particles is wellcharacterized. However, most particles in industry and geophysics are nonspherical. Here, using discrete element method simulations of gravitydriven freesurface granular flows, we characterize the segregation of bidisperse mixtures of noncohesive, mmsized particles that vary widely in their size and shape (disks, rods, and spheres). The segregation velocity for nonspherical particles depends on the local shear rate and the species concentration, as is the case for spherical particles. The propensity to segregate, measured in terms of a segregation length scale that characterizes the segregation velocity of the two species, can be predicted based on only the volume ratio between the two particle species, regardless of particle shape. The segregation length scale increases linearly with the log of the volume ratio for volume ratios varying from 0.1 to 10 in the same way as it does for bidisperse mixtures of spherical particles. [Preview Abstract] 

H15.00010: Modeling Granular Flow with Heterogeneous Mixtures Under a Movable Gate. Michael RoeingDonna, Nicholas Pohlman, Jifu Tan The transfer of material using a conveyor system is used in almost every modern manufacturing process. The predictability of this mass transfer is critical to the efficiency of the process and can cause issues when the material flows irregularly, but efficient control of the opening gate for a heterogeneous mixture is not fully understood. We used a discrete element method (DEM) approach to simulate granular flow in a conveyor system to understand the role of complex particle geometries and a dynamic gate on the mass transfer. A uniform material model was validated previously with experiments on local granular velocity profile and mass transfer rate. Next, we modeled the impact of the nonspherical material and the dynamic exit area on the flow profile. Two parameters characterized behavior, the material mass flow rate decreased by nearly 15\textbraceleft $\backslash ${\%}\textbraceright and local orientation of the elongated granular material aligned with the belt. The orientation of the shearing, nonspherical particles can be important when attempting to optimize the local flow profile for temporally consistent mass flow. Spatial and temporal analysis of an adjustable exit is performed to identify its effect on producing consistent flow. [Preview Abstract] 
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