Orientation, flow, and clogging in a two-dimensional hopper: Ellipses vs. disks

Abstract

-Two-dimensional (2D) hopper flow of disks has been extensively studied. Here, we investigate hopper flow of ellipses with aspect ratio α = 2, and we contrast that behavior to the flow of disks. We use a quasi-2D hopper containing photoelastic particles to obtain stress/force information. We simultaneously measure the particle motion and stress. We determine several properties, including discharge rates, jamming probabilities, and the number of particles in clogging arches. For both particle types, the size of the opening, D, relative to the size of particles, is an important dimensionless measure. The orientation of the ellipses plays an important role in flow rheology and clogging. The alignment of contacting ellipses enhances the probability of forming stable arches. This study offers insight for applications involving the flow of granular materials consisting of ellipsoidal shapes, and possibly other non-spherical shapes.Hopper flows of granular materials involve dynamical granular states with important industrial applications [1,2]. Time-averaged granular flow theories, often using hopper flow as a test case, have progressed from continuum mechanics models to mesoscopic models [2][3][4][5][6]. Fluctuations and clogging (or jamming) are also important characteristics for hopper flow. Experiments [7][8][9] have examined the the clogging transition of hopper flow for different grain properties and hopper geometries. Most recent results from [8] imply that all hoppers have a nonzero probability to clog. Other studies [10][11][12][13][14][15] have also sought to understand flow and clogging (or jamming) mechanisms from a microscopic viewpoint. However, for simplicity, theories developed from the above studies often tend to assume spherical particles, including disks in two dimensions (2D). The effect of particle shape on hopper flow is usually not their focus. In reality, particle shapes are often not spherical; rice and M&M's are roughly ellipsoids; sand particles have irregular shapes. Thus, it is scientifically and industrially relevant to explore how particle shape affects flow rheology and clogging mechanisms.A simple way to explore particle shape effects is to contrast 2D hopper flows of disks and ellipses for the time-averaged discharge rate,Ṁ , and jamming probability. Discharge rates of hopper flow often follow the wellestablished Beverloo equation [16], which relatesṀ to the hopper opening size, D :Ṁ ∝ (D − kd avg ) (n−1/2) , where n is the spatial dimension (e.g. n = 2 or 3 for two or three-dimensional systems). D is reduced by kd avg due to boundary effects, where d avg characterizes the grain size, and k is an order-one constant [2]. Recent studies [17,18] have provided micromechanical insights into this equation with a coarse-grain technique. An important open question concerns the relevance of this relation for non-spherical particles. Several studies have used DEM simulation methods to understand how the aspect ratio of an ellipse could affect the discharge rate [21][22][23][24][25][26][...

Simulating competitive egress of noncircular pedestrians

“…Note that the shape of the particles has been shown to play an important role in dense granular flows [16][17][18], and in particular in granular flows through bottlenecks [19][20][21]. Thus, it is expected that in competitive pedestrian dynamics, where the "granular" or contact component is important, this parameter is also relevant and its implementation could improve the model performance.…”

Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers

“…[10,11], which happens less frequently for larger holes and is unavoidable for holes smaller than about four to five grains across. Details depend on grain shape (see, e.g., [12][13][14][15]), and similar phenomena arise in other contexts, ranging from transport in electronic [16] and particulate [17,18] systems with spatially distributed pinning sites to grains in channels and pipes [19,20], grains driven by fluid flow [21,22], and even grains with brains: pedestrians [23], traffic [24], and livestock [25]. For noncohesive compact grains, in air or vacuum, there is general agreement that clogging statistics are Poissonian [6,7,13,26,27].…”

Linking bottleneck clogging with flow kinematics in granular materials: The role of silo width

“…The placement of an obstacle above the orifice can prevent clogging if its position is appropriately selected [6]. Other variables that have been shown to affect clogging are orifice geometry [16,17], particle shape [18][19][20], particle polydispersity [21], and gravity [22][23][24]. Nevertheless, we are not aware of any work looking at the influence of the width of the silo, a variable that in most of the existing experiments and simulations remains uncontrolled.…”