epl draft Orientation, Flow, and Clogging in a Two-Dimensional Hopper: Ellipses vs. Disks

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 [2–6]. Fluctuations and clogging (or jamming) are also important characteristics for hopper flow. Experiments [7–9] 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 [10–15] 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 relates Ṁ to the hopper opening size, D : Ṁ ∝ (D − kdavg), where n is the spatial dimension (e.g. n = 2 or 3 for two or three-dimensional systems). D is reduced by kdavg due to boundary effects, where davg 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 [21–27]. Their results are not consistent due to different assumptions such as particle shapes, frictional properties of particles and etc. A recent study by Liu et al. [28] utilizing both DEM and experiments, suggests a modified Beverloo equation for ellipse flow. They also show observations of flow characteristics based on their simulation results. To our knowledge, experimental investigations of hopper flow of ellipses based on particle-levels dynamics are still lacking. In this paper we experimentally test the applicability p-1 ar X iv :1 51 0. 07 94 0v 2 [ co nd -m at .s of t] 2 9 O ct 2 01 5 J. Tang and R. Behringer Fig. 1: Sketch of the synchronized camera set up. Light emerging from the hopper is split and imaged by two synchronized high-speed cameras, one with and the other without a