Dynamics and Rheology of Hopper Flow: Two and Three Dimensions, Effects of Particle Shape and Cohesion

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Author Last Name: 
Robert P. Behringer
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Research Area: 
Powder Flow
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United States


Over the past several years, IFPR-supported work at Duke has focused on understanding jamming and flow properties in a quasi-2D hopper. During that time, we first carried out extensive measurements to characterize the basic physics of hopper flow, including measurements of jamming probabilities, flow rates, velocity fields, and force fields for circular polydisperse particles. We showed that the flow rates are well described by the Beverloo equation. Using the idea of a free-fall region near the outlet that implies uncorrelated motion near the outlet, we developed a probabalistic model that describes the observed jamming statistics as a Poisson process. In the past year, we have implemented a two-camera approach that allows us to simultaneously image the particles with and with and without polarizers. Data with polarizers yields the particle-scale force. Data without polarizers allows us to track the kinematic properties of the particles. We have also carried out extensive studies of the flow and jamming properties of elliptical particles in our 2D hoppers. These studies show surprising scaling that also gives a broader insight into the jamming of hoppers. In particular, the semi-major axis of the ellipse appears to set the length scale associated with flow and jamming. Yet, the particle orientation near the outlet is contrary to this expectation. An ongoing aspect of the present work is to provide an understanding of jamming in hopper flow in light of the shear jamming process. The discovery of shear jamming was made during the course of work that is not supported by IFPRI. This work involves an understanding of jamming in a different sense, namely as a shear-induced transition between states that are fluid-like and states that are solid-like. This work has appeared in Bi et al., Nature (2011) and Zhang et al., Granular Matter (2010). As it turns out, the Bi et al./Zhang et al. work now seems of particular relevance to jamming in hoppers, and hence, to the IFPRI project. The important connection comes through the dominance of shear in hopper flows. I discuss this further below. The Ph.D. student supported by this project, Junyao Tang, successfully defended his Ph.D. dissertation on November 17, 2012. An additional project involves the IFPRI-NSF Collaboratory, which at this stage mostly involves the writing of papers. I will also briefly discuss experiments in 3D where we can correlate the grain scale response and the macroscopic response to strain. This latter work is primarily supported by other means, but it is of interest to the present studies.