Modeling Segregation in Spherical and Non-Spherical Granular Materials

Jones, Ryan Patrick

doi:https://doi.org/10.21985/n2-jht3-rh15

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Modeling Segregation in Spherical and Non-Spherical Granular Materials

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Although flowing granular materials have been formally studied for over two hundred years, their behavior is still poorly understood relative to fluids, solids, and gases. Sheared granular materials with differing particle properties (e.g., size, density, shape) segregate (de-mix) due to percolation (small particles fall between large ones) and buoyancy (light particles rise). Understanding and predicting segregation is important both academically, to move toward a general model of granular motion, and industrially, where unwanted segregation is costly. This dissertation focuses on quantifying segregation rates, using discrete element method (DEM) simulations, for mixtures of spherical particles at various concentrations and for mixtures of non-spherical particles. The asymmetric concentration dependence of the segregation flux is quantified for bidisperse mixtures of spherical particles. Using DEM simulations of mixtures with different inlet concentrations of each particle species, a quadratic model for the segregation velocity and a cubic model for the segregation flux are found empirically. The segregation flux dependence on particle size ratio and species concentration is used to demonstrate improved continuum model predictions of segregation, relative to a segregation velocity linear in concentration, for flows with large concentration differences. The same model for segregation velocity and segregation flux can be applied to both size- and density-bidisperse mixtures of spherical particles. The dependence of the segregation flux on size ratio and concentration is quite similar to the ``kinetic sieving" model of Savage and Lun [J. Fluid Mech. 189, 311 (1988)]. The segregation rate for bidisperse mixtures of cylinders and bidisperse mixtures of cylinders and spheres is also investigated. A major challenge to accomplish this is the adaptation of the standard DEM simulation approaches used for spherical particles to the less-symmetric non-spherical particles. This is accomplished by using a super-ellipsoid representation of cylindrical particles, both disks and rods, and a stepwise approach for contact screening, detection, and resolution. All simulations are computed using a parallelized code for Graphical Processing Units (GPUs) in the Nvidia programming language, CUDA. Using this custom DEM code, mixtures of cylindrical particles, with varying length and diameter ratios spanning a large range of shape differences, are used as a proxy for convex non-spherical particles in general. The segregation velocity for non-spherical particles can be modeled in the same manner as for spherical particles and depends on the local shear rate, concentration of the other species, and the empirically measured segregation length scale. As with mixtures of spherical particles, the segregation length scale depends on a particle length scale and the log of the volume ratio between particle species, although the volume ratio was previously reduced to the diameter ratio for spherical particles. Using the diameter of the volume equivalent sphere for the species with the smaller particle volume as the particle length scale, the dependence of the segregation length scale on the species volume ratio for bidisperse mixtures of cylindrical particles and bidisperse mixtures of cylinders and spheres is remarkably similar to that for bidisperse mixtures of spherical particles. These results demonstrate that the volume ratio is the primary driver for segregation in these mixtures of shape-disperse particles. Therefore, to reduce segregation, which is desired in most industrial situations, particle species should be similar in volume, regardless of shape.

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