AbstractGranular materials exhibit behaviours reminiscent of solids, liquids and gasses, and typically contain particles with various sizes, densities and shapes. In dense liquid-like flows, particles are sorted efficiently by size, producing inversely graded layers of large particles above small, since smaller particles are more likely to fall through void spaces. Size segregation in geophysical avalanches may increase run-out distance and destructive capacity. Granular materials are also handled in many industries, and rotating drum flows in which two or more granular materials are tossed together provide an eminent example of size segregation. Here, segregation is confined to a thin free-surface avalanche through which material is continuously entrained, resulting in an extraordinary variety of pattern formations and presenting a formidable obstacle to mixture uniformity. In this thesis, a theoretical and numerical method for coupling rheology and size segregation in polydisperse granular flows is developed, using the partially regularised mu(I)-rheology (adapted to reflect the sizes and frictional properties of the local mixture composition) in an incompressible Navier-Stokes framework, along with segregation and diffusion rates tied to the bulk flow properties. The numerical method is tested using inclined plane flow simulations and the DEM data of Tripathi & Khakhar (2011), before the petal-like pattern in a square rotating drum is computed. The segregation and diffusion dependencies confine particle redistribution to the free-surface avalanche, and the drum simulation gives promising qualitative results. Triangular rotating drum experiments with varying fill fractions and mean particle concentrations are then performed with bidisperse mixtures. The mixtures are enclosed in a thin channel by clear lateral sidewalls which exert a frictional force on the flow, producing a very thin avalanche which induces intense segregation. This is incorporated into the theoretical and numerical model using width-averaged mass and momentum balance equations with Coulomb slip assumed on the sidewalls, resulting in a two-dimensional system with an additional momentum term representing sidewall friction. The adapted numerical method is tested using an enclosed infinite shear cell and used to compute triangular drum flows with parameters matched to the experiments. The pattern formations and timescales of the simulations give excellent qualitative agreement with the experiments. A novel method for quantitative analysis is used to project a concentration field onto laboratory images based on pixel intensities, and strong quantitative agreement between the segregation intensities of the experiments and simulations is observed. Complex rheology-segregation feedback interactions are identified and clarified using the experimental and numerical results. A tridisperse triangular drum flow is then computed, correctly predicting the pattern formation observed experimentally. These results suggest that all the key features of continuously avalanching rotating drum flows may be captured in a fully coupled, incompressible continuum framework. Furthermore, by unifying previously disparate theories for rheology and segregation, this research provides a powerful tool for extending understanding of polydisperse granular flows in general.
|Date of Award||1 Aug 2023|
|Supervisor||Nico Gray (Supervisor) & Christopher Johnson (Supervisor)|
- Rotating drums
- Granular flow
- Particle-size segregation