Couette Flows of Granular Materials: Mixing, Rheology, and Energy Dissipation

Abstract

This thesis examines the behavior of a granular material sheared in a gap between two moving boundaries. In fluid mechanics, this type of flow is known as a Couette flow. Two different kinds of granular Couette flows were studied. First, gravity-free flow between two infinite plates moving in opposite directions was investigated using computer simulations. Second, flow between a stationary outer cylinder and an inner rotating cylinder was studied using both experiments and computer simulations. Two-dimensional discrete element computer simulations of infinite planar Couette flows were used to study the rheology, energy dissipation, and other flow properties in flows of particles of uniform size for three different gap widths. The energy dissipation rate was measured and a thermal analysis was conducted to determine the thermodynamic temperature rise and heat flux of such flows. Given a constant wall velocity, all of the properties in flows of identical particles were found to depend on the value of the solid fraction at the walls, which in turn depended on both the average solid fraction and the gap width. When the average solid fraction reached a critical threshold, the amount of work done on the flow drastically increased, increasing the average strain rate, granular temperature, wall stresses, and energy dissipation in the flow. This solid fraction threshold occurred after the center region of the flow had reached a dense limit and any further increase in solid fraction necessarily occurred in the wall regions. Various results from computer simulations were found to compare reasonably well with past results derived using kinetic theory. Mixing and other flow properties were also investigated in planar Couette flows of two different particle sizes, as functions of the size ratio and solid fraction ratio of the two species. Larger particles were found to migrate away from the regions of high fluctuation energy near the two moving boundaries in all cases. Mixture flows were found to behave very similarly to flows of mono-sized particles at high ratios of the solid fraction of small to large particles. As the solid fraction ratio decreased and the number of large particles increased, results deviated from the corresponding flow of identical particles. Flows with large size ratios of large to small particles deviated the most from the result of mono-sized particles, because stresses and energy dissipation rates are both mass-dependent. The second type of Couette flow, between two concentric cylinders, was investigated in a horizontal orientation (with the axis of rotation perpendicular to the direction of gravity) and in a vertical orientation (with the axis parallel to the direction of gravity), using both experiments and computer simulations. In the horizontal geometry, high-speed imaging was used to calculate experimental mean and fluctuation velocity profiles that were compared to results from three-dimensional discrete element simulations. Segregation of binary particle mixtures was also investigated in this geometry. Segregation in this flow was driven by a percolation mechanism acting at the free surface, causing large particles to migrate to the top. Computer simulations compared well qualitatively with experiments, successfully predicting the velocity profiles and the segregation pattern at the surface. When compared quantitatively, however, fluctuation velocities in the simulations were considerably greater than those found in the experiment, and the radial segregation observed in experiments did not occur to the same extent in simulations. The vertically-oriented cylindrical Couette flow experiment was used to measure the shear stress on the outer cylinder wall as a function of different variables. The shear stress was found to be independent of the inner cylinder rotation rate, because the material was unconfined and allowed to dilate. The measured stress showed a linear dependence on the height of material in the apparatus, indicating a hydrostatic variation of the normal stress. The shear stress also varied significantly with the ratio of the gap width to the particle diameter.