This thesis presents studies focused on a better understanding mixing and segregation of granular flows in rotating tumblers. Axial segregation of size varying bidisperse granular mixtures in long cylindrical tumblers was studied to understand the dependence of band formation and evolution on the relative concentration of small and large particles and the rotation rate. In attempt to shed new light on the phenomenon, two new approaches to analyze size-varying band forming systems were proposed. One is an analogy between the phase diagram of a granular system and that of a binary chemical system in which band formation is shown to have "phase transitions" analogous to spinodal decomposition and nucleation. The other, a dynamic scaling approach, was applied to coarsening granular patterns similar to that previously used for reacting lamellae in fluid cavity flows. The scaling indicates a universality of band thickness distributions.
The critical speed for centrifuging of monodisperse granular materials in rotating tumblers was investigated through experiments in a quasi-2D tumbler. The commonly used dimensionless number is the Froude number, Fr = ω 2R/g, which is the measure of the ratio of inertial forces to gravitational forces. The generally accepted value for centrifuging of Fr> 1 is not accurate. Preliminary results show that centrifuging depends on more than just Fr. Important factors include the tumbler fill fraction and particle interactions due to friction, but particle size plays only a minor role.
Finally, a mixing mechanism without stretching and folding, referred to as "cutting and shuffling," is introduced. The mechanism has theoretical foundations in a relatively new area of mathematics called piecewise isometries (PWI). Mixing of granular materials is considered in a half-full three-dimensional spherical tumbler undergoing a protocol of repeated brief rotations about two different horizontal axes. Experiments for monodisperse particles over several iterations can be simulated to a high degree of accuracy with a continuum model. The similarity between the model and PWI results indicates that the theory captures the essential kinematic features responsible for mixing. It is shown that mixing protocols and orientations of the axes of rotation that minimize symmetries provide the best mixing.
|Advisor:||Motter, Adilson E.|
|Commitee:||Lueptow, Richard M., Ottino, Julio M., Schellman, Heidi M.|
|Department:||Physics and Astronomy|
|School Location:||United States -- Illinois|
|Source:||DAI-B 70/12, Dissertation Abstracts International|
|Subjects:||Chemical engineering, Mechanical engineering, Plasma physics|
|Keywords:||Granular flows, Granular mixtures, Mixing, Rotating tumblers, Segregation|
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