Mixing and Segregation of Granular Flows in a 3D Tumbler Mengqi Yu Granular mixing has received less attention than fluid mixing due to the unique properties of granular materials and the complexity of their flow behaviors. Unlike fluid flows, where a continuum perspective accurately captures flow behavior, neither a continuum nor a discrete perspective by itself can describe the global behaviors of granular flows. The tendency of particle mixtures to segregate based on varying physical

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... es further complicates the mixing problem. In this work, a 3D granular tumbler flow system is considered as a prototype to study the behaviors of granular mixing that can be understood using dynamical systems approaches based on the "cutting-and-shuffling" mixing paradigm. The proposed mixing mechanism is a synergy of "cutting-and-shuffling" and "stretching in the flowing layer," a combination of discrete and continuum perspectives. This dissertation aims to tackle two main points, mixing and non-mixing behaviors induced by the underlying flow dynamics (no segregation), and the interaction between segregation and the said flow dynamics. The role of mixing with "cutting-and-shuffling" is first studied by taking into consideration of uncertainty in operations in a simplified one-dimensional case. In the 3D granular flow system, x-ray based particle tracking techniques are used to identify mixing and non-mixing behaviors corresponding to dynamical systems features predicted by the continuum model.