Low Reynolds number multiphase flows are prevalent in many industrial applications, such as separations processes, cell growth in bioreactors and catalysis operations. Due to the interplay between phases, the characterization of these flows is rather complex yet necessary to fully understand the intrinsic dynamics. This study discusses the interactions between a viscous fluid phase and rigid particles dispersed within the fluid.The particles are observed to spontaneously migrate within the toroidal structures that form between rotating flat-disk impellers to repeatable non-trivial asymptotic locations. The stability of the asymptotic migration positions is dependent on flow and particle conditions and includes both the exact center of the torus as well as other intermediate locations that are classified as higher order clusters. It is of particular interest that the particle clusters coincide with the location of unmixed islands within the underlying flow, illustrating significant coupling between the solid and fluid behavior. Furthermore, the results also show that migratory competition can occur when multiple particles are introduced into the same flow region. This behavior is also examined using a one-way coupled Lagrangian-Eulerian model based on the Basset-Boussinesq-Oseen (BBO) equation. In this approach, particle motion is captured by incorporating a variety of fluid-particle force models into a Eulerian treatment of the flow field. Although a regular cellular flow is able to capture rotation rate and particle diameter effects, it is unable to provide insight into interactions between the particles and any secondary island structures that exist in many rotating flow systems. Thus, a 2D approximation of the experimental cellular flow is obtained by a perturbing a cellular flow streamfunction to produce fluid island structures. The model was then used to analyze a dilute suspension of slightly non-neutrally buoyant solid spheres as they migrate across the curved fluid streamlines of the viscous flow. The effect of the Saffman lift force on the lateral migration of the solid spheres is also evaluated. Without this additional term, the BBO model predicts an inward motion solely for light particles, whereas heavy particles are predicted to migrate outwards. However when included into the BBO model, both types of particles exhibit inward migration which is analogous to our experimental work. The equilibrium particle location could be manipulated by varying the flow characteristics and stability of the fluid islands.%In addition, the preliminary results of a more robust continuum method to evaluate the flow field within a stirred tank are presented. Finally, possible experimental and computational directions of this research are presented, particularly as it applies to other simple rotating flows. It is believed that this thesis significantly contributes to the understanding and perhaps eventual manipulation of the hydrodynamic interactions within such systems to yield spontaneously organized, `structured suspensions'. This work can be extended to study the migration behavior of other discrete entities within a flow such as bubbles or droplets by appropriate modification of the experimental and computational procedures to other geometries.
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