Particulate flows are encountered in numerous industrially-important processes. However, process steps involving particulate materials often cause severe scale-up and commissioning problems, such as flow stoppages and particle segregation, due to a lack of rigorous design methods and a reliance on trial-and-error. Thus improving our fundamental understanding of particle segregation mechanisms is crucial for numerous industries. In addition granular flow instabilities and segregation problems have attracted much attention from a theoretical point of view. So far the majority of rheological studies on granular materials have been confined to nearly mono-disperse systems, where the particles have equal density and equal size. However, a real system is always characterized by some degrees of poly-disperse particles that have different sizes and densities. It is well known that multiple components and particle size distributions clearly complicate flow behavior. Segregation by particle size, shape or density is a common behavior in many processes, such as shearing, shaking and pouring. A natural starting point to understand the effect of the poly-dispersity on the flow behavior and mixture rheology is an investigation of a bidisperse system of smooth and slightly inelastic spheres.

In the present work, we employ Couette flows as a metaphor for a variety of more complex, equipment specific geometries because Couette flows have proven invaluable in the investigation of dynamics, stability and mixing of granular flows. First, we examine steady state Couette flows with a bimodal particle mixture using two kinetic theory models for rapid granular flows. One was proposed by Jenkins and Mancini (1989) (JM model), and the other was proposed by Iddir and Arastoopour (2005) (IA model). In JM model, energy equipartition is assumed, but this assumption is relieved in IA model. We found the energy equipartition is broken down with an increase in the system inelasticity and mass ratio, while there is only a small effect of the size ratio if the two particle species have the same mass. By examining the solids fraction profiles based on JM and IA models respectively, it was shown that the segregation of total particles and each individual particle species is enhanced when the effect of non-equipartition granular energy is considered. We found the segregation is due to the competition of three diffusion forces: the pressure diffusion force, the thermal diffusion force and the ordinary diffusion force. Then we compare the simulation results from the binary kinetic theory model with those from particle dynamic simulation. Results compare favorably except one exception. Two forms of segregation are observed in particle dynamic simulation when the two particle species have equal density. With low mean solids fraction large particles accumulate in the low granular energy region, while small particles accumulate in this region at high solids fraction. This flux reversal is not captured using the kinetic theory model. We believe this is due to the instabilities in the particle dynamics simulations and the effect of vorticity seen in the simulation cannot be captured using the current steady state continuum solutions.