(597e) Segregation of Granular Materials in Couette and Channel Flows

Flows composed of solid particles are encountered in numerous industrial processes, including solids mixers and hoppers, chute flows, pneumatic conveyors, and fluid catalytic cracking. Collisions between particles are responsible for energy dissipation and transfer, leading to particulate clusters in the flow regimes. Furthermore, the granular medium is often composed of particles that have different mechanical properties, such as size and/or density. It is well known that multiple components and particle size distributions clearly complicate flow behaviors. Segregation occurs if particles differ in size, density, shape, or other characteristics. 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. Therefore, controlling unwanted segregation of components within a particle mixture is a longstanding goal in particle processing technologies.

Transport equations for slightly inelastic particles in rapid granular flows have been extensively studied using kinetic theory of a dense gas. In the present work, we investigate the steady state solutions of Couette and channel flows with a bimodal particle mixture using kinetic theory proposed by Iddir and Arastoopour (2005) who considered the effect of a non-Maxwellian velocity distribution and non-equipartition of granular energy in their model. Although the granular systems studied in this work are quite simple, they can be used as a metaphor for a variety of more complex, equipment specific geometries because they include both shear and physical boundary interactions that are essential ingredients of most practical applications.

We find that under our specific situations the solids fraction and granular energy profiles are quite similar between the Couette flow and the channel flow. For the equal density mixture, the accumulation of particles has a transition from the walls to the center when the restitution of coefficient decreases from 1 to 0.99. This sensitivity is reduced when the system becomes more inelastic. By comparing with the monodisperse system, we show that if larger particles are mixed in the system the sensitivity of the total solids distribution to the restitution coefficient is suppressed, while if smaller particles are added in the system the situation reverses. The system inhomogeneity and the segregation between two particle species are enhanced with an increase in the system inelasticity, the mean solids load or the size ratio. The physical mechanism leading to the species segregation can be attributed to the competition of three diffusion forces: the thermal diffusion force, the ordinary diffusion force and the pressure diffusion force. In addition, we find a competition mechanism exists in the equal density case since in the equal mass case, small particles have a higher concentration in low energy regions whereas in the equal size case, light particles have a lower concentration in low energy regions.