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.