A mathematical model has been developed to investigate the mixing behaviors of solid particles within an inclined fluidized bed, which is a system of particular interest for applications of downcomers in circulating fluidized beds. Incorporating Newton's second law of motion for calculating particle motion, the interaction among particles is successfully simulated using the discrete element method (DEM), in which the motion of fluid is modeled in a two-dimensional scheme and the motion of spherical particles is considered in a three-dimensional domain. Based on simulations, as angles of inclination are increased from 0 degrees, 10 degrees, 20 degrees to 30 degrees with respect to the vertical axis, the simulations demonstrate particle mixing phenomena with respect to fluidizing characteristics. The simulations provide a unique microscopic viewpoint of particle motion inside the bed, which cannot be observed experimentally easily. Fractional fluidization arising from distribution of gas flow along the cross-section of the bed has been found to be affected by the angle of inclination. Moreover, knowledge of microscopic mixing of solid particles, caused by circulating flow, has been explored. (c) 2006 Elsevier B.V. All rights reserved.