Three-dimensional particle diffusion in a rotating drum reactor

Mixing of non-cohesive granular solids in a partially-filled, horizontal, rotating drum occurs in the axial, radial and angular directions. Mixing in the axial direction is purely diffusive and can be represented accurately by a one-dimensional diffusion equation. From the abundance of experimental data in the literature, an empirical design correlation was derived to relate the particle dispersion coefficients in the axial direction to rotational speed, degree of fill, drum diameter and particle size. The axial-dispersion coefficient ranged from 1 × 10−7 to 1 × 10 −4 m2/s and in most cases increased with speed, drum diameter and particle diameter.; Unlike mixing in the axial direction, particle mixing in the radial and angular directions is a combination of convection and diffusion. Also, little published data exists to quantify the dispersion coefficients let alone the effects of rotational speed, degree of fill, drum diameter and particle size.; Dispersion in each direction is primarily due to the same phenomenon i.e. random collisions in the active region. Relationships between the axial, radial and angular dispersion coefficients are proposed, allowing the radial and angular coefficients to be predicted from the more easily measured axial coefficient and an approximation of the relative thicknesses of the active and static regions. The proposed relationships are consistent with the radial and angular coefficients that can be determined from the limited experimental data available in the literature. The radial-dispersion coefficient is usually about 2 to 4 times larger than the axial-dispersion coefficient.; A granular solids mixing model for the transverse plane in a partially filled horizontal rotating drum is developed. The model includes convective mixing and particle diffusion perpendicular to the circulation streamlines. Using the proposed relationship between the axial- and radial-dispersion coefficients, the model simulates the effects of initial tracer orientation, fill level and scale-up on the mixing rate.; By adding heat conduction in the radial direction, the mixing model is extended to simulate wall-to-bed heat transfer. The model is used to predict the significance of mixing and scale-up on the wall-to-bed heat transfer.