Axial dispersion of granular material in horizontal rotating cylinders

Residence Time Distribution of Non-Spherical Particles in a Continuous Rotary Drum

The motion of non-spherical particles with sharp edges, as they are commonly involved in practice, was characterized by residence time distribution (RTD) measurement in a continuous drum. Particles with two sizes, 6 and 10 mm, and two densities, 750 and 2085 kg/m3, were used in the experiments. The effects of rotation speed (3–11 rpm), incline angle (2–4°), feed rate, and mixture composition were investigated and compared to the results of other researchers on particles without sharp edges. We also fitted the RTD with an axial dispersion model to obtain a better insight into the flow behavior. MRT of non-spherical particles with sharp edges depends on ω−α similar to other shapes, while the value of alpha is higher for particles with sharp edges (0.9 < α < 1.24), especially at high incline angles. The MRT depends on incline angle, β−b, where b varies between 0.81 (at low ω) and 1.34 (at high ω), while it is close to 1 for other shapes. Feed rate has a slight effect on the MRT of particles with sharp edges and the effect of particle size diminishes when rotation speed increases. The MRT linearly increases with volume fraction of light particles in a mixture of light and heavy particles (from pure heavy to pure light particles).

Is axial dispersion within rotating cylinders governed by the Froude number?

Axial dispersion rates of particles within horizontal rotating cylinders have been calculated for a decade of cylinder diameters. Throughout the range studied the rate of axial dispersion was found to be independent of the cylinder diameter. This phenomenon has been investigated further by spatially resolving the local contribution to the axial dispersion coefficient. This analysis demonstrates that, although the highest rates of axial dispersion occur at the free surface of the bed, there is a significant contribution to axial dispersion throughout the flowing region of the bed. Finally, based on an analogy with a Galton board, a linear relationship is proposed between the local rate of axial dispersion within a horizontal rotating cylinder and the product of the local particle concentration and the local shear rate in a plane perpendicular to the cylinder axis.

Resolving a paradox of anomalous scalings in the diffusion of granular materials

Granular materials do not perform Brownian motion, yet diffusion can be observed in such systems when agitation causes inelastic collisions between particles. It has been suggested that axial diffusion of granular matter in a rotating drum might be "anomalous" in the sense that the mean squared displacement of particles follows a power law in time with exponent less than unity. Further numerical and experimental studies have been unable to definitively confirm or disprove this observation. We show two possible resolutions to this apparent paradox without the need to appeal to anomalous diffusion. First, we consider the evolution of arbitrary (non-point-source) initial data towards the self-similar intermediate asymptotics of diffusion by deriving an analytical expression for the instantaneous collapse exponent of the macroscopic concentration profiles. Second, we account for the concentration-dependent diffusivity in bidisperse mixtures, and we give an asymptotic argument for the self-similar behavior of such a diffusion process, for which an exact self-similar analytical solution does not exist. The theoretical arguments are verified through numerical simulations of the governing partial differential equations, showing that concentration-dependent diffusivity leads to two intermediate asymptotic regimes: one with an anomalous scaling that matches the experimental observations for naturally polydisperse granular materials, and another with a "normal" diffusive scaling (consistent with a "normal" random walk) at even longer times.

Axial transport within bidisperse granular media in horizontal rotating cylinders

The discrete element method has been used to examine axial dispersion within rotating cylinders containing two sizes of particle. Two bed configurations are considered: initially segregated, which consists of a pulse (narrow axial band) of small particles within a bed of large particles, and initially mixed, in which the cylinder is loaded with a homogeneous mixture of the two particle sizes. The dispersion of the small particles within initially segregated beds is found to depend strongly on the initial length of the pulse of small particles. Initially mixed beds are found to undergo a transient period in which the small particles disperse rapidly. Following this transient, axial dispersion of both particles sizes is found to follow Fick's second law, in that the mean squared deviation of the axial position of the particles is proportional to time. Axial dispersion coefficients have been calculated for initially mixed beds that have reached steady state; the axial dispersion coefficients of both particle sizes decrease as the volume fraction of small particles is increased.