The axial dispersion of approximately monosized particles in rolling mode in rotating cylinders with bulk flow is examined using a Monte Carlo model and discrete element method (DEM) simulations. The Monte Carlo model predicts that the mean square displacement relative to the mean axial displacement of the bed undergoes oscillations in time. The nature of these oscillations depends on the fill level of the cylinder and the extent of particle mixing during avalanches. When the cylinder is half full the Monte Carlo model predicts undamped oscillations, whereas a filling fraction of 0.26 produces oscillations whose amplitude decreases with time. If mixing during avalanches is assumed to be perfect then the oscillations occur about a linear increase with time. In contrast, if it is assumed that the particles do not mix during avalanching, the oscillations occur about an increase with time which has a gradient which increases with time. There is good qualitative agreement between the Monte Carlo model with perfect mixing and the DEM when the filling fraction is 0.26. For a filling fraction of 0.5 the DEM data show oscillations about a faster than linear increase with time.
This work reports experimental measurements of the dispersion of particles during rotation in a horizontal cylinder. The axial dispersion of a pulse of approximately monodisperse black glass ballotini into a bed of clear glass ballotini of the same size is analysed. This is done using a sectioning technique, where the concentration is determined throughout the cylinder for a given rotation time and speed. The concentration profile is fitted to an appropriate solution of Fick’s second law to determine the dispersion coefficient. The dispersion coefficient is compared for various drum rotation rates and glass ballotini sizes. The cylinder was filled to 35 % by volume and rotated at a range of speeds between 5 and 20 rpm. The particle sizes vary from 1.14 to 3.15 mm. The dispersion coefficient was found to be dependent on both particle size and rotation speed. As the rotation speed, \(\omega \), was increased the dispersion coefficient increased proportionally to \(\omega ^{0.8}\). As the particle diameter, \(d_p\), was increased the dispersion coefficient increased proportionally to \(d_p^{1.84}\). These results are compared with previous experimental and simulation data, in particular the simulations of Third et al. (Powder Technol 203:510, 2010). Strong agreement was found between the simulations of Third et al. and the experimental results.
