SIPHPM simulation and analysis of cubic particle mixing patterns and axial dispersion mechanisms in a three-dimensional cylinder

The mixing characteristics of cubic particles in a cylinder mixer are analyzed by the SIPHPM simulation in comparison with spherical particles. The assembly of cubic and spherical particles of uniform size is pre-divided into two parts in the axial, circumferential or radial directions respectively. Then they are mixed when the cylinder is rotated at different rotational speeds of Ωd = 15–60 rpm. The mixing degree is evaluated by either the Lacey mixing index or the mixing information entropy. A normalized mixing entropy is proposed here to compare the absolute degree of mixing with non-equivalent particle numbers. It is found that, for cubes, the radial mixing efficiency is higher than the circumferential, and the radial and circumferential mixing degrees are both larger than the axial. Compared with spheres, cubic shape may enhance the circumferential mixing whereas reduce the axial mixing levels at high rotating speeds. However, at low rotating speed, cubic shape always reduces the degree of mixing of all the three patterns. Moreover, the axial dispersion characteristics are also explored by the probability density functions and the axial paths. The spatial and temporal diffusion coefficients of concentration and kinetic energies are illustrated and used to explain the axial dispersion mechanism in analogy with diffusion equation. The mean diffusion coefficient of rotational energy is independent of rotating speed, which means the axial diffusion of rotational energy depends on the eccentric feature of cubic particle, i.e. rotational ability. In contrast, it is preferred to regard the axial dispersion mechanism of spheres as convection rather than diffusion.