SIPHPM simulation and analysis of cubic particle mixing in a tilted tumbler and application of a new mixing index construction principle

The mixing phenomenon of particles in a tilted tumbler is studied by the SIPHPM simulation. The particle motion in the tilted tumbler with three rotating velocities ω = 1π, 1.5π and 2π rad/s at tilt angles of α = 5°, 10°, 15°, 20°, 25°, 30°, 45° and 60° are simulated. We propose a construction principle of mixing indices depending on particle concentration. The mixing degree of these cases is evaluated by the new construction-principle-based mixing indices (NCPBMI). In addition, a modified formula is added to the construction principle, so that it can be used to evaluate the particle system with various particle sizes, and the difference between the two calculation methods of the total mixing index in the new mixing index construction principle is compared. In addition, the differences in the application range of various mixing indices are summarized. It is found that the influence of inclinations on the axial mixing of cubic particles in the inclined tumbler varies. At low inclinations, the particle system hardly mixes; at medium inclinations, the inclination plays a positive role in mixing; at high inclinations, the positive influence of inclination on mixing decreases. Also, the rotating speed is a negative factor for cubic particle mixing.