Numerical study of particle mixing in a tilted three-dimensional tumbler and a new particle-size mixing index

A new mixing index is proposed, which is an improved Lacey index based on coordination number fraction. The differences and similarities among many mixing indices are compared, including the new mixing index, the information entropy based on coordination number fraction, the Lacey index based on local concentration, and the information entropy based on local concentration. The first two indices are microscopic since the coordination number fraction is on particle-scale, whereas the latter two are mesoscopic as the local concentration is mesoscopic scale. The newly proposed mixing evaluation indices does not include inauthentic temporal oscillations. Moreover, using mixing index, the mixing characteristics of particles in a tilted tumbler are studied by discrete element method (DEM). The tumbler’s angle of tilt α = 0°, 10°, 20°, 30°, 40°, 50°, 60° and 70°, at five rotating velocities ω = 0.175, 0.35, 0.5, 0.6, 0.7 and 1.4 rad/s corresponding to Froude number Fr = 0.0025, 0.001, 0.002, 0.003, 0.004, 0.016 respectively are simulated. It is found that both increasing the tilt angle and the rotating speed have negative effects on the particle mixing within the scope of this study.