Numerical study of mixing of binary-sized particles in rotating tumblers on the effects of end-walls and size ratios

The mixing characteristics of binary-sized particles in rotating tumbler are studied by discrete element method (DEM). The cases of diameter ratios of RD = 1:1, 2:1 and 3:1 under three rotating velocities ω = 1.0, 2.0, 3.0 π rad/s with or without friction from front and rear walls of the tumbler are simulated. Short and long tumblers (L = 0.15 and 0.3 m respectively) are used with stationary or rotating end-walls. Considering the local granular concentrations of binary-sized particles, an improved information entropy function is proposed to evaluate the overall mixing degree of particles in the tumbler. Moreover, the kinetic energy and the radial distribution function are also explored to discuss the impacts of friction from front and rear walls, the size ratios and the rotating speeds on particle mixing. All the analytical results indicate that the friction from the stationary front and rear walls play a significant role in degrading the flow regime and suppressing particle mixing especially in short tumblers because of the motion resistance. When the effective contact area for end-walls is larger than the lateral wall, it may be even more important than the rotating speed for determining the mixing degree. The lengthened tumbler may attenuate the effect of end-wall frictions. The size ratios play either a positive or a negative role in influencing particle mixing, caused by the static feature of size difference and the dynamical different property inducing size segregation respectively. In addition, the rotations of end-walls may have an effect of mixing enhancement that is reverse to the stationary end-walls.