A macroscopic and microscopic study of particle mixing in a rotating tumbler

Abstract The microscopic and macroscopic mixing of granular particles in a two-dimensional rotating tumbler is studied using the discrete element method (DEM). For microscopic study, a dimensionless function ξ ( c a , c b ) is proposed to evaluate the degree of mixing of particles on the scales of particle size. It is demonstrated that the mixing interface is exponentially increased when the measurement scale decreases. Thus, a fractal structure of the mixing interface is indicated. By numerical analysis on the dimension of the interface, it is indicated that with the same rotations, a slow rotation speed is positive to particle mixing. Moreover, under the same time, there always exists a limit state under which the mixing is fully developed. On the other hand, by calculating the mean auto- and cross-radial distribution functions, the mixing dynamics is evaluated based on a macroscopic point of view. By the radial distribution functions, a Shannon entropy-based numerical analysis is carried out. It is indicated that, analogical to theory of thermodynamics, the mixing is an information entropy-increased process, and the level of mixing is well evaluated by the value of Shannon entropy. Moreover, the increase process for the Shannon entropy is oscillated during the transition from one state in ‘equilibrium’ to another. The frequency analysis indicates the close relationship between the oscillation in entropy and the external effects, such as the rotational acceleration of the tumbler.

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