Dispersion properties for residence time distributions in tumbling ball mills

The present paper deals with a theoretical analysis of the dispersion properties, the dispersion coefficient and the Peclet number, of particulate material in a continuous ball mill. In the analysis, a dispersion zone where the brief dispersion of particles occurs, is postulated in the lower portion of an operated mill called the grinding zone. Consequently, the dispersion coefficient is derived to be a function of the size of the dispersion zone and the mobility of balls in the grinding zone and the Peclet number is a function of the dispersion coefficient, the axial mean velocity of material flowing and the mill length. Results derived from the theory are within reasonable agreement with reported data for dry and wet grinding operations, although minor variations are observed between theory and experiment. Additionally, the mill diameter and length are predicted to affect greatly the Peclet number, implying the importance of designing mill sizes for required product size distributions as the residence time distribution is dominated by the Peclet number. Further, a proportional relationship to predict the Peclet number is derived, which appears to be valid as confirmed with data regardless of the mill sizes tested.