Investigating grinding mechanisms and scaling criteria in a ball mill by dimensional analysis

A dimensional analysis of the ball mill process is carried out through the Buckingham-Pi method. The dimensionless quantities identified are discussed and used in order to suggest scaling criteria for ball mills. The flowability and the particle size distribution of an alumina powder ground in laboratory ball mills of various dimensions are compared in order to discuss the influence and the relevance of each dimensionless numbers. Some geometrical, kinetics and dynamic similitudes are highlighted both theoretically and experimentally. In particular, the conservation of the Froude number and the fragmentation number lead to relevant scaling criteria for mills of 1, 2 and 7 L inner volumes. The importance of the ratio between the pebble size and the vessel diameter is also discussed. Finally, the preponderance of the fragmentation number over the number of revolutions of the vessel is interpreted in terms of particle fragmentation mechanisms.