Estimation of shear rates inside a ball mill

• Published in: International journal of mineral processing 1999-09, Vol.57 (3), p.167-183
• Main Authors: Shi, F.N., Napier-Munn, T.J.
• Format: Article
• Language: English
• Subjects: Applied sciences; ball mill; charge motion; comminution; Crushing. Screening (sizing). Classification; Exact sciences and technology; Metals. Metallurgy; Ores; Production of metals; rheology; shear rate
• ISSN: 0301-7516; 1879-3525
• DOI: 10.1016/S0301-7516(99)00016-2

Grinding slurries are known to be non-Newtonian. For such suspensions, slurry viscosity is not a constant, but is a function of shear rate. This study was aimed at the derivation of an estimate of a typical shear rate range inside a ball mill, in order to determine appropriate values of apparent viscosity for studies of the effects of rheology on grinding. Shear rates were estimated by considering the ball charge motion inside the mill. Two types of ball motion, cascading and cataracting, were taken into account. For the first type of motion, Morrell's power model approach [Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics: Part 1. A continuum approach to mathematical modelling of mill power draw. Trans. I.M.M. 105, C43–C53] was employed. This approach considers the mill charge to be comprised of layers or `shells' which slide against one another. The relative velocity between layers of the charge was calculated. Distance over which this change in velocity occurs was determined from the slurry volume filling the interstices of the charge and from the contact area between the slurry and ball surfaces. Shear rate defined as the velocity gradient between layers of the charge in the cascading motion was hence estimated to be 13 s −1 as a lower limit of the shear rate range for a ball mill of 4.57 m in diameter. For the second type of motion, the velocity of a free-flight ball striking the mill shell was resolved into two components, and a typical shear rate of 730 s −1 was estimated from the tangential velocity of the ball for the same ball mill. It is therefore recommended that a shear rate in the range of 13–730 s −1 be used to characterise the apparent viscosities of slurry in grinding applications.