Estimation of sheer rates inside a ball mill

Grinding slurries are known to be non-Newtonian. For such suspensions, slur ry 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 i nside a ball mill, in order to determine appropriate values of apparent vis cosity for studies of the effects of rheology on grinding. Shear rates were estimated by considering the ball charge motion inside the mil. 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. P ower draw of wet tumbling mills and its relationship to charge dynamics: Pa rt 1. A continuum approach to mathematical modelling of mill power draw. Tr ans. I.M.M. 105, C43-C53] was employed. This approach considers the mill ch arge to be comprised of layers or 'shells' which slide against one another. The relative velocity between layers of the charge was calculated. Distanc e over which this change in velocity occurs was determined from the slurry volume filling the interstices of the charge and from the contact area betw een the slurry and ball surfaces. Shear rate defined as the velocity gradie nt 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 velocit y of the ball for the same bah mill. It is therefore recommended that a she ar rate in the range of 13-730 s(-1) be used to characterise the apparent v iscosities of slurry in grinding applications. (C) 1999 Elsevier Science B. V. All rights reserved.