Minerals Engineering 24 (2011) 138–151

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Minerals Engineering

journal homepage: www.elsevier .com/ locate/mineng

Is media shape important for grinding performance in stirred mills?

Matthew D. Sinnott a,⇑, Paul W. Cleary a, Rob D. Morrison b

a CSIRO Mathematical and Information Sciences, Clayton, Victoria, Australiab Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Brisbane, Australia

a r t i c l e i n f o

Article history:Received 26 July 2010Accepted 29 October 2010Available online 4 December 2010

Keywords:Discrete Element Method (DEM)GrindingStirred millsComminution

0892-6875/$ - see front matter Crown Copyright � 2doi:10.1016/j.mineng.2010.10.016

⇑ Corresponding author. Tel.: +61 3 9545 8034; faxE-mail address: Matthew.Sinnott@csiro.au (M.D. S

a b s t r a c t

Models for understanding the basic concepts of fine grinding and how they apply to the design of stirredmedia mills have not yet matured. While spherical media in tower mills has previously been studied, realgrinding media shape in stirred mills can range from spherical (steel/ceramic balls) to highly non-spherical (sand or slag) resulting in very different media and grinding dynamics. Handling the contactmechanics of non-spherical particles is a challenge for numerical models, and very few studies dealingwith non-spherical particle shape exist in the literature. Discrete Element Method (DEM) simulationsof dry media flow in a pilot-scale tower mill are performed for four cases with different shaped grindingmedia, in order to understand how flow and energy utilisation within a stirred mill depend on mediashape. Differences in media transport, stress distribution, energy dissipation, and liner wear wereobserved in the tower mill for the spherical and non-spherical cases. A significant departure fromsphericity of the media leads to strong dilation of the bed, reduced bulk density, and a reduction in activevolume and collisional power levels leading to a reduction in power draw for the mill. In addition, highlynon-spherical media tend to pack tightly near the mill walls forming a near solid layer around the insideof the mill shell which results in poorer transport and mixing, as well as increased wear rates on thescrew impeller. Grinding performance in stirred mills appears to deteriorate strongly when using highlynon-spherical media.

Crown Copyright � 2010 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Liberation of base and precious metals from complex, fine-grained ores can require size reduction below 10 lm to producea saleable concentrate. In contrast to tumbling mills, models forunderstanding the basic concepts of fine grinding and how theyapply to the design of stirred media mills have not yet matured.For example, it is not currently understood what role media shapeplays on the grinding performance within a stirred mill or on thewear of mill liners.

Stirred media mills typically consist of a stationary grindingchamber filled with grinding media (such as steel balls), and arotating internal agitator or impeller that mobilises the media,generating large numbers of collisions between the media. Mostsuch mills can typically operate with dry or wet feeds, but wetgrinding is generally more efficient since the liquid can be usedto transport the fines out of the mill. The tower mill and pin mill(Jankovic, 2003) are examples of vertically stirred mills, and theIsaMill (Pease et al., 2005) is an example of a horizontal stirredmill. Tower mills use a screw agitator which generates a strongrecirculation within the mill as media is conveyed upwards inside

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: +61 3 9545 8080.innott).

the flights of the screw and flows downwards outside the screw.The tower mill was found to have excellent transport propertiesand to maintain very good media participation rates throughouta large fraction of the grinding chamber volume resulting in a sig-nificant increase in grinding performance over pin mills (Sinnottet al., 2006). Most of the grinding in tower mills occurs within ahigh shear, annular zone located between the outer edges of therotating screw and the stationary mill shell.

Little work has been done in studying the effect of media shapeon grinding. Existing studies focus on grind performance in ballmills. The effect of non-roundness of the feed rock in tumblingmills was first considered in DEM by Cleary (2001b) with mild in-creases in shoulder position and power draw observed at sub-critical mill speeds. Cylpebs (slightly tapered cylindrical media)have been considered as an alternative to steel balls with conflict-ing claims by manufacturers. Shi (2004) compared cylpebs andsteel balls and found that for the same mass and size distributionthat cylpebs generated slightly less oversize, but when comparingsame surface area and size distributions that the cylpebs produceda coarser product. The cylpebs mill required more power than theball mill under comparable mass charge conditions. Ipek (2006)found that cylpebs produced faster breakage rates in lab scale teststhan balls under the same conditions, and that this was more sig-nificant for coarse fractions. The impact of worn, non-sphericalmedia on breakage rates and power draw in a ball mill have been

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investigated by Lameck and Moys (2006) and Lameck et al. (2006)with only marginal differences observed in breakage rates com-pared with perfectly spherical media, but significant changes ob-served in power draw and load position. However, it is generallyaccepted that highly non-spherical debris from balls which breakor spall due to manufacturing defects do reduce ball mill grindingperformance.

DEM is a computational technique that allows particle flows invarious types of equipment to be simulated. It involves followingthe motion of every particle (coarser than some cut-off size) inthe flow and modelling each collision between the particles andtheir environment, such as the mill liner or screw agitator. Thishas the advantage of being able to simulate equipment under verycontrolled conditions and to be able to make detailed predictionsof specific outputs while providing insight into the flow patternsand breakage processes. DEM has been used extensively in thesimulation of tumbling mills (Mishra and Rajamani, 1992, 1994;Moys et al., 2000, 2001; Herbst and Nordell, 2001; Cleary, 1998,2001a,b,c, 2004; Cleary et al., 2003, 2008; Morrison and Cleary,2004, 2008), in modelling stirred mills (Sinnott et al., 2006; Clearyet al., 2006, 2008; Jayasundara et al., 2008, 2010; Gers et al., 2010)and in comparing ball mill and tower mill energy efficiency(Morrison et al., 2009).

The general DEM methodology and its variants are well estab-lished and are described in review articles by Campbell (1990),Barker (1994) and Walton (1994). Here we use a conventionallinear-spring and dashpot variant of DEM which is described indetail in Cleary (2004). For this study, we apply the modellingtechnique to the analysis of media flow in a tower mill.

Different types of grinding media are used in stirred media millsand can have different shapes, size distributions, densities andmaterial properties. Media shapes can vary from roughly spherical(ceramic/steel balls) to more complex shapes such as sand or slag.During the lifetime of the media in the mill, media shape can fur-ther evolve as the media wears. Handling the contact mechanics ofnon-spherical particles is a challenge for numerical models, andvery few numerical studies dealing with non-spherical particleshapes exist in the literature (see Latham and Munjiza, 2004; Kha-nal et al., 2008). Different media shapes for a given reference sizeand material can have different surface areas (affecting the contactmechanism for grinding), particle weight (based on compactness),and bulk density (based on packing). At rest, blockier particles packtogether more tightly than spheres resulting in a stronger granularforce network (or microstructure) and increasing the yield strengthfor the bulk material to flow. Blocky, elongated particles have asphere of revolution larger than their close packing dimension,and therefore the surrounding bed must first dilate before such aparticle can begin to flow. Particle shape has been found to be par-ticularly important for packing (Delaney and Cleary, 2009), shearflows (Cleary, 2008), and mixing (Cleary and Sinnott, 2008). Flowof the grinding media and the nature of the collisional environmentin different parts of the tower mill might therefore reasonably beexpected to depend on media shape.

Here we use super-quadrics (SQs) to describe non-sphericalparticles, with general form:

xa

� �mþ y

b

� �mþ z

c

� �m

¼ 1 ð1Þ

The resultant particles are somewhere between an ellipsoid anda rectangular box with the angularity/blockiness of the cornerscontrolled by the choice of m (with m = 2 being ellipsoidal andlarge m being a box) and the aspect ratio, b, being controlled bythe ratios of the semi-major axes (b/a and c/a). SQ particle shapesare able to capture the most essential elements of real particleshape and greatly extend the range of applicability of DEM withonly moderate increase in computational cost.

The DEM study in this paper aims to analyse differences in drymedia dynamics in a stirred mill environment for a number of dif-ferent media shapes. We choose the tower mill as a general repre-sentative of the stirred mill class, both because it has been wellstudied previously (Sinnott et al., 2006; Cleary et al., 2006) and be-cause this type of mill is broadly used and has good performancecharacteristics. The key grinding mechanism in these mills is theshearing of fine particles between adjacent layers of media withhigh differential shear and high pressures. This is common to allstirred mills despite the variety of mill shapes and impeller de-signs. So although we use the tower mill to explore the effect ofmedia shape, we expect that the behaviours identified will bebroadly characteristic of other stirred mills. To do this, we will firstconsider the flow and energy utilisation within the mill for thespherical media case. This will be done by examining flow patternsand patterns of energy absorption. We will then investigate howmedia organisation, flow field, energy utilisation, force network,and liner wear change with increasing departure of the media fromsphericity. Our results are summarised in discussion at the end ofthe paper in the context of the impact that highly non-sphericalmedia has on grinding performance in stirred mills.

2. Description of tower mill configuration

2.1. Model geometry

The tower mill employs a double helical, steel screw agitator in-side a cylindrical grinding chamber. The pilot-scale tower mill usedin this study is shown in Fig. 1 with dimensions summarised inTable 1. The screw stirs the media while simultaneously lifting andcirculating it throughout the mill. This is the same mill that was usedin previous studies (Cleary et al., 2006; Sinnott et al., 2006).

2.2. Media shape cases

DEM simulations were run using this tower mill geometry forfour cases of media shape. Examples of each of these cases, in apacked bed, are shown in Fig. 2. The four cases are:

� Spherical particles (see Fig. 2a).� SQ case 1 (see Fig. 2b): SQs with mild angularity m in the range

2.0–2.5, and mild aspect ratios in the range 0.9–1.0 (for theintermediate and minor axis ratio to the major axis length).� SQ case 2 (see Fig. 2c): SQs with moderate angularities in the

range 2.5–3.5, and aspect ratios in the range 0.8–1.0 for theintermediate axis and 0.8–0.9 for the minor axis.� SQ case 3 (see Fig. 2d): SQs with more strong angularities in the

range 4.0–6.0, and higher aspect ratios in the range 0.7–0.8 forthe intermediate axis and 0.6–0.8 for the minor axis.

Dry ceramic media were modelled with the assumption of nobreakage or attrition of the media particles over the short durationof the simulations. Feed powder material was neglected since thisis typically of the order of �100 lm and is not directly resolvablewith DEM in these mill scale simulations. Its presence is not ex-pected to significantly affect the media behaviour because of thedominant masses of media particles (see Cleary and Morrison,2008).

2.3. Simulation set up

A spring constant of 50,000 N/m was chosen for the simulationsto give average particle overlaps of about 0.5% of the smallest par-ticle diameter for all cases. For the spherical case, ceramic mediadiameters were created uniformly in the range of 9–14 mm. These

Fig. 1. 3D CAD geometry of the pilot-scale tower mill used in the DEM models. Themill shell is transparent in order to make the screw agitator more easily visible.

Table 1Specification of the pilot-scale tower mill as used for the DEMsimulations.

Rated power 1.5 kWAngular speed 100 rpmChamber volume 39 LStirrer Double helical steel screwChamber diameter 0.24 mChamber height 1.2 mStirrer diameter 0.14 mStirrer shaft diameter 0.04 mPitch 0.18 m

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media were poured into the mill chamber up to a height well abovethe top of the screw blades. This gave a total media mass of 58.4 kgfor 29,800 particles. For each of the SQ cases, the major axis of themedia was chosen to give the same average particle volume asused the particles in the spherical case. This means that the num-ber of particles and mass of charge were within 3% of that of thespherical case for all cases, in order to ensure that they are directlycomparable. The specific gravity used for the ceramic media was2.7. A coefficient of restitution of 0.3 and a friction coefficient of0.5 were used for media–media and media–boundary collisions.

3. Spherical media case

3.1. Flow environment

Fig. 3 shows flow pictures of the grinding media coloured bytangential and axial speed after the flow has reached a steady-state. Here, the tangential and axial directions are defined in thecontext of the rotating screw impeller. Fig. 3a shows that tangen-tial speed is small (but never zero) near the mill shell and increaseswith decreasing radius until a peak speed is reached near the edgeof the screw. The tangential speeds decline at smaller radii as theshaft is approached. The radial trend for tangential speed is similaralong much of the length of the mill, except near the top and bot-tom corners of the charge where the tangential speed is very closeto zero.

Media within the flights of the screw are elevated upwards atspeeds of 0.1–0.2 m/s as shown in Fig. 3b. There is a correspondingdownwards flow of media in an annular region between the screwand the mill shell. This flow in this region is not completely steadybut has fluctuations with alternating regions of downward andnear stationary flow along the length of the mill. This occurs be-cause dilation of the charge by the screw opens up dilute regionsnear the screw edge and media conveyed by the screw are occa-sionally able to move off the edge of the screw and join the down-wards travelling stream. The combined tangential and axial flowfield characterises the swirling recirculation pattern that is respon-sible for transport of media inside the tower mill.

3.2. Energy dissipation

Fig. 4 shows the grinding media coloured by normal (Pnorm) andshear (Pshear) collisional power. These are calculated by summingall the energy dissipation occurring for each media particle per unittime. High levels of both components of the energy dissipation areconcentrated in an annular region between the edge of the screwand the mill shell. This corresponds to the high shear region be-tween the upwards and downwards flowing streams as shown inFig. 3b. Energy is predominantly dissipated in shear interactionswith the shear power �3.5 times that of the normal collisionalpower. This indicates that shearing of feed particles that are caughtbetween media particles sliding past each other is the dominantmechanism for size reduction in stirred mills. The grinding zoneextends from the top of the screw to the floor of the mill and thelevel of collision energy dissipated by media does not appear to de-pend on their height within the mill.

We can gather further details about the energy environmentwithin the mill by considering energy loss statistics for media–media and media–mill collisions. Fig. 5 shows collision energyspectra plotted as the total energy dissipation rate in the systemfor each collision energy level. This describes how the energy isbeing utilised inside the tower mill. Fig. 5a shows total, normaland shear energy absorbed in media–media collisions only. For col-lision energies below 4 � 10�6 J, dissipation predominantly resultsfrom many low energy, head-on collisions between media. At col-lision energies above this, shear interactions dominate and con-tinue to dominate up to the highest collision energies, which are6 � 10�4 J for the normal component and about 0.01 J for the shearcollisional component. The collision level that contributes most tothe energy dissipation (and by inference to the powder grinding) is6 � 10�5 J. Fig. 5b shows total, normal and shear energy absorbedin media–mill collisions. The trends are very similar to themedia–media collisional spectra, with normal dissipationdominating for collision energies below 4 � 10�6 J. Peak normalcollision energy (4 � 10�4 J) for media–boundary collisions andpeak shear collision energy (6 � 10�3 J) are both smaller than for

Fig. 2. Packed media for: (a) spherical media, (b) SQ case 1 with mild angularities and aspect ratios; (c) SQ case 2 with moderate angularities and aspect ratios and (d) SQ case3 with stronger angularities and higher aspect ratios. Note the strong orientational ordering of the particle microstructure.

Fig. 3. Spherical media distribution shown in a clipped section of the tower mill at 10 s. The particles are coloured by: (a) tangential speed Vtang, and (b) axial speed Vz.

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Fig. 4. Spherical media distribution shown in a clipped section for the tower mill at 10 s. The particles are coloured by: (a) normal collisional power, and (b) shear collisionalpower.

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media–media collisions. The peak dissipation rate is 8 times smal-ler for media–boundary collisions indicating that less energy isconsumed in boundary wear than in media–media grinding.

4. Non-spherical media shapes

We now consider the effects of varying the media shape on theflow behaviour and energy usage in the tower mill. We consider arange of different media from spherical to more extreme shapes(such as found for sand or slag). Since we are primarily interestedin the independent axial and radial variations of key flow attributesand wish to compare these for different charge shapes, we there-fore average the flow properties over the other two spatial dimen-sions to give variations with either radius or height.

4.1. Effect of media shape on bed structure and media transport

4.1.1. Average media speedThe radial dependence of the mean axial speed is shown in

Fig. 6. Particles within the central cylindrical region surroundingthe screw and a small distance outside the screw are transportedupwards by the screw. Particles in the annular region beyond thatdistance travel downwards driven by gravity. This demonstratesthe system wide recirculation that produces the grinding in themill. For the spherical media, the highest upward mean speed of0.1 m/s occurs at 0.058 m, which is well inside the outer edge ofthe screw (at 0.07 m). The upward speed of the screw surface is0.3 m/s and represents the maximum axial transport speed. Thelower observed media speed means that particles are able to rolland/or slide downwards relative to the blade leading to reducedefficiency in transport. At smaller radii, the axial speed declinesas the screw becomes increasingly inefficient at transporting parti-cles upwards. Beyond the peak, the mean axial speed then de-

creases almost linearly with the flow changing to a downwarddirection outside a radius of 0.08 m. The speed of the downwardflow increases until it reaches a peak speed of 0.05 m/s at 0.1 m.Only a small decrease in speed is observed out to the mill shell.There is significant slip observed in the axial direction at the wallwith the media there still moving downwards at 0.05 m/s. Forthe mill to be in equilibrium the upward and downward flux ofparticles must be equal. The upward moving material is in anannulus with a small cross-sectional area and a moderate solidsfraction. In order to balance the flow in the outer annulus, whichis more densely packed and has a larger area, the upward axialspeed must be much larger than the downward axial speed.

The flow speeds found for media with a mild shape (SQ1) arevery similar to that of the spherical media. So, mild media non-sphericity has a negligible effect on the axial flow behaviour. Largermedia shape variations (SQ2 and SQ3) significant reduce all the ax-ial flow speeds, with particularly large effects at small and large ra-dii. The peak upward velocity is reduced by 25% for the moderateshape and 32% for the more extreme shape. Close to the screwshaft the axial speeds have been reduced by 70% and 77% respec-tively. The radius at which the peak upward speed is observed alsoincreases modestly with increasing non-roundness of the media.The peak downward speeds are also reduced by 17% and 25%respectively, and the radii at which they occur decreases sharplyfrom 0.1 m to 0.09 m for SQ2 and further to 0.087 m for SQ3. Thereduced distance between the peak up and downward speedscounteracts the reduction in these peak speeds to give axial shearrates in the active shear zone (which is the main grinding region)that are very similar for all media shapes. The radius at whichthe flow switches from upwards to downwards also decreases withincreasing non-roundness of the media. For the spherical case andmildly non-spherical case, the outer downward moving annulus ofmaterial travels at nearly constant speed. For the more non-roundmedia, the axial speed drops rapidly with increasing radius

Fig. 5. Total energy dissipation rate for spherical media for each collision energylevel for: (a) media–media, and (b) media–mill boundary interactions. Spectra areshown for normal, shear and total components.

Fig. 6. Radial dependence of mean axial speed for the different media shapes.

Fig. 7. Dependence of mean tangential speed for the different media shapes on: (a)radial position, (b) axial position.

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reaching zero at the mill shell. This means that there is no wall slipand that a region of near stagnant material forms adjacent to themill shell for more extreme shaped media. For moderate or moreextreme media shapes the axial transport capacity of this mill issharply reduced.

Fig. 7 shows the dependence of the mean tangential or swirlingspeed of the media on its shape. The radial distribution (Fig. 7a) hasa similar form for all the media shapes. From the screw shaft, thetangential speed increases with radial distance up to a maximumat around two thirds of the way to the edge of the screw blade

and then decreases rapidly over the main shear zone (shown bythe region of high shear rate in Fig. 6) and then more slowly be-yond a radius of around 0.085 m. However there are significantvariations in the magnitudes for the different media. For compari-son, the rigid body velocity of the screw is also shown. For thespherical/near spherical shape media the velocity near the shaftmatches that of the screw indicating that the media is co-rotatingwith the screw at this point. With increasing radii the media speedincreases more slowly than that of the screw indicating that thereis increasing slip between screw and media. The spherical mediareaches a maximum tangential speed of 0.35 m/s at 0.053 m. Incontrast, the strongly non-spherical media (SQ2 and SQ3 cases)swirls more rapidly around the mill than the rate at which thescrew rotates. This is due to higher momentum transfer from largerradii transmitted by the more strongly interlinked particle micro-structure that occurs for more blocky shapes. The maximum tan-gential speed is higher than for the spherical media and occurs ata smaller radius. The peak tangential speed is increased by 12%and moves inwards by 0.02 m for moderate shape, and is increasedby 11% and shifts 0.06 m inwards for more extreme media shapes.

From the point of the peak tangential speed, there is an almostlinear decrease in tangential speed out to a radial distance of be-tween 0.085 and 0.090 m for all media shapes. The shear rate(the speed difference over the high shearing region divided by itswidth) increases strongly as the media shape becomes increasinglynon-spherical. This is in contrast to the axial shear rate which re-mained almost constant with media shape changes. Interestingly,all the tangential velocity curves intersect at a radius of 0.067 m

Fig. 8. Average volume fraction for the different media shapes as a function of: (a)radial distance from the mill centre, and (b) height.

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which is just inside the outer edge of screw. At 0.085 m, there is aninflexion point for the spherical media case and the shear rate de-creases sharply over the remaining annular region of downwardflowing material. As the media shape becomes more extreme, thisinflexion point moves slowly outwards and the shear rate in thisregion increases modestly. For the spherical and near sphericalmedia shapes, there is significant slip between the media and themill shell (as there was also in the axial direction), with a slip speedof around 0.1 m/s. For the more extreme particle shapes, the tan-gential velocity reaches zero before the shell is reached (as wasalso observed for the axial speed), so there is a stationary ‘‘frozen’’layer of depth between 10 mm and 15 mm (around 1 or 2 particlediameters) packed against the mill shell. The flat sides of theblocky media are pressed against the shell and they are restrictedfrom rolling or sliding.

Fig. 7b shows the variation in the mean tangential speed withheight in the mill. The behaviour is qualitatively similar for allmedia shapes, but again there are large variations in magnitude.The tangential speed starts at a reasonably high level near the baseof the mill and bottom of the screw. It increases sharply withheight as the screw progressively mobilises the media. It then in-creases linearly but more slowly along the length of the screwreaching a peak at a height of around 0.65 m. It then declines shar-ply as the top of the screw blade and the free surface are ap-proached. The mild shaped media (SQ1) have similar tangentialspeeds to spherical media throughout the mill and only a mildreduction in relative speed at each horizontal layer below 0.5 m.For cases SQ2 and SQ3, the mean tangential speed is almost con-stant over a large range of mill heights from 0.15 to 0.6 m butthe magnitude is strongly reduced to 0.15 m/s for moderate shapesand 0.12 m/s for more extreme shapes. The reason for the large de-crease in average tangential speed with height compared to themore moderate change seen with radius is that the weighting ofparticles at large radii are much higher due to the much larger par-ticle numbers in each annular interval.

4.1.2. Average solid fractionFor all media shape cases, the packing density (as measured by

the solid fraction) of the media is not constant throughout the mill.Fig. 8 shows the variation of media solid fraction with radius andheight in the mill. A strong radial dependence is apparent inFig. 8a. Spherical particles pack only loosely within the flights ofthe screw with a solid fraction of around 0.43 from near the screwshaft radius out to the outer edge of the screw at radius 0.07 m. Justinside the screw edge at a radius of 0.062 m, there is a mild de-crease in packing density. From the tip of the screw at 0.07 mout to a radial distance of 0.08 m, there is a rapid increase in solidfraction (up to 0.51). This region of strong density change corre-sponds to the region of high shear rate in the tangential direction.From 0.08 m out to 0.1 m, the solid fraction increases more slowlyto a peak of 0.55. It then is almost constant out to near the millshell. The rotating screw imparts strong tangential speed to thesurrounding media which creates a strong outwardly directed cen-trifugal force which presses the media radially outwards until theyare confined by the outer cylindrical mill wall. The result is a tigh-ter granular packing and a stronger microstructure in the regionsbeyond the screw. The material in the outer downwards flow re-gion is densely packed and has low levels of axial and tangentialshear, and so behaves almost like a rigid body.

The solid fraction distribution for mild shaped media (SQ case1) is very similar to that of the spherical case. This continues a pat-tern of small deviations from sphericity of the media having littleeffect on the media dynamics. For the moderately non-round med-ia (SQ case 2) there is greater change. The solid fraction near thescrew shaft remains the same as for the spheres but declines to aminimum of 0.38 at a radius of 0.062 m. It then increases rapidly

over the width of the shear zone (out to 0.095 m) remaining justlower than for the spherical case. The solid fraction then increasesin the same way as the spherical case out to radius 0.1 m where itreaches its peak. At this point there is a sharp divergence with thesolid fraction for SQ2 rising steeply to a maximum of 0.61 near theshell. This occurs because the more blocky particles pack moredensely with their long axes aligning with the mill shell leadingto strong orientational ordering in the microstructure. This order-ing can be seen in Fig. 2c and allows particles to pack more denselythan can be achieved by spherical particles. This increase in pack-ing density is also enabled by the very low rates of axial and tan-gential shear (previously observed in Figs. 6 and 7). For highlynon-round media (SQ case 3) the same types of changes occurbut they are much more extreme. Inside the screw, the media ismuch more dilated with solid fractions reduced to around 0.37near the shaft and a minimum of 0.36 at a radius of 0.058 m. Thelocation of this minimum occurs at a smaller radius as the mediashape becomes more extreme. The solid fraction then increasesstrongly and almost linearly up to 0.65 near the mill shell. Thereis no intermediate plateau region of near constant density for thisshape media. The much denser packing near the mill shell is againdriven by the development of even stronger orientational ordering(see Fig. 2d) and again enabled by the very low velocities and shearrates in this region. The very high solid density adjacent to the millshell is consistent with the formation of a frozen autogenous layerof densely packed media.

The reduced volume fraction inside the screw for blocky mediais due to its increased resistance to flow which both restricts the

M.D. Sinnott et al. / Minerals Engineering 24 (2011) 138–151 145

amount of material that can enter the screw at the bottom and re-duces the loose packed limit of the solid fraction. The reduction inthe solid fraction between its minima just inside the edge of thescrew and the middle of the downward flowing material outsidethe screw is due to shape induced dilation in the active shear zone.Particle rotation is a critical component of flow behaviour in shear-ing granular flows. Non-spherical particles require their volume ofrevolution to be predominantly empty of particles in order to ro-tate. So close packed neighbours can restrict the ability of such aparticle to rotate and therefore increase the resistance to flow(Cleary, 2008). In contrast, spherical particles can always rotate be-cause their volume of revolution is the same as their physical vol-ume. This makes spherical particle materials much easier to shear.In the tower mill, the amount of shear is controlled by the motionof the screw. In order for the packed microstructure of stronglynon-spherical particles to shear at this rate, the microstructuremust dilate sufficiently for the volumes of revolution of the parti-cles to become substantially empty and allow the shear inducedrotations to occur. This produces the much lower solid fraction ob-served in the shear zone around the edge of the screw in the towermill. Beyond the shear zone, both the SQ2 and SQ3 cases demon-strate much stronger packing near the wall. At the wall, the flatfaces of these blocky media align with the wall and surroundingmedia tend to ‘‘brick up’’ (as demonstrated in Fig. 2c and d). Thisforms a packed autogenous layer that lines the wall and whichhas limited and sometimes no particle motion. From an operationalperspective, this has the advantage of reducing the shell wear be-cause it is protected by the autogenous layer, but has the disadvan-tage of reducing both the mill volume available for active grindingand the rate of media circulation in the mill.

Fig. 8b shows the variation of average solid fraction with heightin the mill. It is almost constant at 0.44 from 0.1 to 0.85 m forspherical media. Below 0.1 m, there is a modest reduction due toagitation by the screw as particles are drawn into the empty screwvolume. The top of the screw blade is at 0.86 m. Above this heightmedia can no longer be lifted by the screw and the momentum im-parted to the particles that were lifted past the top of the screw issteadily dissipated by frictional interaction with other media. Asthe lifting influence of the screw wanes with height, the bed be-comes increasingly quiescent and gravity causes the particles topack more densely (with the peak solid fraction of 0.52 at0.92 m). Above this level the solid fraction falls off quickly as thefree surface is approached. For the mild shape case (SQ1), the solidfraction behaviour is again very similar in form to that of thespherical case but consistently just slightly lower. The moderateshape case (SQ2) also follows the spherical case closely but isslightly more densely packed for most of the mill height. This re-flects the higher packing of the blocky particles in the autogenouslayer which outweighs the reduced solid fraction inside the screw.In contrast, the solid fraction of the SQ3 media is noticeably smal-ler than the spherical media by 5% due to the strong dilation of theextremely non-round media in the shear zone and the reducedpacking inside the screw. In contrast this media packs much moredensely in the quiescent upper zone with a higher peak density of0.56.

Fig. 9. Dependence of average granular temperature for the different media shapeson: (a) radial position, and (b) axial position.

4.1.3. Average granular temperatureGranular temperature links and helps explain the variations ob-

served in the velocity fields and solid fraction. It is the fluctuatingcomponent of the velocity field and is a measure of the degree of‘‘turbulence’’ in a granular flow. It plays a similar role in granularthermodynamics as the temperature plays in conventional ther-modynamics. High granular temperature leads to strong pressuresthat lead to strong dilation of the flow leading to low densities(Cleary, 2007). Similarly, low granular temperatures leads to low

pressures and increased density of the flow potentially leading togranular freezing.

Fig. 9 shows the dependence of average granular temperatureon radius and height for the different media shapes. For sphericalmedia, the granular temperature increases quadratically withincreasing radial distance from the shaft up to a peak at 0.07 m cor-responding to the edge of the screw blade (see Fig. 9a). It then de-clines rapidly with increasing radius out to the mill shell but doesnot reach zero there. The central region of high granular tempera-ture indicates a high level of fluctuation and turbulence in the flowand corresponds to the locations of the high levels of shear in boththe axial and tangential directions. The minimum solid fractionalso occurs near the radius at which the granular temperature isa maximum indicating that the dilation of the bed from the shearis at a maximum. As the granular temperature falls off withincreasing radius, there is a matching increase in the solid fractionas the turbulent stresses decrease and are unable to support suchdilation in the bed. Although the granular temperature also fallsoff with decreasing radius, the solid fraction is unable to increasebecause the screw restricts the flow of new material into these lessdense regions.

The granular temperature for the mild shape case is very similarto that of the spheres with just a mild reduction at the wall of a fewpercent. This is the reason for the strong similarities in the radialdistributions of the other dynamic quantities for the mild non-round media. For the more blocky media, the peak granular

Fig. 10. Dependence of the mean normal collision force (or bed pressure) for thedifferent media shapes on: (a) radial position, and (b) height.

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temperature increases by 11% and 20% respectively, the location ofthe peak moving slowly to small radii. For smaller radii the granu-lar temperature is independent of media shape because thedynamics in this region are controlled by the screw. At larger radii,the drop off of the granular temperature is much faster and it fallsto zero at or just before the mill shell. The rate of decline of thegranular temperatures is increasingly fast as the media shape be-comes more extreme. The reason for the increasing peak granulartemperature with increasing non-sphericity arises from therequirement for increasing amounts of dilation in the shear zonein order to make the space available to enable the rotation thatis needed for the enforced rate of shear. The increased dilation isproduced by a strong expansionary pressure whose magnitude iscontrolled by the granular temperature. In contrast, the very lowgranular temperature in the outer regions means that there areno expansionary pressures and the granular material ‘‘freezes’’with the particles ceasing motion and increasing in packing densityto the point where the contact forces can support all the weight ofthese particles above. This directly leads to the generation of the‘‘frozen’’ or ‘‘bricked up’’ layer of particles observed against the millshell for the more blocky media shapes.

Fig. 9b shows that the distribution of average granular temper-ature with height is very similar for the different media shapes.From 0.15 to 0.8 m, the granular temperature is almost constantfor each case indicating that there is little change in the mill behav-iour with height. Below 0.15 m, there is a peak in the granular tem-perature at 0.05 m corresponding to the bottom of the screw whichagitates the bed and draws particles upward. Above 0.8 m, there isanother peak in the granular temperature at 0.85 m which occursas the fast moving stream of particles rising with the screw entersthe more quiescent surface boundary region generating significantfluctuations as the stream is forced radially outwards and backdown the outside of the mill. Above this the granular temperaturerapidly falls to zero at the free surface. The granular temperature ishighest for the spherical media and modestly lower for the non-spherical cases.

4.1.4. Average collisional forceThe stresses acting on the media in the mill are of three types.

The first arise from the forces applied by the screw to the mediait is lifting. Much of the weight of these particles is transmittedto the screw. The second contribution is from the streaming or tur-bulent stresses which are proportional to the granular tempera-ture. These forces support much of the weight of the media inthe annular dilated shear region centred on the edge of the screwblade. The third contribution is from the collisional stresses – theseare forces transmitted via inter-particle collisions or long durationparticle contacts. Fig. 10 shows variation of the average normal col-lision force (which is a measure of bed pressure) with radius andheight. There are two distinct patterns of variation for the nearspherical and blocky media. For spherical or near spherical media,the peak collisional pressure occurs near the edge of the screw (at0.075 m) and declines both for smaller and larger radii. There isalso a small increase near the mill shell. For more blocky media,the pressure distribution changes radically with a substantialreduction throughout most of the bed (by around 50%) counter-balanced by a very strong increase in pressure beyond a radius of0.1 m. The large reduction in collisional pressure within the screwresults from the large reduction in solid fraction in this regionwhich means that the mass of media is lower and therefore theweight to be supported is lower. Within the shear zone (centredaround the outer radius of the screw) the reduction results fromboth the lower mass of material there (due to the decrease in thesolid fraction) and from the higher granular temperature whichindicates that streaming stresses make a larger contribution tosupporting the media. In the outer regions of the mill, the granular

temperature approaching zero means that the full weight of thecharge must be supported by the collisional stresses, so these risesharply for the blocky media. This is again another indication of thedevelopment of the dense packing of media in a frozen autogenouslayer adjacent to the mill shell.

Fig. 10b shows the dependence of the mean collision force onheight. For reasonably spherical media, the mean bed pressure islow at the bottom of the screw increasing by around 30% overthe first 0.05 m. The bed pressure increases mildly with height(around 20% between 0.05 and 0.55 m). From 0.55 to 0.8 m, thepressure is relatively constant. There is a small peak of additionalpressure at 0.87 m caused by the re-direction of flow from thetop of the screw radially outwards and back down. The pressurethen declines to zero as the free surface is approached. For blockymedia, the relationship between bed pressure and height is com-pletely different. The maximum pressure is observed near the bot-tom of the screw and then decreases steadily with height. The localincrease associated with the media departing from the top of thescrew and starting to recirculate is still observed. The pressurethen drops as the free surface is approached. The trend of decreas-ing pressure with depth is analogous to the hydrostatic pressuregradient in a vertical column of fluid and reflects the effect of thestatic weight in the frozen media layer at the mill shell.

Since the majority of the grinding is done in the shear zone, thereduction in bed pressures and the increased dilation for increas-ingly non-spherical media are likely to be detrimental to grindingperformance. The reduced circulation rates for the media representa significant reduction in the transport efficiency for getting feed to

M.D. Sinnott et al. / Minerals Engineering 24 (2011) 138–151 147

the grinding zone and to remove ground product. Another impor-tant consideration is the distribution and transport of slurrythrough the media. Sinnott et al. (2010) used a 1-way coupledDEM-SPH model to study the prediction of slurry transport. The so-lid fraction of the media was found to be a significant controllingfactor on this transport. The changes in the solid fraction observedhere for blocky media indicate that flow of slurry in the more den-sely packed downward moving media will be significantly re-stricted. The reduced solid fractions in the screw and the shearzone mean that most of the slurry will be present in and trans-ported through this much smaller volume of the mill. This is alsounlikely to be beneficial to grinding performance. Slurry may lubri-cate the media or wash the finer feed out from between the mediabefore it can be comminuted.

4.2. Effect of media shape on energy utilisation

4.2.1. Power drawFig. 11 shows the power draw for the mill operating at 100 rpm

for each media shape. Cases are represented by their average sphe-ricity which is the ratio of surface area of a sphere (having the samevolume as the media particle under consideration) to the surfacearea of the particle. Sphericity can be thought of as a measure ofhow compact a particle is and has a value of unity for spheres.For blocky or elongated particle shapes, the sphericity value willbe progressively less than one. The power draw for spherical mediais about 275 W. The mildly non-spherical media (case SQ1) has asphericity of 0.93 and has a mildly reduced power draw of270 W which is only slightly lower than for spherical media. Thesphericity of the SQ2 media is 0.67 and this has a power draw thatis 22% lower than for spherical media. The SQ3 shaped media (withsphericity 0.58) gives an even larger reduction in power by 30% rel-ative to spherical media. This demonstrates that non-sphericity ofmedia has a significant and detrimental effect on the power draw.

4.2.2. Collisional power dissipationTo better understand where and why such large reductions in

power draw occur we look at the spatial distribution of the powerdissipation in media–media and media–mill collisions. Fig. 12shows the radial distribution of average normal and shear colli-sional power. As previously observed in Fig. 4, the peak collisionalpower occurs near the edge of the screw. Shear dissipation is thedominant energy loss mechanism with the shear power beingaround 3.5 times higher than the normal power. This means thatthe large majority of energy is dissipated by shearing or slidingcontacts rather than from head on impact of the media surfaces.

Sphere

SQ1

SQ2

SQ3

Fig. 11. Predicted power draw for the screw as a function of media shape(sphericity).

For spherical media, we observe a quadratic increase in normal dis-sipation with increasing radius out to the edge of the screw(0.07 m). The rate of increase then declines quickly creating abroad smooth peak of 13.5 mW at 0.08 m just beyond the screwedge. This is the radius that separates the upward moving anddownward moving streams of particles (see Fig. 6) and also corre-sponds to the inflexion point at the edge of the dilated high shearzone where the solid fraction gradient suddenly declines. The nor-mal dissipation then declines almost linearly out to the mill shell.Similarly, the shear dissipation also shows a quadratic trend withradius up to a peak of 47 mW, this time at a closer distance of0.07 m (corresponding to the edge of the screw blade). This peakwill be due in part to glancing interactions between media strikingthe edge of the screw. There is an initial sharp decrease in sheardissipation up to 0.08 m (corresponding to the peak of the normalenergy dissipation), followed by a short gentle plateau region andthen a faster almost linear decline out to the mill shell. The two keydynamic quantities that control energy dissipation in collisions arethe granular temperature (which controls the collision frequency)and the collisional pressure (which controls the intensity of forcesin these collisions). The energy dissipation distributions are there-fore unsurprisingly very similar to the granular temperature distri-bution. The sharpness of the central peak is amplified by thepeaked nature of the pressure distribution, which is much weakerat smaller and larger radii and largest around the edge of thescrew.

Fig. 12. Comparison of the radial and axial dependence of the average collisionalpower for the different media shapes as: (a) normal and (b) shear components.

Table 2Modal peak values for energy loss spectra for media–media and media–linerinteractions in terms of energy dissipation rate.

Media–media energy (lJ) Media–liner energy (lJ)

Total Screw Shell liner

Spheres 62 107 42SQ case 1 66 110 42SQ case 2 70 152 19SQ case 3 74 252 20

148 M.D. Sinnott et al. / Minerals Engineering 24 (2011) 138–151

For mildly non-round media (SQ1) the normal dissipation peakshifts closer towards the edge of the screw but is otherwise verysimilar to the spherical case. In contrast the shear dissipation peakremains in the same place (centred on the edge of the screw) butincreases by 3%. It also declines slightly near the mill shell. Formoderately non-round media (SQ2) the peak regions of both thenormal and shear dissipation are little changed compared to thoseof the SQ1 case. However the power components decline modestlyat smaller radii (inside the screw) and decline very substantially inthe outer annular region where the media for the slow moving al-most frozen autogenous layer. For the most extreme non-roundmedia (SQ3) the normal dissipation peak moves again to smallerradii and is now located at the edge of the screw matching the loca-tion of the peak shear dissipation. The magnitude of the peak en-ergy dissipation rates also increase around 20%. The normaldissipation rate within the screw declines moderately, but thereare further large decreases in energy dissipation for all radii be-yond 0.08 m reaching close to zero in the autogenous layer whichis now fully frozen against the mill shell. So the dominant effects ofthe increasing non-roundness of the media are to increase the en-ergy dissipation in a very narrow region of high shear around theedge of the screw blade, but to significantly decrease energy con-sumption in the rest of the charge. This decrease occurs particu-larly in the large downward moving outer annular region, muchof which has limited shear motion and which can freeze up entirelynear the mill shell. The increase in power consumption around thispeak region is overwhelmed by the decline in the outer half of themill leading to the significant decline in the power draw observedin Fig. 11.

One may be tempted to consider that the higher central peak ofenergy consumption might lead to at least a local enhancement ofthe grinding rate, but even this may not be true. Only the media areincluded in these simulations, but an important consideration forgrinding is the ability of the media to trap the fine feed particlesbetween media particles during their collisions. The denser themedia are packed the more easily feed particles can be trappedand broken. In this region where there is significant dilation ofthe charge, the powder or slurry (depending on whether the towermill is operated dry or wet) will also have a lower solid fraction(since the amount of fine material locally does not change as thecharge dilates) so the fill factor of the fines in these regions willbe well below 100% (fully filled). The significant increase in theamount of dilation of the shear zone observed for reasonablynon-spherical media is likely to have a serious impact on the abil-ity to trap and therefore break the feed particles. The decrease insolid fraction represents a significant increase in the pore spaceavailable in the shear zone for the fine feed particles to be ableto move out of the way of the media particle surfaces during mediacollisions. This increase in feed particle mobility is therefore likelyto sharply reduce the fraction of the energy available in the media–media collisions that is actually transferred to the feed particlestrapped between them. So we conjecture that grinding in this re-gion is likely to be worse due to the dilation even though there ismore energy available in the media collisions. This would meanthat the extra energy is most likely to be absorbed by the mediarather than by the feed which is more able to escape from betweenthe balls and avoid collisions. This suggests that the media wearrates will also be higher with wear occurring preferentially at thecorners and asperities of the media causing them to become morerounded.

We suggest that this dilation effect is a significant contributorto the reduced efficiency of fine breakage that is typically observedin fine and ultrafine grinding mills when slag or sand is used formedia. This hypothesis has been confirmed for fine stirred millingby several researchers. Savage and Yan (2006) showed thatrounded Nambucca sand media reduced the product size (i.e.,

P80) more effectively than angular Yuleba sand media. Similar re-sults have been reported for various types of slag media (Jankovic,2003). However, mass reduction during rounding may also lead toless severe breakage for some feed materials. If media particles arereally ill-shaped like pieces of slag, they will lose significantamounts of mass from preferential fracturing of the corners beforethey are round enough to do much damage to the interstitial feedparticles. By then they may not have enough mass for their colli-sions to exceed the elastic strength of the feed particles. This willworsen still further the grinding performance of highly blocky,irregular or elongated media.

4.2.3. Collisional energy spectraFig. 5 showed the collisional energy spectra for the mill for

spherical particles. The form of the spectra does not change withchanges in media shape, but the location of the modal peak foreach spectrum does. These median collision energies are sufficientto characterise the changes in the collision environment and theseare given in Table 2. There is a steady increase in the median col-lision energy for media–media collisions with increasing non-roundness of the media. These collisions are the ones that mainlyoccur in the high energy dissipation shear zone (see Fig. 12). Themedian media–screw collisions increase much more strongly,increasing by about a factor of 2.5. The impact of this on screwwear will be seen in the next section. These significantly strongercollisions also contribute to the increase in the collisional energydissipation observed in the narrow band around the edge of thescrew. In contrast, the median energies for collisions with the millshell decline strongly as the increasingly quiescent and solidboundary layer acts to protect the mill shell.

4.3. Mill wear

Wear in a tower mill is predominantly by abrasion (see Clearyet al., 2006) and the abrasive wear is known to be proportionalto the shear energy absorption by solid surfaces (Cleary et al.,2010). Fig. 13 shows mill geometry coloured by the rate of shearpower absorption for each of the different media shapes. There issignificant abrasion on the outer half of the top surface of the screwand around its spiral outer surface. The highest concentration oc-curs on the top edge of the screw at the intersection of these sur-faces. There is little change in the wear for the mildly non-sphericalcase (SQ1). For the more blocky media the pattern of abrasion doesnot change but there is a strong increase in its magnitude. For themore blocky media, the pattern of abrasion is very similar to that ofthe spherical media except for two aspects: there is a reduction inwear rates at low radii near the screw shaft, and there is an in-crease in magnitude of wear rates at the edge of the screw blade.This increase in the abrasive wear is consistent with the increasedintensity of the energy dissipation by the media at the edge of thescrew in Fig. 12 and in the increase in the strength of the individualcollisions with the screw (as shown in Table 2). The increasingnon-sphericity of the media not only leads to declines in thepower draw and likely weaker grinding performance, but also

(a) Spheres

(c) SQ Case 2

(b) SQ Case 1

(d) SQ Case 3

Fig. 13. Abrasive wear as measured by the shear power absorbed by the screw and mill shell for: (a) spherical media, (b) mildly non-spherical media (SQ case 1), (c)moderately non-spherical media (SQ case 2), and (d) strongly non-spherical media (SQ case 3).

M.D. Sinnott et al. / Minerals Engineering 24 (2011) 138–151 149

significantly increases the wear on the screw. Wear on the millshell is significantly weaker than for the screw. Fig. 14 shows thetotal power absorption (the total power available for wearing thesesurfaces) as a function of media shape. For spherical media, thescrew absorbs only around 30% more energy than the mill shell.The total wear on the screw is almost the same for the SQ1 and

Sphere SQ1 SQ2

SQ3

Fig. 14. Total energy absorption for the screw and mill shell surfaces as a functionof media shape (sphericity).

SQ2 cases and consistent with the redistribution of wear rates atlow radii towards the screw edge, but there is a sharp increase of45% for the more extreme shape (SQ3). In contrast, the total powerabsorption by the mill shell declines modestly for the SQ1 mediaand very strongly for the more blocky media that generates thenear stationary packed autogenous layer adjacent to the mill shell.

5. Conclusion

This study has investigated the dependence of media flow andenergy utilisation in a tower mill on the shape of the grinding med-ia. The tower mill was chosen as a generic representative of stirredmills and the conclusions drawn are expected to be broadly repre-sentative of the behaviour of mills for which high speed shear be-tween layers of grinding media is the dominant comminutionmechanism.

For spherical media, the screw motion transports media insidethe screw upwards and there is a corresponding downward spiral-ling motion in an annular region adjacent to the mill shell. This de-scribes a swirling recirculation pattern for the media inside themill. The high rotation rate of the screw blade sets up large tangen-tial speeds in the surrounding media which then experience astrong outwardly directed centrifugal force. This pushes the mediaoutwards until it is confined at the mill wall. The result is a tightgranular packing (and strong microstructure) well outside thescrew. A narrow annular region of high shear energy is observed

150 M.D. Sinnott et al. / Minerals Engineering 24 (2011) 138–151

between the upwards and downwards flowing streams and occursnear the outer edge of the screw. This indicates that shearing offeed particles that are caught between media particles sliding pasteach other is the dominant mechanism for size reduction in stirredmills. The shearing between upward and downward flowing layersalso results in a local dilation of media in this region. As observedin Sinnott et al. (2006), the level of collisional energy does not varyto media height within the mill. This is a key reason for a towermill having a similar behaviour to that of other kinds of stirredmills.

Media with shapes that only mildly depart from spherical werefound to behave very much like spherical media.

Media with more blocky shape (either from moderate aspectratios or having more angular corners) such as unconditionedsand or slag have significantly different behaviour from that ofspherical media. Changes are observed in the structural organisa-tion of the charge, the nature of the flow, the amount of energyconsumed and the way in which this energy is used. Key observa-tions of changes in flow behaviour (as media shapes become morenon-spherical) that are likely to impact on grinding performanceare:

� Much reduced rate of media circulation.� Axial shear rates are invariant but the axial shear zone becomes

narrower.� The tangential shear rates increase in the shear zone.� Lower packing of media in the screw is observed as it is harder

for blocky media to flow in between the screw flights.� More blocky media leads to increased dilation in the shear zone

because of the need for more space to allow particle rotations.This leads to higher feed particle mobility as the pore spacebetween media is larger enabling feed to escape from betweenmedia–media collisions leading to decreased grindingperformance.� Formation of a densely packed, slow moving and sometimes

frozen annular autogenous annular layer adjacent to the millshell in which the granular temperature is close to zero andthe particles are supported almost entirely by collisional stres-ses that are moderately hydrostatic in nature.� The shear zone is a region of high granular temperature reflect-

ing the strong turbulent motions in the flow. The peak granulartemperature increases with the blockiness of the media but alsobecomes narrower.� The pressures in the shear zone are much reduced for blocky

media.� Strong dilation of the media inside the screw and in the grind-

ing zone around the outer radial edge of the screw blade with acorresponding reduction in bulk density.� Power draw for the mill is significantly reduced and so there is

less energy available for comminution in the mill.� Normal and shear collisional power dissipation are higher in the

shear zone.� The region of peak collisional power shrinks in a similar way to

the narrowing of the axial shear zone and it shifts closer to theedge of the screw.� The reduced mobility of angular, elongated media in the outer

layers of the charge causes a strong reduction in collisionalpower between the edge of the screw and mill shell. This reduc-tion is much larger than the increase in the dissipation rate inthe shear zone, leading to the strong reduction in overall powerdraw.� Abrasive wear rates along the screw blade edges are increased

for blocky media. This will result in faster rounding of screwblade edges. The autogenous media layer at the wall acts to pro-tect the mill chamber due to the much reduced mobility ofmedia at the wall.

Our study suggests that in using reasonably non-spherical med-ia in tower mills (and by analogy other stirred mills) one would ex-pect a negative impact on grinding performance due to poorermedia transport, increased dilation in the grinding zone leadingto reduced comminution rates, a reduction in active bed volumeavailable for grinding, poorer distribution and transport of intersti-tial slurry, much higher abrasive wear rates for the screw and re-duced levels of collisional power in much of the media leading toa lower energy consumption. Slag and sand media can be expectedto wear to approximately spherical shapes in any milling environ-ment which is dominated by shear, which means that the grindingperformance will vary according to the changes shown here as themedia shape evolves. However, if high strength synthetic media isnon-spherical beyond a small degree, it can be expected to retainits shape and will continue to cause the effects identified here overthe life of the media.

Acknowledgement

This work has been partially funded by the Centre for Sustain-able Resource Processing.

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