POWDERTECH NOlDGY

ELSEVIER Powder Technology 86 (1996) 171-178

Jie Zheng, Colin C. Harris, P. SomasundaranH~nry Krumb School of Mines, Columbia Univ~rsily, N~w York. NY 10027. USA

Received 18 December 1994; ~cepted 9 June 1995

Abstract

Grinding and energy input in stirred media mills are studied as functions of grinding time, stirring speed, media size and density, solidconcentration, impeller and lank dimensions and design, and other relevant variables. Ground prOduct size and surface area are determinedwith respect to the above variables. Changes in energy input and media/pulp rheological properties during grinding are described. The bestconditions for grinding limestone in the laboratory stirred media mills have been identified. Equations for correlations involving power andmodified Reynolds numbers have been established.

Keywords: Grinding; Energy input; Stined media mills; Ground product size; Rheological properties

interchangeable fittings on the drive shaft, and two typicalimpeller designs used are shown in Fig. 2. A water bath isused for temperature control. Torque is measured by torquepick-up and indicator, and speed control is obtained by meansof a d.c. motor with' a rectifier and voltage regulator. Power(P) is calculated from the measured net torque T (gross

1. Introduction

Stirred media mills are used in numerous industriesbecause of their high energy efficiency, fine and ultrafinegrinding ability, and reduced contamination. In view of theirgrowing importance, basic research on power characteristicsof stirred media mills has been carried out [1,2]. In thisresearch, the torque required to rotate impellers immersed indense particulate media with supernatant versus impellerrotational speed has been found to display four regionsmarked by sharp transitions: transition from static to dynamicfriction; channelling; dispersing; and centrifuging. Equa-tions, including dimensionless group correlations of powerand modified Reynolds number, have been established forcorrelating power, speed, impeller and tank dimensions anddesign, media size and density, solid concentration, and otherrelevant variables. Scale-up guidelines for stirred media millswith respect to power consumption are proposed on the basisof the correlations and an example of power consumptionscale-up has been provided. From the results obtained, it isclear that the relationships between grinding and energy inputas functions of the operating variables require systematic

study.

Fig. I. Experiment apparatus alTangement.

2. Experimental

The stirred media mill employed is illustrated in Fig. 1. Awide range of impeller designs can be accommodated by

Iw.F 4-PIC IMPELlER 6-P1N IMPELLER

Fig. 2. Impeller designs

I This work was presented at the SME annual meeting. Denver. CO.

March. 1995.

0032-S910/9ti/SI~ 00 e I~ F.I~vi.,.. ~"~nrf'" 4 411 ri"hr. rv..rl

172 J. Zll.Ng.' at I PoW., T.dmololJ 86 (/~' 171-113

6 .s;= - (1= I; 2) (2)d;.MA

where d;. MA is the mean diameter of the area distribution,which is calculated according to

EV;dMA= E<W (3)

where VI is volume percent in i size interval and Xi is the meandiameter of interval [3).

The specific surface area was also detennined by Quanta-sorb (based on the multiple point BET method) and theFisher sub-sieve sizer (on the basis of the principles of airflow through porous media) for comparison.

To present the grinding results, three parameters definedbelow, increase of specific surface area (AS), volume-basedenergy or specific energy (Ev) and energy efficiency (Ef),are used

AS=Sp-S, (4)

where Sp and Sf are the specific surface area of the productand feed. respectively.

EEu=-

V(5)

where E is the energy input during grinding and V is thevolume of ground material.

Ef=~Eu

torque less idling torque) and speed N (P= 21rNT). Torquereadings or power values taken at one minute intervals duringgrinding were used to determine the energy input(E=IPdl).

High purity limestone (96% Caco), which is processedfrom the deposit of natural calcite located Adams, MA. andobtained from Specialty Minerals Inc., was used for the grind-ing experiments. Samples were taken from a well-mixedbatch. Feed size distribution is shown in Fig. 3. Glass beads(2.5 g/cc) were used as mill media for grinding limestone,except for a few instances when steel media were used. Inorder to observe the ftow pattern of medial pulp, a transparentglass cylindrical tank was used. Otherwise. steel grindingchambers were employed.

At the end of each test, all the media and ground samplewere removed from the mill, and the media were separatedfrom the particle by screen washing. The particle size distri-bution was analyzed mostly by a Microtrac particle size ana-Iyzer. which utilizes low-angle, forward-scattering light froma laser beam. Since the upper limit of the operating range ofthis device is specified to be 106 p.m average size, the samplewas washed through a screen to obtain 106 p.m undersizeparticles for test, with the 106 p.m oversize fraction analyzedby wet sieving. The data obtained from Microtrac and wetsieving were combined to obtain a complete volume or weightsize distribution (both methods determine particle size dis-tribution by volume or weight). Specific surface area basedon combined Microtrac and sieving was calculated using the

equation

3. Results and discussion

3.1. Effeclofgrinding lime

The effect of grinding time on the product size distributionwas studied by conducting a series of grinding tests at differ-ent grinding times with other conditions maintained constant.Size distributions obtained for grinding times of 5. 10 and 15min are shown in Fig. 3 along with that for the feed. Asgrinding time is extended, the product size distribution curve.as expected. shifts to finer sizes. resulting in an increase ofthe specific surf~e area- Table 1 shows the values of specific

Table)Specific swface ~ detennined by different methods for ground productunder ) 06 IJ.fnS-J.S. +f~

where S is total specific surface area, S. is partial specificsurface area for products under 106lJ.m and S2 is the partialsurface area for products above 106 IJ.m. I. and h are thevolume or weight fractions of particle size < 106 p.m and> 106 p.m, respectively. S. and S2 are calculated based onthe assumption of solid, spherical or cubic particles, and com-puted according to the equation

Grinding time(min)

Specific surface area (mJ/cmJ)

BETmedIOd

MicrOlrac Fislasize

5 2.31 1.50 0.8615 5. 1.62 1.94

J. Zheng et al / PowMr Technology 86 (1~' 111-118 173

area: calculated specific surface area based on Microtrac par-ticle size distribution gives values between those determinedby BET and Fisher sub-sieve sizer methods. Grinding for 15min produced about twice the specific surface area as that for5 min. In the following, in order to compare all grindingresults on the same basis. specific surface area will refer tothat calculated from Microtrac and sieving combined using

Eqs. (1)-(3).

3.2. Effec.l of impeller rotational speed

~N!.w~uCu

~~>..

'uc

...

the

0 5 10 15 20 25 30 35

Grindin8 Time (Min)

Fig. S. Effect of grinding time on energy efficiency. Conditions: D = 6.S cm;

T-II.8 cm;c-80%; R=3;d=4.4mm; V= 150cm3.

100

RPM0500.750v 1000.. 1500

lltioniffer-.tant.\d 151Asurve,ISe ofecific

The effect of impeller rotational speed on grinding lime-stone without initial supernatant liquid is shown in Fig. 4. Asimpeller speed is increased both product surface area andenergy input increase, but energy efficiency declines. Thisfinding. that higher speed results in lower energy efficiency,is in accordance with the results reported by Mankosa et al.[4] and Gao and Forssberg [5]. However, if the objective isto obtain higher specific surface area in a given grinding time.then higher speed is needed.

The combined effects of grinding time and stirring speedare shown in Fig. 5. Both lower speed and shorter grindingtimes give better energy efficiency. Energy efficiency as afunction of the number of revolutions (Nt) is shown in Fig.6 and a rough correlation is that energy efficiency is propor-tional to the number of revolutions to -0.57 power.

Fig. 7 shows the results of grinding limestone with initialsupernatant liquid in stirred mills. The average torque versusspeed curve displays several distinct regions, in agreementwith the results reported by Zheng et al. [I] for a loading ofglass beads only with supernatant liquid. In that case, it wasobserved that the process passes through four regions: tran-

sition from static to dynamic friction; channelling; dispersion;and centrifugation. The drop in torque from channelling todispersion region can be explained by media dispersion intothe supernatant causing a drop in concentration and thus a

decrease in viscosity.Stirring speeds chosen for grinding test with supernatant

condition were 260. 500 and 1000 rpm, which correspondrespectively to: channelling; onset of suspension; and full

'2...c~ki~"c.~ki'"~~ I-I

10 I_. ..., . .C ,-~J1000 10000 100000

Number or Revolul.ion. NI.

Fig. 6. Effect of number of revolution on energy efficiency. Conditions:D~6.5 cm; T= 11.8 cm;c~80%;R=3;d=4.4mm; v~ 150cm).

~

~calculaled accordinc loEf - 6132 (Nl)'-O568

-Ftshersize

-0.861.94

surface area determined by various methods at two grindingtimes for the ground product under 1 ~ J.Lffl. It is known thatdifferent methods give different values of specific surface

J. Zhmg et aL / powder Technology 86 (19961 J71-1n

However, grinding energy or specific energy was found to bealmost the same for the case of 260 and 500 rpm, which canbe explained by the drop in torque due to the transition fromchannelling to dispersing region, while higher energy con-sumption was obtained at a speed of 1000 rpm. Therefore,the best energy efficiency is obtained for grinding at thestirring speed of 500 rpm, which corresponds to the lowestpoint in torque versus speed curve which occurs in the 'onsetof suspension' region.

00c-- 00

00.Ez~ 03.~0-'0

I-

000

ie~OO ~~

. .,.99V

V9VVVVVVVVVU as

:-.000000

.. I 8

~ r- <"".)

3.3. Effect of solid concentrationtJ'-:"

Fig. 8. Effect of total solid concentration on torque. Conditions: D =6.5 cm;T-II.8 cm; t= IS min; R~ 3; d=2.0S mm; V= ISO cm3.

From the discussion of the cases with and without super-natant liquid, it is evident that total solid (combination ofmedia and particles) concentration is a very important factorin a wet grinding operation because of its direct influence onthe ground product fineness and operating power or energyconsumption. The effect of solid concentration on torqueduring the grinding process is shown in Fig. 8. The torqueincreases with increasing solid concentration over the entiregrinding period studied. It is noted that the changes in solidconcentration are produced only by means of water dilution,while the media and particle weight or volume remains the

same.Effect of the solid concentrations by volume (60% to 80%)

on the grinding limestone is shown in Fig. 9. It is seen thatthe product surface area increases with solid concentrationfrom 60 to 75% and then decreases a little at 80%. Observa-tion through the transparent tank during the stirring test at thesolid concentration of 80% reveals that only the solids (mediaand particles) around the center of the impeller are stirredwhile beyond the impeller pins the solids remain almost sta-tionary. It is those nearly unground particles in that stationaryregion that account for the decrease in product fineness.

Volume-based energy increases with increasing solid con-centration as shown in Fig. 9, which also summarizes theresults shown in Fig. 8. From Fig. 9, it can be concluded thatthe best energy efficiency is at the concentration of 65%,which corresponds to the conditions when there is minimalinitial supernatant liquid in the system.

Dry grinding (i.e. concentration 100%) results are alsoshown in Fig. 9. In comparison with wet grinding, dry grind-ing results in lower product fineness, higher energy con-sumption and the lowest energy efficiency.

3.4. Effect of ratio of media to particle volume

Total solid (media and particles) concentration at constantratio of media to particle volume has been found to be impor-tant. The following series of experiments were designed to

study the effect of ratio of media to particle volume on specificsurface area, specific energy and energy efficiency. Here, thesolid concentration is fixed while the ratio of media to particlevolume is changed from test to test, and the volume of par-ticles decreases while that of media increases with increasing

dispersion region. Product surface area shown in Fig. 7 wasfound to increase when the stirring speed was raised whilemaintaining other conditions constant. This result is similarto that found in the case without supernatant liquid in Fig. 4.

J. Zhengetal. /PowderTechnology86(1~} 171-178 17S

where media packing porosity is Em and particle (limestone)packing porosity is Epo In this case, Em = 0.4 and Ep = 0.47

give R=2.8. Consequently, the best grinding conditionsoccur when the voids in the grinding media packing are justfilled with the particles.

'JQ0;-

4.~ 'sco

OEf "-0.. !" 0;-~ S .9 .. . - e, 4.0 OJ ~

- .~ . ~ ... >-C '". .co >.II ,~~ 02 t~ c", ..... -a- .~ ...J . . .D

J.O :; t- S0 ~

! -0

101' , . . '25501>0 1 2 J 4. ~ oS

""';0 Size, d (mm)

Fig. II. Effect of media limo Conditions: D=6.5 cm; T- 8.5 cm: N-IOOOrpm;t= 15 min; c=7S,*,; R-2.8; V=60.S Cm3.

3.5. Effect of media size

:c~ 25N!w~ 20c.

~W>.~ 15...c

,.,

6

})Fig. 11 shows the effect of the media size on grinding and

energy consumption. The product surface area becomesgreater as the media size is decreased. This tendency contin-ues until the media size becomes too small to cause particlefracture effectively. The use of finer media also results inreduced energy input probably due to increased 'fluidity'.These results agree with those reported by Orumwense andForssberg [6] for dolomite samples ground in an annular ballmill.

Fig. 11 also shows that the best energy efficiency isobtained at media size 2 mm. Feed mean size calculated fromthe volume distribution is 166 JLm, so that best ratio of mediato feed size is 12: I, which is nearer to the middle of theoptimum range of 7: I than to the maximum 20: 1 suggestedby Conley [7]. However, our best ratio is less than the valueof 20: 1 recommended by Mankosa et al. [8], possibly due todifferent minerals and media density, in their case coal andsteel balls.

TliJle 2~son of grinding results by using steel balls and glass beads

Grindingmedia

AS(m2/cmJ)

Density(g/cm3)

Ef(m2/Wh)

Eu

(Wh/cm3)

Steel ballsGlass beads

7.8

2.5

4.283.98

0.520.26

8.2415.06

COOditioos:N= 1000 rpm; t= 15 min;D~6.Scm; T-II.8cm;d-4.4mm;c=75%;R-2.8; v-ro.Scm'.

3.6. Effect of media density1...'00c

OOOQO 001>0 The effect of media density on the grinding of limestoneis shown in Table 2. It is seen that higher media density resultsin slightly higher specific surface area but also in much higher(almost double) energy consumption, and thus much lowerenergy efficiency in comparison with less dense media. Dur-ing the experimentation. it was observed that steel mediaproduced much greater heat and noise than the glass mediaaccounting for greater wasted energy.

0000

1.v

E.!.! 0.8

!06

D(cm) T(cm)0 10 118. 8.5 118V 8.5 8.5

:00-; the

that 0.4 ii.. vvvvvv.iiii...~~

0 2 4 6 8 10 12 14 16

Grind;n9 T;me (Min.)

Fig. 12. Effect of impeller and lank di~nsions. Conditions: N = 1 CXM) rpm;/-15 miD; d=2.05 mm; c=75%; R=3; v= 150 cm) for T= 11.8 cm;V-57.7 cm) for T=8.5 cm.

3.7. Effect of impeller and tank dimensions

Fig. 12 shows the effect of impeller and tank dimensionson the torque. It is clear that torque or power input dependsprincipally on the impeller diameter but hardly on the tankdiameter. However, the product fineness as shown in Fig. 13relies chiefly on the ratio of tank to impeller diameter. Theproduct fineness decreases with increasing the ratio. Thisfinding is also demonstrated by the data for 60S given in Table3. Therefore, the closer the impeller to the tank wall or thelower the ratio of tank to impeller diameter, the more com-plete is grinding in the mills. Table 3 also shows specificenergy and energy efficiency. Specific energy declines withincrease in the ratio of impeller to tank. diameter. As a result,maximum energy efficiency is obtained at the highest ratio.However. comparing energy efficiency with 60S value for thecase of 11.8 cm tank for 10 cm impeller, it can be seen thatthe specific surface area increases by a factor of2.5 but energy

ratio. The results given in Fig. 10 show that the specificsurface area increases with increase in the ratio from 1 to 2.8,and then decreases. Specific energy increases with increasein the ratio over the studied range. The best energy efficiencyand product fineness are obtained at the ratio of 2.8. Accord-ing to the ideal packing condition for two component

mixtures, the critical ratio of filling is given by

:7)I-Em

R=W~

176 J. ~/lg et aL I Powder Technology &S (J~J 171-:-171

3.8. Effect 01 impeller design

The effect of impeller design is shown in Table 4. It is seenthat use of the full 4-pin impeller results in higher both ~Sand Ev value. Consequently, energy efficiency is almost thesame for both cases.

3.9. Effect of pulp viscosity

MI. 13. Effect of impeller and tank dilrlenSiolls on penick size distribution.a..ditiOI\S:N-I(MX)rpm; ,-IS min;d-2.0S mm;c- 7S...;R-3; v- ISOcm) forT-II.8 cm; V-S7.7 cm) forT-8.S cm.

Table 3Effect of impeller and tank di~ 00 grinding and energy input

D(cm)

T(au)

F/(rIi1/Wb)

~S(m'l/cm')

Ell(Wb/cm1)

U U 3.61 0.11 21.03U 11.1 1.18 0.056 33.61

10 11.1 4.74 0.21 22.43

The procedure to determine the effective viscosity duringthe grinding process rather than at its termination has beendescribed by Zheng et aI. [ 1,2]. This procedure uses the non-Newtonian power law equation involving consistency andflow index, which are estimated on the assumptions that shearrate is proportional to impeller speed and shear stress po-portional to torque. The effective viscosity can be related tothe consistency and flow index by the equation

JL=Kan-lNn-1 (8)

Power consumption with respect to stirred media mills canbe described by the following equation [ 1]

P=CKan-INn"l~ (9)

Combining Eqs. (8) and (9), the effective viscosity can be

represented by

10)pp. ~ 'CN2D3

Table 4Effect of i...la- design on grinding and energy input

Impellerdesign

F/(ml/Wb)

AS(m1/cm')

Eu

(Wb/cmJ)

Ful14-pinHalf 4-pin

4.143.IS

0.210.15

22.4322.26

Conditions: N- J(XX) wpm; ,-IS miD; 0-10 CRt; T-IJ.8 cm; d-2.OSmm;c=7S";R-3; V-JSOcm).

This equation can be obtained more directly from thepower and modified Reynolds number correlation. but thatroute does not enable the estimation of the consistency andflow index values. The effective viscosity values have beencalculated according to Eq. (10), and the relationshipbetween effective viscosity and solid concentration is shownin Fig. 14. The effective viscosity increases with increasingsolid concentration. Circular symbols represent the experi-mental data while the continuous line shows the calculatedrelationship according to Eq. ( 11) correlated from the exper-imental data

JJ. = 132S2JJ.~725 (II)

It is noted that this equation for media/pulp system is differ-ent from that for media only [ 1) .

3.10. Correlation between grinding and energy input

Energy efficiency and increase of specific surface area arerespectively plotted as a function of volume-based energy inFigs. 15 and 16. The straight lines in the figures are drawnby using Eqs. (12) and (13)

Ff= 10.56(&) -04 (12)

~S-9.27(Eu)o.54 (13)

efficiency decreases by a fa(:tor of 0.67 in comparison withthat obtained with a 6.5 cm impeller.

The regression coefficient for Eq. (12) is 0.92 and that forEq. (13) 0.95. and both standard deviations are 13%. The

J. Zheng elaL I Powder Technology 86 {1996} 171-1.

I~ encing the power consumption for media and liquid systemin stirred mills [ I]. Similarly, power and Reynolds numbersfor media, particles and liquid system can be calculatedaccording to the following equations, respectively

p

::c-.,"-N

!~~(Jc:--

~W>. 10~--c:

w

Np=~

N~pRe=7

14)

.IS)

where Jl. is effective viscosity, computed using the proceduredeveloped in an earlier paper [ I] and p is the total density ofthe media and pulp system. Power and Reynolds numbers forgrinding limestone are correlated by a single straight line ofslope - I for all studied variables in the case of full 4-pin

impeller.

vo..-

andlear>ro-d to

0.001 0.01 0 1 .-

Volume-based Energy. Ev (Wh/cm~)

Fig. 15. Relationship between energy efficiency and volume-based energy.

(8) . c-60Xv d=tmm. sleet mediaC dry crindinc. half 4-pin0 all other

4. Conclusions

./0

0 ..

-f' 101e I"'" '...'e~

....

.:....c~ 1.'t~..

5" L. I;

i 01Eo 0001 001 01 1

Volume-based Eneray. Ev ( Wh/cm'a )

Fig. 16. Relationship between increase of specific surface area and volume-based energy.

I thethat

, and

been

lship10wn

asing

:pen-11ated

xper-

Jregression power constants reported by Stehr and Schwedes[9] for a horizontally oriented stirred ball mill, were - 0.228and 0.772, respectively, while the constants found fo the millused in this investigation are shifted downwards by about 0.2.The spread of the correlated points results from a wide rangeof operating conditions the detailed effects of which are stillto be evaluated. However, the points in both figures whichresult from lower solid concentration, smaller media size.

higher density and dry grinding. are not included in the cor-relations probably due lo their different grinding mechanism.The results from using half 4-pin impeller is included in the

correlations, which implies that grinding may not be toodependent on the design of this type of impeller.

(II)

ea aret'gy Indrawn

3.1 J. Dimensionless correlation

Specific energy (volume or weight based energy) inputhas been considered as the basic criterion for reliable scale-up of stirred media mills [10-12]. This specific energy canbe obtained by introducing average power. Dimensionlessgroup correlations of power and modified Reynolds numberhave been established for correlating the parameters in flu-

(12)

(13}

Grinding and energy input in stirred media mills have beenstudied as functions of grinding time, stirring speed, mediasize and densilY, solid concentration, ratio of media to particlevolume, impeller and tank dimensions and design, and otherrelevant variables.

Lower stirring speed gives better energy efficiency forgrinding without supernatant liquid. However, for the case ofgrinding with supernatant, the best energy efficiency occursal the stirring speed corresponding to the lowest point intorque versus speed curve, in the 'onset of suspension' region.

The solid concentration for the best energy efficiency cor-responds to the value at which there is minimal supernatantliquid in the system. Wet grinding is more energy efficientthan dry grinding.

The critical ratio of media to particle volume for the bestenergy efficiency is 2.8 for grinding limestone using glassbeads as media and the equation giving this critical ratio offilling is confirmed.

The optimum ratio of media lo particle size is 12: 1 for thecase of grinding limestone using glass beads.

In the same size range, glass media is more energy efficientfor grinding limestone than steel.

The torque or power input depends principally on theimpeller diameter but hardly on the tank diameter. The closerthe impeller lo the tank wall or the lower the ratio of tank toimpeller diameter, the finer the product. However, the max-imum energy efficiency may be obtained at the high~st ratioof lank to impeller diameter due to the lowest power input.

Both greater product fineness and higher energy consump-tion are obtained by using the full 4-pin impeller rather thanhalf 4-pin impeller, but the energy efficiency is not muchaffected by such difference in this impeller design.

The relationship between effective viscosity and total solidconcentration has been determined. Effective viscosity is pro-portional to the solid concentration to the 3.7 power.

hat for~. The

171 J. Zhengetal./PowderTechoiogyM(I9NJ 17/-/73

The correlation between grinding and energy input can bedescribed by the equations derived for energy efficiency andincrease of specific surface area respectively as a function ofvolume-based energy for most cases studied. Power con-sumption for grinding in stirred media mills can be describedby correlations involving power and modified Reynolds num-bers that relate the relevant variables studied.

~II.P1Pa-T

particle packing porosityviscosityviscosity of liquid

densityshear stress

torque

AcknowledgementsS. List or symbols

This research has been supported by the Department ofInterior's Mineral Institute Program administered by theUnited States Bureau of Mines through the Generic MineralTechnology Center for Comminution under Grant NumberG1145249.

C

d

dMA

D

E

Ef

Eo

K

n

N

Np

NRe

P

R

S

Sf

Sp

4S

References

TVVIXt

volumetric concentration of solids (media and parti-cle combined)impeller geometry constantmedia particle diametermean diameter of area distributionimpeller diameter

energy inputenergy efficiencyvolume-based energy (specific energy)consistency coefficientpower law indeximpeller rotational speedpower numberReynolds number

powerratio of media to particle volumespecific surface areaspecific surface area of feedspecific surface area of productincrease of specific surface areagrinding timetank diametervolume of ground materialvolume percent in a size intervalmean diameter of interval

Greek letters

(I] J. 2Jleng. C.C. Hanisand P. So~.PreprinlN-wr94.II8.Soci~ty ofM~c/rallical EngiM~rs A-. M~~I.. Albuquerque. NAt. USA,F~b. 14-17. 1994.

(2) J. ~ C.C. H8ris and P. Somasundaran. in 1st Int. PGrtic/~T~chnofogy Fonml. Denv~r. CO. USA. Aug. 17-19. 1994. Pan 2. pp.135-141.

[3) T. Allen. Particle Siu MeQSllremenl. Chapman and Hall. New York,4thedu..I990.

[4] M.J.Mankosa,G.T.AdelandR.H. Yoon.PowderTechnol..59(1989)2S5.

[5] M.W. Gaoand E. Fonsbetg.lnl. J. Miner. Process.. J7 (1993) 45.[ 6) o. Orv--. P"D. 1MsU. Lulea Uni Yersity of T edIIM»Iogy. L8Iea.

Sweden. 1990.(71 R.F. CooleY. in S.G. MalgiIM and P. ~odann (eds.). c-t

Proc. U11rafin~ Grinding and Separation o/lndJUlrial Minerals.SocieIy of Mec;hanaJ Engi~1 American Instit.-e of ~EnIi-rs. New York, 1983. pp. 37-48.

(8) M.J. Mankosa,G.T. AdelarKlR.H. Yoon.PowderTecNlol.. 49 (1986)75.

[9] N. Sieilrand J. ~ ~r. Chelll. Eng.. 6 (1983) 337.( 101 JL.S. Jimenez. P"D. Dissertation. UniversilY of UIaII. SaIl Lake City.

UT.I98I.(II) H. Weit, J. Schwedes and N. SIeiK'. 61h Ellr. Symp. CommilUllion.

N.rnberg. ~nnany. 1986. pp.709-723.(12) Q.Q. 7JIIO. J. W. Lapcxte. J.M. Leidven and JJ. Harrington. 1st Int.

Particle T«hnoIoO Fonml. Den~r. CO. USA, All&'. 17-19. 1994. Part2. pp. 142-147.

a

~

impeller shear rate constantmedia packing porosity