POWER CONSUMPTION OF STIRRED MEDIA MILlS

J. Zheng

C.C. Harris

P. Somasundaran!,II Columbia University

New York. New York

For presentation at the SME Annual MeetingAlbuquerque, New Mexico - February 14-17 t 1994

Permission is hereby given to publish with appropriate acknowledgments, excerpts orsummaries not to exceed one-fourth of the entire text of the paper. Permission to print in moreextended form subsequent to publication by the Society for Mining. Metallurgy, and Exploration(SME), Inc. must be obtained from the Executive Director of the Society.

If and when this paper is published by the SME, it may embody certain changes made byagreement between the T echnicaJ Publications Committee al1d tl1e author so that the form inwhich it appears is not necessarily that in which it may be published later.

Current year preprints are available for saie from the Sf-iE, Preprints, P.O. Box 625002.Littleton, CO 80162-5002 (303-973-9550). Prior year preprints may be obtained from theEngineering Societies Ubrary, 345 East 47th Street, New York, NY 10017 (212-705-7611).

~:

,::

~

PRE PRINT AVAILABILITY LIST IS PUBLISHED PERIODICALLY INMINING ENGINEERING

1

operate on tbe same principle. The basic principles ofstirred media ID111s, in whidl impellers djspI~ themedia to cause particle fraCtUre. have been known for60 ycaq. The indU5trial applications of high-speedstirred media mitis have been greatly extended sincethe introchlction of Du Pont's 8sand mill-. Despitereports of superior performance [Wins, 1992] a.odlimited supportiDg data, detailed operating andperformance characteristics of stirred media ~ a.reproprietary: contrast this situation ~ith the freeavaiJablility of information conc;,emiDg tumbling mills.Published laboratory investigatiODS are few andincomplete and are (On~rned more with theperfonnance of the stirred mill. often as comparedwith tumbling and other mills, ratheT than on thedynamics of the mill and posslule S<:a1e-uprelationships. The present investigation aims to st'.ldythe ~r~ mptiond1arad;e risti~ of stirred mediamills in order to relate ~r draw with 10111dimensions, design. and operating variables, based onmill dynamics. by an approach developed from workon stirred reactors. Since the power required forcomminution can only ~ introduced into the mill viathe impeller, extemjve stirring tests have been carriedout. In order to limit the number of varied par'a1De.tCIs.stirring ~t.~ with grinding media or liquids or both,but without comminution, were performed during theinitial stages of this investigation.

Abstrad Power consumption of stirred ax-.diamills bu been studied by an approam developed fromwork on stirred reacton. Relationships between torquerequired 10 rotate b<)tb di~ and pin jmpeUersimmersed in dense partiallate media as a function ofspeed, impeDer and tank dimeO$ioos. aDd otherrelevant variables are evaluated. Data collected duringnumerous different experimental roudibOtlS areanalyzed The results can be S1lmmarized andpresented in the form of characteristic plots, generalequations and dimensionless group correlationsinvolving p<YNCr and modified Re}"DOlds numben.Special attention is directed towards the rheologicalproperties of the media, which is considered as non-Newtonian liquids and hence, the equation of JX>Weftaw liqui~ is employed. Procedure for estimatingparameters of effective ~ty and scale-upguidelines with respect to power CODStlmption are putforward.

1 latrodUdloD

Z Apparatu$ and ExperiDieatal

Technical innovations over the ~t severalyears in many industries such as meuillurgicai. mineral,ceramic, electronic, pigmenu, paint and lacquer,cl.emica1. bio-technology, rubber, roaJ and energy haveresulted in burgeoning demands for ultrafine ( micronand sub-micron size) materials with specific properties(Jimenez, 1981; Stehr, 1988; OnlmweDSe andFomberg. 1992]. The ~ energy (X)5ts involved inultrafine grinding and the stringent qualityspecificatious for the final products bave createdinterest in the development and impr(J\'elnents of fineparticle ~ction techniques.

Bulk production of fine particles is mostly8d1ieved by comminution methods. The types of millused in fine grinding operations inchIde tumbling,planewy, centrifugal, fluid energy, vibratory antistirred mil1s.1be tumbling mill, whicb is used mainlyfor the production of material in the sieve range. basbeen inlensivcly rcxarcbed Reliable estimates can bemade of mill power draw from information abuut milltype, dimcnsio~ loading and speed related by mean~of dyna.-nic and 5enli-empirical models [Harris ct aI.,1985). However, tumbing mill is very inefficient i~energy utilization [Somasundaran and Iin, 1972}, aIXiother methods have bcen sought for the production ofultrafine material. The stirred media mill, whichoperates at about an order of magnitude: higher powerinteD.\ity ( power per unit volume) tban the tumblingmill, especially has attracted attention because of itsreported bigh energy efficiency. ability for grindinginto the mkron and sub-micron range and tedu~dcontamination. On account of their growingimponan~ in recent years. there is a ne';4";d for basicresearch on this type of mill.

Stirr~.d media mills are ooUectively named torefer to a group of mills, such as Tower, sand. C..oBa1land Perl milk, which employ grinding media and

The ar1"~~ ri the experimental ~~ in the present investigatitm is mlistiated in Fig. 1.'(be driving mechanism was equipped withinterchangeable tittinp to accept a wide range of'impeller d~, and several tank designs and si7.eswere available so that this unit oould be convertedfrom a simple agitator to any kind of laboratoryvertical stirred machine. Three i)pical impeller desipare ~ in Figure 2 A strain gauge torqueme:aswiog ~cer and pho~ter ~re buiJtinto the driving mecl1anism. and .\peed variation wasobtained by means of a dc motor with a rectifier and

voltage regu1Btor.The ~ of f{XqUe am &1)eed ~~

was estimated to be about 2%, aIKi therefore the~(.y of power wu estimated to be better than S%. Power was calculated from the measured nettorque ( gross torque less idling torque) aDd speed( P=2JrN!' ). The entire torque mca.\uring assernb1ywas calibrated frequently by applying knC1ND torqueincrements under static loading conditions.

F"mt, stirring testS were carried out usingNe.wtonia.n liquids to determine the instrumentparameters. In the second part of the investigationspberi<:a1 glass grinding bea.<b with ditIerent diameterswere employed.

Visrosity of liqui~ wa.~ measured uswf;rotatioaai ~ters. Internal fk1'N patterns of

2

.

media/pulp and rotating impeller was ~WAmined usingstrotN>t3C and ~ delay. In order to observe the flowpatt.em of media/pulp, a transparent glass cylidricattank was u.~. Otherwise. steel grinding chamberswere ~ The tanks were immersed in a water bathfor temperature c:outroL

To improve the reliability of the experimentaldata a 1WD1ber of safeguards were obse~'ed: (1)temperature mntrol of the grinding chamber w~mHinmined to reduce viscosity clJang~ duringoperation; (2) to account for bearing losses, the idlingtorque was detennined; (3) long-term operation athigh speed with highly viscous calibration liquids wasavoided to reduce accumulation of entrained airbubbles. which alters viscosity.

gIy~rol and ~ In order to achieve 8nawroP riaterange of Reynol~ number, impeDer speed w-asincr~ stepwise from 250 to 1200 rpm. Tests werecarried out in the three mills with tiU'ee different typesof impeller. Fig 3 shows the test results for the threemills. Power numbers according to Eq. [2] are plottedvs impeller Reynolds numbers, Eq. [3). The slope ofthe lines is -1.

~ present Clperimeuts a>Dfirm that ~ }X1Netwnsumption of the impeller in a stined media millcan be cala1lated using Eq. [5). Different impellerdesigns result jn different C values in Eq. [5]. Forgiven operating conditions and geometrical data, thepower number can be determined as a function of theReynolds number. With the knowledge of the powernumber, the power consumption can be calculatedfrom Eq. [2). However, this procedure applies only tooperation with Newtonian liquids.3 Power CoDsumptlon with Newtonian Liquids

5 Power CoDswuption with mediaBecause of the complex motion in stirring

process in stirred media mills. dimel!Sional anaJysis [Rushton et aI., 1950] is used to establish relationshipsbetween power consumption and the controllingvariables. For a fixed stirrer geomcny the expressionused is:

Np = f I Naco N~ [1)

t where Np is the power mlmber. analogous to a dragcoefficient, and is defined:

Since an equation for the power consumptionwith Newtonian liquids is available. similar equationsfor the lXY"'er consumption with grinding media wereinvestigated. An assumption made by Weit andScbwedes [Weir and Schwedes, 1987] who use theNewtonian case by ronsidering grinding beads asinsens in the grinding machine is avoided in thecurrent work, which recognizes the non-Newtoniannature of the media in the stirred mill [ Inoue andN onaka, 1986 ] .

Considering the media as Non-Newtonianliquids. the shear Stress may be related to the shearrate by an equation of the form:

Np = P/pN30S {2]

NRe is the impeller Reynolds n1lmber:

a=Ky. (6]N. = NJ>:lp/p [3)

Np, is the Froude number:

NPr = N:O/g [4)

where K is called the consistency coeffici~nt and n thepower law index. liquids for which equation (6] islippropriate are called power law liquids.

Since the vis<:osity II at a particular shear ratey and shear stress C1 is defined by the equation

For 1amin~r stirring conditions ~ similargcometry. the relationships become: " = a/y (7J

Np ~ C/N.. [5] combining equations [6J and [7] gives

C is specific to the impeller/tank geometrytested but independent of scale. p=a/y.;;Kya-l [8]

The average liquid shear rate 'Y in an agitatedvessel can be related to the impeller speed N by theeqttation (Metzner and Otto. 1.957).. Results of Stirring Tests with NeMonian liquids

y=aN {9)In order to determine the C term foc apartiallar impeller design, a purely Newtonian liquidwas used for the tests. In the case of Newtonianliquid..~ the values ,: and p are well defined and,ben~ the power and Reynolds number can be easilydetermined by measuring the power comumption andimpeller speed during the tests. Test liquids used were

fwhere ~ ~ the impeller shear rate <X>DStant and can beevaluated for some .\imple geometries ( e.g. cylinder.cone and plate )

Combine equations (8} and (9) to give

IS = ~..IN..1 [It

..

~ 3.c~ This value of ~ may be incorporated in the~ Reynolds number;f~ ND2o ~-.Dsp [11]I N...~= - JL Ks.-l-

t The power number equation [5] may be

rewritten as"c-

;':c N ..q~~.e.J-1 [12]-~ r r ..1

.a

~&1ation [12) is a useful design equation if thevalues of n and ~l are known.

In order to determine the Bow index. weassume that the shear stress is direCtly proportional totorque:

a::8.,. [13)

': where 8 is the impeller shear stress oonstant; Combining equations (8). [9] and [Ll) gives

't" =.!.K 1N.~AN. [14)P

where

A.~Kc.-l (15]p

From equation [14J. a plOt of torque r versusimpeller speed N on log-log coordinates gives astraight line of slope D and the vllue of A can bedetermined from the intercept.

Equation [12] can be rewritten ~

N = CK~~~-L- {16]p ~-AD1p N2"'D2p

~i~I: where

! I=CKu.-l

I ~ Since n value is known, a plot of Np versus-j- ~D2p on log-log coordinates sh.ould ~e a straightI -: line of slope -1. and the value of I 15 obtained from the

'~ intercept Hence. Kct"t-i is obtained from rIco

, :; Therefore. effective viS<X>Sity caD be calculated,: acoording to F..q. [10].

I~e;:: p-cP.. +(1 -c)p,

KcynolOS DUmber:

~~~~

KcynolOS DUmber:

~~~~~

-:

I

~~~

I

~~

I.:: .:

'J~;:j,~,

~~

~

~J

~I;1;jt~;~;~

~

~

;I t

; :~: :,..

; :f

~

several rontrolled speeds, impeller and tankdimensions, geometrical designs, and other relevantvariables.

Fig. 4 aOO 5 present some of the pw of torquevs rotational speed. which show a number of di!tinctregions implying changing behavior. Observationthrough a transparent tank and also with stroboscopicjl1umiuation allows Ii description of the sequence ofe'Jents associ~te~ with the various regiom of the aJrve.Figure 6 p~ides a schematic summary: the system isbatch with a four.pin spindle immersed jn a media ofmonooize glass spheres in water with supernatant.Other relevant details are provided m the legend.

Before rotation ~ the tcxque iIx:Jeases thendrops sharply as rotation rommences (AB): this istransition from static tn dy11am1c frictiOJl and thetorque at point B is analogous to yield stress in non-Newtonian fluids. Thercafter, torque (region DC)jncreases with rotational speed and obserYat:ion showsthat the spindle arms channel thrwgh largelystationary media forming cavities at the trailing edge.At lower speeds the ca";ty fills with media but athigher speeds filling'~ not fast enough, so that aQ)ntinuous dJannel is formed. Towards the upper endof the DC region the entire media mass begjns torotate and the UPlX'-r layers oogin to levitate into thesupernatant resulting in a drop in solid concentrationand a sharp drop in media effective vi.scosity. Forexamplc, the Krieger high sbear equation [ jJ.J p, =(l-cjO.68)-I.!l ] [ Krieger, 1m I shows that a~tration decrease from 60% to 55% results in adrop in relative ~ty from 49 to 20. This drop inconcentration and consequently in viscosity a.cc:ountsfor the drop in torque CD. If there is no supernatantthe concentration does not decrease and me~ntiDui1y does not 0CQIf. 4~ still higher speeds themedia becomes further dispeIsed (DEF), and laterfully dispersed, attaining uniform ro~on (EF).FmaIly, the system develops a marked vortex and themt;dja tcJxk to ~tJifuge towards the waDs of ~ tank(FGH).

Because region EF is uniform and of knownconcentration, it is especially amenable to analysis.The other regiofL~ are less well defined.

The data. C'.an ~ be plotted as power( p ~ 2u N,. ) versus speed but in thi~ repr~tioo the

u-ansitiODS between the regions are not as dearlydefined ~ in the torque plot.

Since the full dispersion region EF is welldefined, the fol1owing discussion will be amfiued tothis region. In the case of full dispersion, density ofmedia is well defined, and is calculated using theequation

it

,,};",:ij~, IT,), Results of StirrinC Tests with GriDdlag Media

., ,~:' '

~ 'f

! ?cJ

When the density of solid particle p. and thedensity of liquid are given, the average demity is afunction of the volume &action of solid particles CoTable 1 shows some results calculated from Eq. [17].

I=,

t'age b OT .w0 UU:)J.:"O "UU"Rea Marvraer . UL>~>b~ruLU~~>Lb

4

Table 1 Relationship between pulp demity tIand VOlltmetric ronceotratioo C ~p-CXc8-iN-+1D'

The above procedw1e pmYictes a method fordetermining power consumption by a large scaledstirred media mill from small scale testS.

c(%) 60481.9L72

so

p (&l cmS)

S8 SS 524S 401.87 1.825 1.781.67S 1.6

1.75

8 Eft'ect of GrindiRg Media and ImpeDer Design onPower Coasamption

Note: c s 60% ~~~um solid concentration;p,=2.5 g,lan,; PI= 1.0 g/cm,

As shown in section 5, effeCtive ~ty can becalallated following the procedure for evaluatingparametCJ1. For the full dispersion oondition, theaverage density can be calallated from Eq. {17].Therefore, power and Reynolds numbe~ arecalallated "using above ~ity and density of themedia. .

Grinding media diameter and concentration,and impeller geometry were kept constant for theabove scale-up. Therefore, effects of changes ingrinding media and impeller design on powercomumption are discussed below.

Fig. 9 sb(,Ns the inftuenre of solid ro~tiooon the flow index parameter n. Circular symbolsrepresent the experiment data while the continuoustine shows the calculated relationship according toequation [20] correlated from the ezperiment data:

Fig. 7 presents an example of plots of powermlmber vs Reynolds number for tests with 4-pinimpeDers with the solid volume fraction a.~ parameter:the rorrelauon is approximated by a single straight lineof slope -1 for all concentrations studied.

cn=O.43(1-Vi

-0.71 PI

The relationship betWeen flow index n aDdooruistency K shown in Fig. 10 leads to the oonelationequation:7 Scale--up of Power ConsumptioD

log K . l.838n - 0.82 ~Certain SQ}c-up guidelin~\ can be put forward

on the basis of the above results. The method assumesaeomctricany similar miUs filled with identical grindingmedia.

Fig. 8 presents a plot of power nwnber V5Reynolds number for thrcc different diameters ofimpeller aM tank at oonstant solid oo~ntration: thefC5Ults can be approximated by one straight line ofslope -1. This result can be employed for scale-up.

1be power and Reynolds numbers for a smallunit operating with NeWtonian liquids can bedetermined experimentally. and hence, the geometricalterm C can be calculated using Eq.[5]. Stirring testswith grinding media are peTfonned with the same unitto determine n and ~t parametcn; and thus;effective ~ty. Average density for full dispersiona»nditions <:an be calallated using Eq.[ 17]. andtherefore, modified Reynolds number can becalculated using Eq.[ 11 J. The power numbers andhence the power consumption for the large unit can becalculated in the following manner.

Assuming that C, K. n and Q parameters remainCOnstant in scale-up. effective \tisco5ity can becalculated using Eq.[ 10]. The power number can becalculated mini Eq.[U], and rearrangement results inpower consumption for the large units

I

Based on the above n and K values, effectiveviscosity ~ be calculated using Eq.[lO). A plot of,viscosity vs solid roncentlaUon is shown in Fig.11 for~ different impeDer speeck. The amtimJ(n~ line is aplot of values waJ)ated from the ~on equationII. oalOOf'1{ 1-(c/0.68)} -1.82 (a)Inp8re with Krieger high

shear equation ).Also, it is seen from this figure that ina'easbJg

solid co~tration will increase effediYe ~ty veryo\1Iarply above about SO percent (:Ooccntration. '(bcmaximum concentration of tbe current system is 00per<=ent. Sin<-.e power consumption is proponional to~ty. the higher the amcentration the higber m thepower comumption. It is valid for aU grinding mediatested in this investigation and illustrated in Fig. 4.

Next, the effeCt of grinding bead diameter wasinvestigated at otherwise constant conditions. Theresult\ obtained for glass beads of 4.4,2.05, 1 and 0.45rum in diameter are sIKJWn m Fig. 14 which representste..~ts with a 4-pin impeller while Figures 13 and 14show the results with the disc and I-pin impeller,

separately.In all the above cases, flow index n depends OD

impeller design but media size does not affCct the flowindex. while consistency K inaeases with inaeasingparticle size, which results in increased power

consumption.

5

.9 ConelusionRefereIICe$

l

2.

3.

..

(1) Power consumption of stirred media millscan be descn"bed in terms of power number andmodified Reynolds number.

(2) Geometrical design facton <:an bedetermined by using the power number and Reynoldsnumber rorrelalion evaluated Wij.ag Newtonian 1iquids.

(3) The torque versus speed curve dUplaysseveral regions marked by sharp transitions. A regionof unifonn concentra.tion has been studied in detail.

( ") The effective viscosity of the stirred mediacan be determined using the non-Newtonian power lawequation combined with the Reynold, Dumber.

(5) Relationships between conc:entration, flowindex, consistenc.y aDd effective YiS(X)6ity have bc;cnevaluated for a number of design geometries. mediaparticle s~ and solid ooncentratioDS.

(6) The dimensionless form of the: relationshipsleads to guidelines for SQIe.up and an example ofpower consumption prediCtion is provided. s.

6.Ackuowledcement

The support of this reSf'.arch project by theDepartment of Interior's Mineral lDStitutes programadministrated by the u.s. Bureau of Mines G 1125249is gratefully acknowledged.

1.

8.

Symbols used 9.

AeCdD

10.

11,hIKnNNp,NpN..pTQ&Y#4#4c#41PPIp.

0f

12.

Hams. c. C, Schnocic, E. M. and Arbiter, N..1985. -Grinding Mill Power ConsumptiOl1, .

MineraJ ~in8 and Tedmolgax Review. I,pp. 134-148Inoue, T. and NoDab. M., 1986. "Production ofCoal Water Slurries by Wet Grinding in theAgitation MilI." 10th International Coai~-~.a ~ E.a~~1, (~~Ja, V. ~Aug. 31-Sept. 5, pp. 40-55IimeneZy J. L S.. 1981, -A Detailed Study onStirred BaIl Mill Grinding;" PhD Dissenation,Meta1luf&Y Dept., University ofUtab, Salt LakeCity, Utah, USAKrieger, L ~ 197}., ~heoJogy of MO1DJ~Latices,. Ad!ID. Colloid Interface SQ.. 3, pp.111-136Metzner, A. B. and Otto. R. E.. 1957, A I. Ch.E.J~3,3Orumwense. O. A. and Forssberg. E.. 1992-~~ aIxi Lt)~ Gri~A ~Survey," Mineral Pr~ and ExtractiveMetalluliX Revicw- Vol. 11. pp. 107-1Z7.Rushton-I. H.. ~ti~ E. W.. and Everett, RI.. 1950, -Power Olaracteristics of ~.fixinSImpellers, Part I,. OIem. EDI. Pr~.. 46, 395Rushto~ J. R. Costicb, E. W.. and Everett, H.J., 19S0, "Power Characteristics of MixingImpellers. Pan 2..~m,-~- rmar.~ 46, 467Soma9~-!'aD, P. and Un, L J..I972, "Effect ofthe Nature of Environment on Comminution~ -.Ind f.DIo Olein- Proc. ~ ~- II,pp. 321-331Stehr, N.. 1988, -aecent Developments inStirred Ball Milling. - internAtional JQUmal Of

MineraJ ~inl- 22, pp. 431444Weit. H. and Schwedes, J., 1987, "Scale-Up ofPCNfer Consumption in Agitated Ball Mills, -

Chen\.. Rnl- TedJ~~l. 10, pp. 398404Wills, B. A.. 1992. "Mineral ProcessingTed~,c 5th F..didoo. Pelga1D(Jn Press, NewYork

I'; .

;°'j

O>nstantVol1lIDetric concentration of wlidshnpeller geometry constantMedia particle diameterDiameter for disc-impeller and leugtlt fOf pm..impellerImpeller immersion in tankConstantConsistency coefficientPower law indexImpeller rotatiOllal speedFroude numberPower numberReynolds numberPowerTank diameterImpeller shear rate constantImpeller shear stress constantShear rateViscosityViscosity of pulpViscosity of liquidDensityDensity of liquidDensity of solid particleShear stressTorque

6

O.J ,-, .', . - T~~ ,-c(X) b(cm)

0 55 3.5. 50 3.6~ 45 2.0. 40 1.0 0T. G7t;tQ 00 0D; 6.~cm 0d: O.4Smm 0 0

. 0

,

0.2

Ez-\AI

g-0 0

oe0ivvv ,..

V V vV vvvvVv y'

y.yy

0.1

..,.

Experimental apparatus yFig. 1anangement 0.0' . . .

. .,00 1000 1500 2000,"'n.LER SPEm (RPM)

0 ~~,,?Fig. 4 Typical examples of torqueversus impeller speed for 4.-pin impeller atdifferent solid concentration and impellerimmersion in tank~-"'LM ""IMMLD

Fig. 2Studied

T)pical impeller desigDS

'.

1~ - - -., . - - . . -~

IMPD.LER D{ OL) C0 4-PIN 8.5 94. DISC., 88V I-PIN 7 34

1.0 . . . . I

c;~ .0: l4cm

t -

T; 2O2cm

d; 0 45mm ,

0.9

0.8 d!,

()

0

"E:'z--w

g.-

~ .,0'°Qo. ,~,

..0

~ ?9;

\ h"=<10..1 -. . . , '-

0 200 400 600 ~ 1000 1200I~EU.£R SPEED (NIM)

v . \,.

0.7

0.6

0.5.v

0..vv

L- ' f .V:V ~

, 10 100

~NIJMm:R

Fig. 3 Power number versusReynolds number for three differcntimpellers in Newtonian liquids

Fig. 5 A iypicaJ Clamp)e of torqueversus impeller speed for 4-pin impellershowing several tramitions

f

7

D.O'ELlnSPEED

AS SI8Ii: &3 ~ ~ ~ B ~.~ to . Jiekt ~ .~ ~~~~--_C .a> 8Iedia bcIia U! ~ 8110 tile ~DE ~J;.,,«~-~~EF -'a 5IDy ~ -1mifiXWI 81 ~.ioa

FG~aI~

Fig. 6 Schematic summary of regions dispiayed by torque versus impeller speed ~"'VCin media with superna."tant liquid

10. . . - . - .-

D(em) T(cm)0 6.5 9.7. 10 17V 1-1 20.ad: O.45mmc: 50~~

"J~

~z

~\oJ~

~

"Go 1 I ---

0.1

10010 1000 100c100

RONOLDS NUU8ER REYNOlDS NUiABE:R

Fig. 7 Power Dumber versusReynoids Dllmber for 4-pin impeller atdifferent solid concentrations

Fig. 8 Power number versusReynolds number for '-Pin impeller atdifferent impeller and tank diameters

8

10 . . . - ~--

d(lnm)0 4.4. ~.OSV 1.0'" 0...5D: 6.5cmt: 9.7cmc: 50~11: 0.98

1.8 r-.~-"...ir

1.6

I ,1.4 ~

\oj~~:J%

~'oj~

~

cJi~~ 1.2

~1.0

I1 ~I ~ "~ ","...

0.8 0"" ~ICCG

0.110 100

.REY~OLDS NUUSf:RFig. 12 Power number versusReynolds number for 4-pin impeller atdifferent media panicle sizes

- - - - , - - ~ ~- - --

d(mm)0 ".4.2.05

v 1.0T 0.45D: 7cm

.. T: 12.8cmfl.: 0.2~ 60%

L"_I-0.50.3 0.4 0.5 0.6 0.7

COtolCENTRATION. c. Fig. 9 Flow index venus solid

amcen:ration ( conditions as in rig. 7)1OCOO -. ! . . ,10

1000

~

t"z

t-:~~u

100 ...0 ~!oJm~;:)z

~~

...8'"

~

~~ ~'°\.

1

0.11-10

1.8.

flow

.0.1 - . . Ij_~!_-0.6 0.8 1.0 1.2 1.4 1.5 .

flOW INOEX. n

Fig. 10 Consistency versusindex ( coDditions as in FJI- 7 )

70 . . .--0 1440Tpm. 900rpm 0

__~_.I ~..100 1000

REYNOLDS NUMBERFig. 13 Power number versusReynolds number for & impeller atdifferent media vanide sizes

---~to

d(mm)0 4-4.2.05~ 1.0.0.45D: 7cmT: 12.~n: 1.57e: 60~

~40l:

~fI'$

20

Q:;Win~;:)%

Qc.

~0Go.

eol

~l

30~

~10 I

I

1

~

~

0.110 100

0 ' '-L--0.3 0.4 0.5 0.6 0.7

CONC(HTRARONFig. 11 Viscosity versus solidconcentration for two different impellerspeeds ( oonditioos as in Fig. 7)

REYNOlDS tfW8£RFig. 14 . Power number veTA1$

Reynol~ number for l-pin impeDer at~:u__. 00 o. .,-.-