An analysis of the influence of grinding aids on the breakage process of calcite in media mills

analysis

of the influence

of grinding

aidson the

of calcite breakage process

inmedia mills

and R. PARAMASVAM 2P. B. RAJENDRAN NAR 1

1Powder

TechnologyDivision,Microfines,72PondyBazaar,T.Nagar,Madras 600 017,India

2Madras 600 036,IndiaDepartment of ChemicalEngineering,Indian Institute of Technology, Received 27 August1998;accepted4 December 1998

of calcium stearate,boricacid,and silica asadditivesfor the fine Abstract󰀀The effectiveness

grindingof calcite in media mills,i.e.ball, rod, andvibrationmills,wereexplored, by following

collected at various time intervals from 15 s of the size distribution of the ground product grindingII

to 30 asize feed. While calcium stearate could achieve a modified min,usingsinglegrindingrateup

factor of 1.5 inthe ball mill and had indicated an optimumconcentrationformaximumperformance,bothboric acid and silica remained inert materials without indicating any influence. It was also found thatthepresenceof calcium stearate duringthe initial stagesofgrindingintroduced a retardation effect on the grinding process, with the product being coarser in comparisonwith the blank sample.To overcome this retardation effect for the breakage process inducedbytheadditive,it was found preferabletodelaythe introduction of the additive byaround 5 min. Analysisof the breakage process was carried out by estimating thebreakage parameters using the G-H solution for the size-discretized batchgrindingequation.It was found that while the additive reduced the breakagerates of coarser size fractions duringtheretardationperiod,ithelpedtosignificantlyincrease the breakagerates of finerparticlesduringthe finer stagesofgrinding.Thehigherbreakageratesat finer stagesofgrindingandthe reduced agglomerationobservedduringthisperiodindicate the acceptabilityof the alterations in the flow behavior of the millchargeas the possiblemechanism for the additive in media milling.Keywords:Mediamills; additive; retardation; delay;G-Hsolution;breakagerate.

NOMENCLATUREABi,jFi (t) Gi (t) Hi (t) KiMi (t)

coefficient

forthebreakageratefunction

cumulativebreakagedistribution function percent passing at time t

G value for ith interval at time t Hvalue for ith size interval at time t

breakagerate for ith size interval

ith interval at time t mass fraction retained on

cumulative

224Gi (t) HI(t)R; (t) tUIt.xt;Z; (t) Greeka13yAyi

coefficient for thebreakagecoefficient for thebreakagecoefficient for thebreakagecoefficientfor the breakagecoefficient for the exponentialcoefficient for the exponential

rate function

distribution function distribution function distribution function functionfunction

G value forith interval at time t Hvalue for ith interval at time t cumulative

size i retained at time t weightfraction of

functionfunction

time of grindingcoefficient for the exponentialcoefficient for the exponentiali th size interval

j th size interval

the combined variable in the G-H back-calculation

scheme

1.INTRODUCTION

Onetechnologicalterm that has becomesynonymouswith the cement industriesover the last quarterof a century,and that is becomingmore and more prominentinmanyother comminution operationsinvolvingmediamills,is'grindingaids'.Morecommonlyreferred to as grindingadditives,theyarecertain surface active chemicals,oftenpolarinnature,addedto the millchargein small percentagestoimprovetheperformanceof the mill.

Even with the two majorconstraints that the benefits of usingsuch chemicals

have no detrimental effect have,theynotonlyoutweightheir cost but should also

either on the downstream processesor on the finished product;avarietyoforganic,

industrialinorganicandpolymericmaterials have alreadyfoundwide-ranging

applications[1].However,the actual mechanism duringthebreakage process isinterpretedin different ways:

various research groups.(1)To assist the processof crack propagation, proposed by

and Rabottino [2].(2)Topreventcrackhealing, proposed by Ghigi Rehbinder[3].(3)To reduce the surface energyof the freshsurfaces,proposed by

West-(4)To reduce the hardness of the crystalline particles, proposed by

wood et al. [5].Somasundaran(5)Toimprovetheflowabilityof the mill charge, reported by [4],as

the various researchgroupsofAustin,Frosberg,Fuerstenau,Roseproposed by

and Moothedath.

225

on the breakagestrengthor hardness of the particles,thenstead of concentrating

the flow behavior last of the above mechanismsis based on the effect of additives on

Iand Vedaraman [6]estimatedof the mill material charge.Recently,Paramasivam

the flow characteristics of the product ground in the presenceofadditives,and

intended emphasizedtheacceptabilityoftheflowabilitytheory.Thepresentwork is

toidentifythe interval of grindingwhen such additives are actuallyeffective,byanalyzingthebreakage parameters.

ANDADDITIVE

2.GRINDING

SYSTEM:MACHINE,

MATERIAL,

Alaboratoryscale ball mill of 140 mm diameter,150mmlength,providinga

20 mm diameter,soas to steel balls of totalmillvolumeof 2300 cm3,with 176

speedof rotation of 96 r.p.m.was the occupy50%of the mill volume,andwith a

experimentalmillusedfor the study.

its medium hardness,the work was calcite because of The feed material chosen for

tendencies at fine brittlenature,minimumagglomerationsizes,availabilityinpure

conditionand,aboveall,itscrystalstructure,makingithighly polar due to the ionic

and [C03 ]2- . The feed material used was of singlesizebondingbetween Ca2+

interval,-2000to+ 1 600 pm.

The additive chosen for the studywas calcium stearate,[cH3(cH2)16cOOhca,which is a fattyacid derivative and is characterized byalong-chainmoleculeof17 carbon atoms and an active carboxylic group (COO-)at the polarend. With

for the agroupelectro-negativityofaround 4.1 [7]andexposedcarboxylic group

to a polarmineral like calcite,thebondingbetweenthe two is verytenaciousand

Thethe molecules can actuallyisolatethe solid surfaces of the calcite particles.

Ieffectivenessof boric acid,alayerlattice structured compound,and silica powder,

a flow activator,were also explored.as beingreferred to

3. EXPERIMENTATION

The feed materialchargewas fixed based on the optimumconditionssuggestedfor

the the void volume of the ball charge,which in ballmilling,i.e. 50% of present

fedmaterial was case is equivalentto 330 gof the singlesize feed of calcite. The

to the ball mill as the blank sampleandthe size distribution of the ground product

15 wasmonitored at s,30s,Imin,3min,5min,10min,20minandupto 30 min

ofgrinding,usingstandard test sieves,DN 4188. The same amount of material was mixed thoroughlywith 0.25% byweight(0.825g)of calcium stearate and theproductsize distribution followed for the same time intervals. Similar experimentswere carried out with 0.5% of silica and 1.0% of boric acid. 3.1.Grinding results from the ball mill

The size distribution of the ground product at various time intervalsupto 5 min of grinding,as cumulative percent passing, aregivenin Table 1 for the blank sample

226

and the sample ground in the presenceof0.25% of calcium stearate. t can be noticed from the data that,upto the grindinginterval of 5 min,the size distributionsof the ground product of the blank samplewererelativelymorefiner,both in termsof the topsize interval disappearanceand the percentof fines produced.From this periodonwards,asignificantchangeinthe size distribution of the additive samplewasobserved,as shown bythedistributionplotsinFig.1.Theground product sizedistribution of the additive more fine comparedtosamplewasbecomingmore and Table 1.

Product size distribution and cumulative percent passing

Figure1. Product size distribution.

227

the blank sample,as the grinding proceeded to finer levels. Table 2shows this more

minofgrinding.It can be the productsafter 30 clearly,with the size distribution of

seen that while the amount of fines produced by the blank samplewas around 59%,theadditivesamplecouldproduceas much as 83% for the same periodofgrinding.Thegradual change inthepercentageof fines producedwith the time of grindingisshowninFig.3.

Theretardingeffect or the the additive noticed duringthenegativeinfluence of

initialstagesofgrinding prompted anexperimentalrun in which the introduction ofthe additive was delayed by 5min,until which periodthe material was groundas a

the additive can be noticedblanksample.Theeffect of this delayedintroduction of

from the size distribution data givenin Table 2and from FigsIand 3. Theproductwas finer than that of the samplewith the additive introduced initially.Table 2.

Cumulativepercentpassing,after 30 min of grinding

*

Additivedelayed sample.

Figure2.Disappearanceoftopsize interval.

228

Figure3.Percentageof fines produced(ballmill).

of additiveconcentration.Figure4. Effect

Theinfluence of the concentration of calcium stearate on the grinding perfor-

mance was 0.1 to 0.5% by weight. analyzed by varyingtheconcentration from

min Figure4 shows the effect in terms of thepercentoffinesproducedafter 30

ofgrinding.Anoptimumconcentration of around 0.4% was noticed for maximumperformance.

229

Regardingthe effectiveness of boric acid and silica,the results were discouraging.

them producedsize distributions similar to Throughoutthegrinding period both of

size distribution thatof the blank sample, except for some statisticalvariations. The

of the productafter 30 min of in Table 2 shows around 57-58% grinding given

other words,bothboricacid and silica passing40pmwith these additives. n

remained inert materials.

AspointedoutbyFuerstenau[1],since most of the surface area data reportedinthe literature were obtained byairpermeabilitymethods,there is every possibility thatitmay magnify the benefits ofthegrindingaids when assessingthe results in

new grindingrate factor is termsof new surface area created. To overcomethis a

definedas,

......

and based on this definition,thegrindingratefactors achieved bythe above- mentionedgrindingconditions after min of grindinginballmillare:30 Calcium stearate (0.25%)initialCalcium stearate (0.25%)delayedBoric acid (1.0%)Silica(0.5%)3.2.Grinding

resultsfromthe rod mill

=1.410= 1.510 = 0.965 =0.985

I

To confirm the effectiveness of calcium stearate as an additive in the context of other media milling systems, similarexperimentswere carried out in a laboratory

steel rods of 20 mm diameterrodmill(150mmdiameter,300 mm lengthwith 14

and 295 mmlength,withaspeedof rotation 90 r.p.m.,with 500 gof feed as blank sampleand 0.4% calcium stearate as the additive).

Comparedto the ball millresults,it was found that the retardation periodduetothepresenceofthe additive was much longerand the tendencycontinueduptoa 10-20 mingrindinginterval.Only during thisgrindinginterval did the ground

in productsize distribution of the additive samplebecome finer comparisonwith

theblanksample, resulting inafinerproductafter20min.Inotherwords,theadditive is interferingwith the normal breakage process for a considerable periodofgrinding.

As in the case of theballmill,thedelayedintroduction of the additive by5minresultedinamuchfinerproduct. Figure 5 shows these variations inperformanceinterms of the percentageof fines produced plotted againstthe time of grinding.Theretardationperiod,thecrossingoveroftheperformanceofthe additive sampleafter

ofgrindingand the finer productsduetothedelayed entry ofthearound 16 min

additive are clearlyvisible from these plots.Thegrindingrate factors estimated for the initial anddelayedintroductionofthe additive were 1.11and 1.23 after 20 minofgrinding.

230

3.3.Grinding results from the vibration mill

The same set of experimentswasrepeatedin a laboratory-scalevibration mill

mm diameter and 82 mm length,(Siebtechnik,Germany),with two chambers of 126

filledwith120 steel balls of 20 mm diameter,soas to occupy80% of the mill volume,vibratingwith an amplitudeof2-3mm,with 250 gof the feed as blank sampleand0.4%of calcium stearateasthe additive.

Figure5.Percentageof fines produced(rodmill).

Figure6.Percentageof fines produced(vibrationmill).

231

the blank and additive samples,Figure6 shows theperformancecharacteristics of

the time of grinding.plottedin terms of the percentageof fines produced against

The initial retardationperiodor the extentof interference due tothepresenceoftheadditive was lower comparedto either the ball millor rod mill. Thiscan be due to the difference in the motion of the the vibration mill grindingmedium in comparedtothatintumblingmills.Theexperimentalrunwithdelayedadditive was not carried out as the initial periodofhinderingwas not significant.Thegrindingrate factor achievedin this case was 1.21 after 30 min of grinding.

4. ANALYSIS OF THE BREAKAGE PROCESS

Theground product size distribution data fromthe ball mill was used for further analysisof the breakage process. Itcanbe noticed from the data inTable1andthetopsize interval disappearance,showninFig.2,that most of the feed material

the 5 mingrindinginterval,and the rate of disappearanceof the disappeared by

topsize,asindicatedbytheslopeof the plots,was more for the blanksample.Duringtheinitialstagesofgrindingasignificantfractionofthe additive remains unadhered to the host the ofenoughparticlesurfaces because of non-availabilitynascent or freshlybrokensurfaces,and this fraction can influence the movement of the ball and material chargeinside the milling system. Estimation of the breakageparameterscanprovidemoreinsightinto these alterations in the breakageprocess,be it the retardation in the initial stagesor the enhancement duringthe finer stagesofgrinding.

5.ESTIMATIONOF THE BREAKAGE PARAMETERS

The size discretizedbatchgrinding equation writtenasthecumulative distribution retainedand the G-Hschemeprovidinganapproximatesolutionfor it [8]can be made use of to estimate the breakageparametersof the process,i.e. the breakagedistributionparameter,B;_j , and the breakagerateparameter,K;.S.l.Breakage

distribution

parameter,

Bi,j

theBass batch grinding equation can be rewritten to Theapproximatesolution for

reduce the order of the time polynomialas:

allsizes,withH;/2as the slopeand the equationcan be plottedasstraightlines for

andG;as the intercept.Asinglesize feed R, (0) = 1 and a plot of -1 / t In Ri (t) againsttime will providetheGandH;values.Inthis case:

232

). Figure7. Ground productsize distribution (ballmill).

). Figure8. G-H plotfor the additive sample(0-5mininterval).

can be estimated and by revoking theUsing equation (2)the set of B;,values

of the parameterthe entire spectrumofB¡,ivalues can normalizability property

be arrived at [8, 9].

Figure7 shows the ground product size distribution of the blank samplefordifferentgrindingintervalsupto 5 min fitted with third-order polynomials.TheG-Hplotsfor these size distributions are plottedinFig.8as -1 / inRi (t) versus

233

Figure9.Breakagedistributionplot.

timeofgrindingfor all particlesizes from 1000 to 40 pm, and from these straight

were estimated lineplotstheGoandH;valueswere estimated. The Bi,lvalues

usingthesevalues and K j estimatedfrom the topsizedisappearancekinetics shown inFig.2. Table 3 givesGi, H; andBi, j valuesestimatedfor all the size intervals.

andFigure9 shows the breakagedistributionplotted against dimensionless size

the estimated Bi, j it can be noticed that from these plotsaswell as from Table 3 I

two powerfunctionssuggested by valuescansafelybe fitted with the sum of

Austin[9].

inshown The G-H plotsof the additive samplefor the same time intervals are

of the can be noticed fromFig.2 that the rate of disappearanceFig.10.While it

the case oftopsize interval in the presenceof the additive was much lower than in

the blank sample,Fig.10explicitlyindicates the vagariesin the breakage process,

values in especiallywithparticlesinthe coarser sizeranges showing negative

the initial stagesofgrinding.It can also be noticed from the Gi(t)andHl (t) values,

relativelylower than that of the blank samplegivenin Table 3,that the values are

duringthis initial stagesofgrinding.5.2.Breakage

rateparameter,

Ki

topresumethat the additive molecules are Just as it is beyondcomprehension

individual particles,it is also not helpingto accelerate the breakagebehavior of

the natural breakagebehavior of particles.possibletoexpectthattheycanretard the

234

not Presumingthat the additives are influencingthebreakagedistributionof the

same irrespectiveof whether the particles,inother words Bi,jvalues remain the

additive,thebreakagerateparametersgrindingwas carried out with or without the

fordifferent intervals of additive delayed samples grindingof the blank,additive and Table 3.

G and Hparametersfrom the G-HplotsinFigs7 and 10

Figure10.G-Hplotfor the additive sample.

235

wereestimated

byback-calculation

[10],usingthegoverning equation:

whereZi (t) = -(C¡ +H¡(t)R¡(t))

and the Gi (t) andHi (t) values are estimated foragiventime interval from the G; (t)-H; (t) plots.

Figures11and12show the G; (t)-H; (t) plotsforthe blank andadditivesamplesfor the grinding period from 5 to 30 min. The C ¡ (t) andH; (t) values for 5-10,10-20 and 20-30 minwere estimated from these plots. Using thesevalues and theground product size distribution for the correspondingintervals,thebreakagerateparametersof various sizes of the three samplesat various time intervals were back-calculated. The estimated values of K;for0-5and 5-30 min are giveninTable 4.

Variation of

thebreakagerate with dimensionless particlesize for the blank samplefor different grindingintervals is

shown inFig.13.t was found that these variations can be fitted with powerfunctions of

the form: ValuesofthecoefficientsA and a estimatedfordifferentgrindingintervals from thebreakagerateplotsinFig.13 are giveninTable 5.

It can be noticed from the plotsinFig.13that,as the periodofgrinding proceeds from coarser to finer ranges,thebreakagerate of particles present inthemillchargegraduallyreduces,so that both the Aand a values decrease with the increase inthe

Figure11. G-H plotfor the blank sample(5-30mininterval).

). 236

Figure12. G-H plotfor the additivesample(5-30mininterval).Table 4.

BreakagerateKifor 5-30 min interval

time of grinding.Thisdecrease in the inmediabreakagerate in finer grinding stages millingwasalready explained byearlierworkers as beingdueto the cushioningeffect of the fine particlesgettingaccumulated in the mill charge,andalso due to thetendencyofthese fine particlesto form agglomeratesandto coat the grindingmedium.

237

Figure13.Breakagerate for the blank sample(0-30mininterval).Table 5.

Powerfunction coefficients A and a for the breakagerateplots

Figure14 shows the same variations of the breakageratewithparticlesize for the

the 1-3 and 3-5 minalongwith that of additivesamplein the grindingintervals of

and a coefficients for the additive blanksamplefor 0-5 min forcomparison.The A

samplesinthesetime intervals are givenin Table 5.

It can be noticed that thebreakagerateplotsof the additive sampleshow visible breaks after the coarser rangesof the particlesize.While the breakagerates are much lower for the particlesin this size range compared to that for the blank sample,itcan be seen that the slopea is verylow for the first section of thebreakage plot, indicatingthat there is only marginal decreaseintheKivalues with particlesize.

238

Figure14.Breakagerate for the additive sample(0-5mininterval).

Figure15.Breakagerate for the additive sample(5-30mininterval).

Inthe case of the second section of the breakage plot withrelativelyfinerparticlesizes,it can be seen that the plotislyingabove the plotfor the blank samplewithboth A andavaluesbeinglower.The lower breakagerates of the coarser particlescan be explainedin terms of the retardation effect of the free additive molecules presentinthemillcharge.Being

239

I

I

Figure 16. Breakage rate for the additive delayedsample(5-30mininterval).

lubricativebyitsverynature and characteristics,this unused fraction of the additive can increase thechances of particles slipping out from the active volume during

the nippingand can also interfere with the motion of the grindingmedium inside

mill.Onecanexpectthisphenomenonto continue at least until most of the additive molecules find nascent host particlesurfacesforadherence.

Figure15 shows the breakagerate versus particlesize for different time intervalsupto 30 minfor the additive sample.It can be noticed that the two sections for thebreakagerateplotcontinue to persistinthe 5-10 min interval and disappearafterthis time interval,when most of the coarser sizes have undergonesizereduction. t can also be seen from Fig.15 that after 20 min of grindingthebreakagerate of veryfineparticlesdecreases,with the plotfor the 30 min grinding falling below that of the 20 min plot,whichmaybe due to the cushioningeffect.However,thebreakagerates of all these sizes were much higherin the entire time interval of 5-30 min comparedto that of the blank sample,as shown bythe data in Table 4.

breakagerate with particlesize for Figure16shows the same variation of

the additive delayed sample. t can be noticed that the breakagerateplotisastraightline,without the two sections observed in the case ofthe additive

Afteronly30minofgrindingthecushioningeffect was indicatedbysample.

thissample.Eventhen,thebreakageplotis still lying marginally above the 20 min plot,whereas in the case of the additive sampleit had already dropped down below the 20 min plot.This enhanced behavior of the additive delayedsampleincomparisonwiththe additive samplecan be attributed to the absence of the initial retardation periodand the effective utilization of the additive when introduced. Since the material has blank alreadyundergonesize reduction as a

the host samplefor 5 min,enoughnascent or freshlybroken surfaces of particles

I

240

Figure17.Breakagerateduring20-30min for different samples.

Figure18.Variation of coefficients Aand a (blanksample).

was introduced. Figure17were available for the additive from the moment it

min of shows the breakagerateplotsof the three samplesafter 30 grindingfor

bettercomparison,andtohighlightthe effect of the additive and the delayed

thebreakagerates of introduction of the additive on particlesatfinergrindinglevels.

the variation of the coefficients A and aofthebreakagerateFigures18-20 show

the blank and was found that both inthecase of parameterwith the grindingtime. t

241

and a (additivesample).of coefficients A Figure19. Variation

Aanda(additivedelayed sample). of coefficients Figure20. Variation

additivedelayed samples these coefficients can be related by exponential functions

of the form:

A = U eÀt

The coefficients of these functions,Table 6.

and

ex = V e'Pt.

(6)

aboveplots,aregiveninestimated from the

242

Table 6.

Coefficients for the exponentialfunctions of A and a

It can be seen from Fig.18 and Table 6 that the values of the coefficients and remainednegativefor the blank sample throughout thegrinding period of 30 min. Inthe case of the additive sample,as can be seen from Fig.19,thevariations of bothAand a did not follow anyspecifictrend and their values varied from interval to interval. This sort of behavior bythe additive sampleis due to the vagariesinselection of theinitialstagesandsubsequentenhancementparticles during duringthe finer stagesofgrinding.

For the additive delayedsampleboth the coefficientsÀ and cp werepositive

value throughoutthe 30 min grindinginterval,althoughafter the 20 mininterval the

of h was found to decrease. n other words,noinconsistent behavior was exhibited bythe same additive when introduced after allowingthe material to undergo partial size reduction as a blank sample initially. Hence,to achieve maximum effectiveness of the additive duringthe batch grindinginmediamills,it is advisable to delaytheintroduction of the additive byat least 5 min.

6. CONCLUSION

an effective additive for the fine (1)Calciumstearate is grindingofcalciteinmedia

enhancement in mills,with the extent of grinding performance depending on the

typeof mill chosen. Both boric acid and silica had no influence,and behaved as inert materials. itsterminologyan additive is meant to aid the (2)Although by grindingprocess,

there exists a distinct interval duringtheinitialstageswhen the additive actuallyretards the processandthisperiodof retardation varies with the typeofmill,with the maximum for the rod mill. the additive to overcome the effect due to initial (3)Delayedintroduction of retardationyieldedbettergrinding performance, quantified in terms of a modifiedgrindingrate factor. even eliminate the tendencies for (4)The additive could reduce or agglomeration

andcoatingof the grindingmediumandmillwall,observedduringthe finer stagesofgrinding.

(5)Analysisofthebreakage process, by estimatingthebreakage parameters using

the Bass batchgrindingmodel and the G-Hsolution for it,showed that

243

the coarser size thepresenceof the additive reduced the breakagerates of

fractionsand increased thebreakagerates of finerparticles,the latter beingmoresignificantduringthe finer stagesofgrinding.

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