Solids Processing

Selecting theProper Mill forYour ProductUnderstanding breakage behavior is crucial in miiis

Kerry JohansonMaterial Flow Solutions, Inc.

Milling is a mechanisticallydriven process that hreakssolid material into smallerpieces. Selection of the

optimal mill is a daunting task thatoften leaves engineers reljáng on ven-dor suggestions to decide which millis right for their job. This article ad-dresses a methodology to score andrank the various mills for use with aparticular material.

In milling, a materials are brokenup due to a few basic breakage mecha-nisms. Some particles tend to split,creating smaller particles that areone-half to one-third the size of theoriginal particles. This type of break-age is termed fracture. In some cases,particles break as corners are knockedoff or subsurface cracks form particlesthat are considerably smaller than theoriginal particles. This type of break-age is termed abrasion. Some materi-als require many impacts or stress-strain events to induce breakage. Thisis termed fatigue and can result inthe formation of both small and largeparticles. The rate of breakage alwayschanges during a fatigue-driven event.Some particles require large strainsbefore breakage occurs. These largestrains may be due to plastic defor-mations, such as in the case of plastic,rubber and ductile metals, separationof fibers and internal structures asin biomass, or due to non-linear elas-tic effects, such as with tissues andcomplex polymers.

The premise for this article's millranking comes from the fact that eachmill induces a unique set of impact orstress-strain events, or both. If a par-ticular material is sensitive to break-age due to stress-strain events, then

mills exploiting stress-strain eventswill be the most efficient choice forparticle breakage unit operations.Likewise, if the material is sensitiveto breakage due to impact, then millsthat exploit impact events are the bestchoice for this material. Materialssensitive to fatigue require mills thathave repeated stress-strain events orrepeated impact events to break par-ticles. Thus, an analysis of the numberof breakage events in a particular millhas some merit in choosing the bestmill. Finally, materials that requirelarge strains to break must be cou-pled with mills that can induce largestrains to effectively break particles.For the purpose of this article, this willbe described as breakage due to shear.We will start by describing t3rpicalbreakage events in various mill typesand assign each mill a score on a scaleof 1 to 10 based on breakage due to im-pact, stress-strain, fatigue, or shear. Ascore of 1 indicates a low propensityof breakage due to this event. A scoreof 10 indicates a high probability ofbreakage due to this type of event.

Following this scoring and rankingsystem, the article will present sometests that can be used to quantify aparticular material's propensity tobreak due to a particular mechanism,and then suggest which mills wouldbe best for use with these materials.It should be noted that general classesof mills will be considered for this arti-cle. The breakage in a specific mill willbe due to the details of operation forthat particular mill. This article sim-ply provides a guide, and the engineermay need to adjust these rankingsbased on a unique mill of a given t3rpe.Likewise, some materials are anisotro-

Actual rupture strength

Ultimate strength N^

Yield point

\

Strain

FIGURE 1. Resilience equals the areaunder the stress-strain curve up to theelastic limit

Ultimate strength

Elastic limit

\

Strain

FIGURE 2. Toughness equals the areaunder the stress-strain curve up to therupture strength

pic and have different breakage ten-dencies in different directions, makingthem subject to breakage events dueto several mechanisms depending onhow the particles are introduced to themill. Again, this article is to be usedas a guide, and the exact behavior willdepend on the material of interest. Inany case, much of the breakage behav-ior depends on the detailed structureof the particle. Some of these effectswill be discussed, but this article is notintended to be a comprehensive analy-sis on the subject.

Material propertiesFor the purpose of this discussion, itis useful to define some engineeringterms common to the study of materialmechanics. For a material to break, itmust pass through all of the stages ona stress-strain diagram. When mate-rial is either compressed or stretched,it undergoes an elastic transition.Relieving stresses under this condi-tion causes a complete rebound in thestrain imposed on the material. Atsome point, the stress becomes greatenough that the material cannot sup-

CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2013 4 7

Solids Processing

port elastic behavior and mustdeform plastically, resulting ina permanent deformation ofthe material. The energy corre-sponding to the onset of plasticdeformation equals the areaunder the stress-strain curve upto the elastic limit and is calledthe resilience {R), as seen in Fig-ure 1. Straining the material farenough will result in the failure

FIGURE 3. The orientation of a crack FIGUREis important in determining material mine thebreakage behavior

4. S-N fatigue curves are used to deter-stress a pure material can withstand

of the material and cause hreakage.The energy associated with this break-age equals the area under the stress-strain curve up to the rupture strengthand is called toughness (T) (Figure 2).We can define a hrittleness number(BR) based on the ratio of the resil-ience to the toughness as descrihedin Equation (1).

BR = - (1)T

A hrittleness numher close to 1 sug-gests that the material will hreak atstrain conditions very near the elasticlimit. This denotes a hrittle failure,suggesting that the material may hesuhject to breakage hy impact condi-tions. If the hrittleness number ismuch less than 1, then particles hreakafter significant plastic deformationsand require significant shear to in-duce hreakage. These particles willlikely he insensitive to hreakage hyfracture. Particles with a low hrittle-ness numher may experience fatigueand can hreak after repeated stress-strain or impact events. Material canexperience repeated stress events andthese tend to open or close cracks inthe particle, depending on the orienta-tion of the crack relative to the direc-tion of impact or application of stress.Figure 3 illustrates this phenomenon.If the impact is perpendicular to thecrack, then the crack closes during im-pact. Conversely, the crack opens if theimpact is in line with the crack.

During every cycle, the regionnear the tip of the crack experiencesstress values in excess of the elasticlimit, causing the crack to grow in-crementally. There is t5rpically littleto no control over the direction of theimpact or stress application relativeto the direction of the crack, so onlya portion of the impacts or stress-loadings actually lead to crack growth

TABLE 1. SCORINGJAW CRUSHER

Jaw crusherRank for different types ofFractureFatigueAbrasionShear

FOR

materials9

3

1

1Score on a scale from 1 to 10 (10 best)

and hreakage events. As long as thestress local to the crack tip exceedsthe elastic hmit, then hreakage overtime can occur. This suggests thatrepeated stress applications that donot exceed the ultimate strength, butare above the elastic limit, can causeparticle hreakage.

Traditionally, charts showing stressapplied versus number of repeated cy-cles (called S-N stress fatigue curves)have heen used to determine the num-ber of life cycles at a given stress apure material can withstand. Figure4 shows an example of an S-N fatiguecurve. If the maximum yield-stressvalue is applied, then one cycle wouldsuffice to hreak the material. How-ever, if the stress is lower, then manyload cycles are required hefore the ma-terial would hreak. The measurementof S-N curves is relatively simple forpure materials, but is much more dif-ficult for particles. For this reason,fatigue characteristics are usually de-termined using a population-balancemodel, which will he explained laterin this article. Although some experi-mental work does exist for heing ahleto measure particle-hreakage andstress-strain behavior on the particlelevel, the more common method ofdealing with fatigue events is througha population-balance model.

Ranking the millsMills can he evaluated hased on their

TABLE 2. SCORING FORCONE CRUSHER

Cone crusherRank for different types of nfiaterialsFractureFatigueAbrasionShearScore on a scale from 1 to 10 (10 best)

9

3

21

usefulness to induce fracture, fatigue,abrasion or shear-hased hreakage.The remainder of this article will dealwith ranking and scoring various milltjrpes. A method to measure a particu-lar material's sensitivity to key hreak-age mechanisms is also presented.Comhining the knowledge of mullingaction with the material's sensitivitywill help engineers select the propermill for their process. Below are somegeneral mill categories, along witheach mill's evaluation.Jaw crusher. A jaw crusher is a typeof mill unit that is used as a primarycrusher. It works hy receiving parti-cles from a feeder and pinching themhetween two jaw-plates positioned toform a converging-plane flow hopper.One jaw-plate is fixed and the otherjaw-plate pivots ahout a fixed point,moving in a circular cam-like motionahout an eccentric hearing (Figure 5).Generally, a drive-wheel attached tothe fly-wheel aids crushing. The jawhreaks the particle into two or threesmaller particles. These particles dis-lodge from the jaw and fall until theyare caught hy the converging set ofjaws and the pinching process is re-peated. The pinching process contin-ues until particle fragments are smallenough to exit the gap hetween thejaws. The final particle size producedhy the jaw crusher is controlled hy thisgap. Typically, this type of crusher canhandle particles as large as 1,000 mm

4 8 CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2013

FeederFly-wheel

Fixed jaw

Northstone

FIGURE 5. A jaw crusher induces breakagebased on primariiy fracture and fatigue

Aubema

Function of impact hammercrushers

FIGURE 7. A hammer mill features afreely rotating hammer-shaft arrangement

TABLE 3. SCORING FOR HAMMERMILL

Hammer mill (with screen)

Rank for different types of materialsFracture

Fatigue

Abrasion

Shear

8

4

3

2Score on a scale from 1 to 10 (10 best)

in diameter and generate particles assmall as about 13 mm. The number ofbreakage events for any brittle parti-cle entering the crusher can be foundusing Equation (2).

Gapln(2) + 1 (2)

This equation relates the maximumparticle size (Dp), the gap spacing(Gap) and the number of breakageevents (n). In general, the number ofbreakage events for this type of millis between four and seven. Jaw mo-tion is relatively slow so that only onebreakage event is generated every fewseconds. This suggests that particlebreakage in this type of mill unit willnot experience fatigue effects. Becauseof the rotary cam operation, there issome shear as the movable jaw trans-

FIGURE 6. A cone crusher rotates, forcingmaterial into a closing gap, thus causing theparticles to break

Sturtevant

Separator

\\

Grinding ° i1j lchamber ^""^JH

Productoutlet

• S ~ ^ | i Feed ^^ inlet

FIGURE 8. In an impact mill, pins or plates cause ma-terial to fracture

lates material in the downward direc-tion. However, this shear effect is verysmall and the major mode of break-age is a direct compression, leadingto fracture of the material. The actualstrain imposed by the motion of thejaw is about 5 to 10%. Thus, a materialwith an elastic limit at strains greaterthan this 5 to 10% will not break inthis type of mill. Materials that haverupture strength at strains greaterthan 5 to 10% will require many cyclesof the jaw to break, making jaw crush-ing impractical as a milling operation.This leads to the scores in Table 1. Formaterials that are sensitive to frac-ture, a jaw crusher is an acceptablemill, hence its score of 9.Cone crusher. The cone crusherworks on a principle similar to thejaw crusher. It can handle materialup to 300 mm in diameter and pro-duce particles around 13 mm in diam-eter. It is typically used as a primarymilling unit.

In a cone crusher, the inner cone ro-tates on an eccentric shaft causing thegap between the outer fixed cone andthe interior moving cone to change asthe cone rotates (Figure 6). Duringrotation, material is pinched betweenthe closing gap, causing the particles

to break into two or threepieces. Most of the actionin this tjrpe of mill is di-rect compression result-ing in fracture, but someof the action can induce ashear force since the gapcloses slowly. This shearforce can induce someshear and, as a result,this mill has a slightlyhigher abrasion score (2)than the jaw crusher'sscore of 1 for abrasion,as seen in Table 2. Likethe jaw crusher, the conecrusher also has an excel-lent score for fracture-based breakage.Hammer mill. The ham-mer mill consists of a ro-tating shaft with rods orhammers that rotate athigh speeds. These ham-mers are either free toswing or firmly attachedto the rotating shaft (Fig-

ure 7). The hammer shaft arrange-ment freely rotates within a housing.An inlet at the top of this housing al-lows particles to enter the mill. Theparticles undergo a series of ham-mer impacts as they travel throughthe mill. An outlet at the bottom ofthe housing allows milled particles toleave the system. Normally, a screenjust above the outlet retains largeparticles in the hammer-mill system,where they continue to be impacted byhammers until the particle size is suf-ficient to pass through the screen, butin other cases, there is no screen andmaterial entering the system is ex-posed to hammer impacts only duringthe time it takes to fall from the inletto the outlet. Sometimes particles areretained in the screen holes whilehammers pass by. In this case, someparticles in the mill will be subject toshear. Particles caught between thehammer and the housing will also besubject to shear during milling. Some-times, particles are trapped betweenthe hammer and the housing andare dragged along the surface of thehousing, causing abrasion. Some milldesigns create a closer tolerance be-tween the hammers and housing nearthe exit. This causes additional shear

CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2013 4 9

Solids Processing

and abrasion. This type of mill typi-cally handles particles about 400 mmin diameter and will create particlesaround 13 mm in diameter. This mill'sbreakage-inducing behavior is rankedin Table 3, showing that it is a goodchoice for products that are sensitiveto fracture.Impact mill. An impact mill consistsof three zones, as seen in Figure 8. Inthe first zone, air enters the mill. Thisair is used to classify the milled mate-rial after the milling process.

The second zone is the milling zone.Impact mills have either plates orpins that rotate at high speed whileparticles are fed into the milling stagethrough an external feeder. The impactof the pins or plates causes some of thematerial to fracture, creating smallerparticles. If pins are used, then theangle of the trajectory during impactcan be variable, as some of the impactswill be glancing blows and some will bedirect-contact blows. Glancing blowstend to induce abrasion effects whiledirect-contact impacts induce fractureevents. There is very little opportunityfor shear in impact mills.

The third zone in the mill is a classi-fier stage. In this stage, gas is pushedor drawn out of the mill at a controlledvelocity, entraining particles of the ap-propriate size with the gas stream. Ifparticles Eire not small enough to exitwith the carrier gas, they fall backinto the grinding stage and are sub-ject to repeated impacts until theyare small enough to be carried bythe induced currents created by thegas stream.

These units typically handle par-ticles around 1 to 2 mm in diameterand can produce particles as small as5 micrometers (pm). Depending on thetype of impact mill, glancing blows cancomprise 30% of the total impacts, re-sulting in abrasion events. The otherimpacts are nearly all fracture-induc-ing events. Because of the classifica-tion section, this mill can induce manyrepeated-impact events. Thus, materi-als that are sensitive to fatigue can beused in this type of mill. These obser-vations are summarized in the rank-ings in Table 4.Horizontal air-jet m,ill. A horizontalair-jet mill uses high-velocity air in alined, cylindrical chamber to induce

Feed funnel

Compressedfeed air orgas Inlet

MIcronized product outlet

Vortex finder

Grinding chamber

Compressedgrind air orgas

Sturtevant

Replaceableliners

Grind air orgas manifold

FIGURE 9.In a horizontalair-jet mill, ahigh-velocity airstream is usedto breai< apartmaterials

Impact box for measuring degradation potential

FIGURE 10. This schematic of an impact degradation box shows Vs of an impactcycle. As the box moves left, the material moves relative to the box and eventuallyimpacts on the opposite side of the box

TABLE 4. SCORING FORliVIPACT MILL

Impact millRank for different types of materialsFracfureFatigueAbrasionShear

7

8

4

1

Score on a scale from 1 to 10 (10 best)

TABLE 5. SCORING FORHORIZONTAL AIR-JET MILL

Horizontal air-jet millRank for different types of materialsFractureFatigueAbrasionShear

3

8

71

Score on a scale from 1 to 10 (10 best)

milling of granular materials. Thematerial is fed into the mill with ahigh-velocity gas stream. This inlet islocated with a tangential entry to themill so that the fiow of gas is directedaround the circumference of the mill.The circular motion keeps the par-ticles with the highest mass pinnedagainst the mill's circumference. Pe-riodic gas-injection nozzles that directthe pinned particles toward the centerof the mill are spaced evenly aroundthe mill perimeter, creating a series ofimpacts around the perimeter duringthe milling operation (Figure 9). Gasentering the mill exits through thecenter of the milling cylinder. Thus,centrifugal forces throw particlesagainst the wall and drag forces pullparticles toward the center of the cyl-inder. This resulting classification al-lows only the finest particles to leavethe system. The majority of impacts inair-jet mills are glancing blows againstthe cylinder wall and collisions withother particles.

Air-jet mills can handle particlesabout 1 mm in diameter and can cre-

ate particles as fines as 0.5 pm. Glanc-ing blows result in abrasion eventsand the collision with other particlesresults in fracture events. Because ofthe classification, this mill can inducerepeated breakage events and materi-als sensitive to fatigue can be used inthis mill, leading to its score of 8 forfatigue in Table 5. No shear is possiblein this style of mill, hence its low scorefor shear.

Tests and modelsThere are many other mills that couldbe ranked, including vertical air-jetmills, ball mills, roller mills, stirred-media mills and impact-jet mills, butthese are not discussed in this article.The next piece of information requiredto select the proper mill is to deter-mine to which milling mechanisms aparticular material is sensitive. Thiscan be done by using the aforemen-tioned population-balance model.

Ideally, one would like to exposematerial to pure impact events, purestress-strain events and pure shear orcutting events. The main goal is to de-

5 0 CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2013

100n

O 80

¡70§60| 5 0 -5 401 30" 2 0

10

Cumulative particle size for

1

10

-o - Os

tàIJ

4/

/y

f-Jr

r• _•«

CaO m

Fateria

n

100 1,000 10,000Particle diameter, \¡m

^^20 s -o-300 s

Breal<age rate for CaO material0.10000

0.0 200.0

«Intial breakage

400.0 600.0 800.0Particle size bin, pm

• Final breakage

1,000.0 1,200.0

FIGURE 11. With an impact velocity of 5.4 m/s, the cumula-tive particle size changes over time

dm, UV{i,j)-Sj • mj \-S¡ -m-

Unbroken

ooo "oooo

Broken

OO O

o o o

oooo

2

3

4

TABLEÓ.SIZE BINS INFORMATION

Size Bin #

1

2

3

4

5

6

7

MinimumSize (Mm)

991

501

253

123

66

32

3

MaximumSize (|jm)

2584

991

501

253

123

66

32

FIGURE 12. The breakage-distributionfunction serves to track particle-break-ing events

termine what the dominant breakagemode is for a particular material whenexposed to these events. For brevity,only the response to impact events willbe considered.Impact breakage test. As a case study,this article will consider calcium oxide(lime; CaO) particles with a maximumparticle diameter of approximately2,500 Jim. Several impact breakagetests could be performed on this mate-rial. For this study, the lime particleswere placed in an impact box, which wasshaken at a controlled velocity. In such atest, the material within the box movesfreely relative to the box and eventuallythe material impacts on the oppositeend of the container, creating an impactcondition, displayed in the schematicin Figure 10.

Each oscillation cycle creates two im-pacts on either end as material is thrownagainst the ends of the box. During theseimpacts, the particles react with the boxwall and with other particles inside thebox. These repeated impacts furtherbreak the particles. The frequency ofthe oscillation governs the impact veloc-ity and the time dictates the number ofrepeated impacts.

FIGURE 13. The breakage rates (S) are much different after 60seconds of repeated impacts

• Cumulative density: R(x, t)• Breakage distribution: B(x, y)• Specific breakage rate: S(x)

The breakage-distribution function(B) is an indication of which particle-sizebin the particle fragments will end upin during breakage. B(x, y) describes thefraction of mass transported from y toxupon breakage ofy. B is often describedas a matrix of numbers indicating thefractional distribution of transfer tosmaller bin sizes than the original. Thenumbers in this matrix represent thefraction of material transferred to ad-jacent particle-size bins during process-ing. The B(x, y) function plays the roleof a weighting function or stoichiomet-ric constant in a reaction. This break-age behavior is portrayed schematicallyin Figure 12.

The S(x) function represents theprobability that a given particle impactor contact will result in particle break-age. It represents an overall rate of oneparticle size breaking into any adjacentparticle-size bins. S functions are therate constants for degradation from oneparticle size to all others [3]. Equationsgoveming the rate of transfer betweenparticle size bins can be written forboth the mass and cumulative densitydistributions, shown in Equations (3)and (4) respectively.

d"hi')_ C...IA

Material was placed in this impact boxand shaken for extended periods of timeup to 5 min at a velocity of 5.4 m/s. Anal-ysis times were selected to correspond to0,10, 20, 60,120 and 300 seconds. Aftereach analysis time, a particle-size distri-bution was measured on the materialwithin the impact box. This generated atime-sequence set of particle-size distri-butions, as seen in Figure 11. Note thegeneral shift to finer particles at largerimpact times.Population-balance model Popula-tion-balance modeling provides a meansof identifying critical particle-breakagemechanisms through the computationof breakage-selection coefficients [1].The first step in using this population-balance model is to divide the particle-size-distribution function into regionscalled particle-size bins. These bins arechosen so that an adjacent bin containsparticles that are roughly half the size ofthe next larger bin, as shown in Table 6.The modehng method monitors the rateof transfer between different particle-size bins. Since the population-balancemodel is at the heart of understandingbreakage rates, it is useful to definesome parameters and fimctions thatdescribe breakage [2].• Mass density: m(x, t)

dt

(3)

dt

For the purposes of this article, it is

CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2013 5 1

Solids Processing

Breakage for CaO material - initial selectivity

4 5 6 7Attrition particle size bin #

• Bin1 • Bin 2 oBin 3 oBin 4 • Bin 5

Breakage for CaO material - final selectivity

4 5 6 7Attrition particle size bin #

• Bin 2 oBin 3 DBin 4

Bin 5Bin 4

Bin 3Bin 2

Bin1

• Bin 5

FIGURE 14. Breakage selectivity functions (B) for breakagebefore 60 seconds

FIGURE 15. Breakage selectivity functions (6) for breakageafter 60 seconds

assumed that the rate constants arenot a function of time (i, in seconds)and will remain constant. This sim-plifies the analysis somewhat. How-ever, many other assumptions arealso possible [4].

The S and B functions are foundsimultaneously from the solution ofEquations (3) and (4). Since masscannot be destroyed, the sum of theB functions for any particle-size binmust equal one. This solution of theabove equations is not a trivial task,but it provides a great deal moreinformation concerning the break-age phenomena experienced by bulkmaterials. Choosing the particle-sizebins such that each adjacent binsize consists of particles one-half thesize of the original bin suggests thatmovement of material to an adjacentbin would be interpreted as splittingthe original particles in half If the Bvalues indicate a large fraction forthe next adjacent bin size, then frac-ture of primary particles is occurring.However, if the B values indicate thatone or more size bins adjacent to theoriginal size have low fractions fol-lowed by large fractions distributedin the finer size bins, then abrasion islikely occurring, as abrasion createsfine particles directly from larger-sized particles.

The probability S function is a valuethat identifies the likelihood that acollision will result in a breakage ofparticles. This probability is a functionof the size of the particles, and typi-cally shows an increasing functional-ity between the particle size and the

probability that a given size of particlewill break. The solution of Equations(3) and (4) can be calculated numeri-cally, but can also be approximated byEquation (5) if the rate constants areassumed time invariant [3].

(5)

Time sequence particle-size data forCaO were used with Equation (5) todetermine the B(x,y) distribution ma-trix and the S(x) breakage-rate func-tion, shown in Figures 13-15. For thepurposes of this article, B values aremost relevant, since they reveal howmuch fracture or abrasion may occurwith the material. However, S valuescan give an indication of fatigue. If thebreakage rates (S values) at the begin-ning of the testing are low and thenincrease, then the material is verysensitive to fatigue events.

The CaO breakage analysis suggeststhat lime material is best describedby a dual-rate breakage. Equation (5)still applies, but must be implementedin a piecewise linear fashion to com-bine the solution of two constant-rateequations. One equation set will con-sider the first 60 s of breakage and usethe initial conditions at zero seconds.The other rate equation will considerbreakage after 60 s and use as initialconditions the particle-size informa-

tion after 60 s of breakage. The initialbreakage rate is much higher than thefinal breakage rate, as seen in Figure13. This suggests that lime may not besensitive to fatigue.

B values were also computed forboth of these breakage rates, shownin Figures 14 and 15. These data showthat about 38% of Bin Size 1 will ini-tially break in half to create Bin Size2 particles; 54% of Bin Size 2 particleswill initially break in half to form BinSize 3 particles and 100% of Bin Size3 and Bin Size 4 materials will breakin half to the next lowest bin size, indi-cating that initial breakage of CaO isdue to significant fracture events.

However, the story changes afterbreakage has occurred for a period oftime. Figure 15 shows the breakageselectivity after 60 s of impact milling.In this case, with the exception of BinSize 2, there is a shift to create par-ticles more by abrasion events. Fromthe Bin Size 1 material, 99% splitsinto particles that are one fourth thesize of the original particles. All ofthe Bin Size 2 material becomes BinSize 3 material. However, only 18%of Bin Size 3 material shifts to be-come Bin Size 4 material and 44% ofBin Size 3 material becomes fine BinSize 7 material. The shift to abrasionis also very evident in the Bin Size 4and 5 particles.

It is possible to average the fractionalB values that shift one particle-size binto determine an overall fi-action that issensitive to fracture. Likewise, the over-all fraction of material breaking intoparticles one fourth the size or less can

5 2 CHEMICAL ENGINEERING WWW.CHE.COM NOVEMBER 2013

Initial Final Averagebreakage breakage breakage

H Fineabrasion

I Mediumabrasion

• Fracture

FIGURE 16. Abrasion and fracture arethe dominant breakage mechanisms forlime (CaO)

be determined by averaging the respec-tive B values. In addition, the averagefraction that shifts to create the finestmaterial can also be computed from theB value data. This gives an indication ofthe amoimt of fracture and abrasion thematerial may be sensitive to (Figure 16).

Cumulative breakage for CaO material

100 .90 r8070

~ 50

350 400

* Bin 1 =: 991 to 2584 Mm

• Bin 4 = 123 to 254 |jm

• Biii7=16to33Mnl

• Bin 2

ÁBin5 =

501 to 991 |im

66 to 123 pm

ÁBin3

Bin 6

= 254 to 501 (im

= 33 to 66 \im

FIGURE 17.Cumulative particle-size distributions asa function of time forlime (CaO) subjectedto repeated impactsat 5.4 ft/s impact ve-locities

Initially, almost 70% of the lime break-age is due to fracture with only 10% dueto true abrasion events. However, after60 s of milling, 33% is due to fracture and28% is due to abrasion. Lime is sensitiveto both fracture and abrasion, but itssensitivity is much greater for fractureevents. Now that the modes of breakagehave been quantitatively determined,the optimal mill can be selected. In thiscase, the optimal mill will be the onewhere the fracture events induced inthe mill are occuring at about 1.5 timesthe frequency of the abrasion events. Ofthe mills considered in this article, the

impact miU rankings most closely matchthe propensity for lime to break. Thus,an impact-style mill is a good choicefor milling this material. It should bepointed out that this is a major consid-eration in the selection of a mill, but notthe only consideration. The tendencyof material to adhere to mill surfacesshould also factor in mill selection. Theexact impact mill presented above hasmany moving parts that may be coveredwith fine adhesive material. If lime ma-terial is adhesive, then another impact-style mill, such as the air-jet impact mill,may be a better choice.

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Solids Processing

As a check of the population-balancemodel analysis, the cumulative break-age data points were plotted along withthe computed cumulative breakagefunctions from the population-balemcemodel (Figure 17). This plot indicates agood agreement between the breakagedata and the values computed from thepopulation-balance analysis.

SummaryMills can be qualitatively ranked basedon their tendency to induce fracture, fa-tigue, abrasion or shear by examiningthe milling action. Mills where classi-fication is part of the milling operationcan induce fatigue events. Mills where

glaincing blows of particles againstsurfaces are dominant cause abrasionevents. Mills where impacts or stressapplication are more direct result in in-duced-fracture events. Particles or ma-terials where toughness is much largerthan resilience require müls with a lotof shear to induce particle breakage. Thepopulation-balance model can be usedwith mill tests to deduce the dominantbreakage mechanisms for a given ma-terial. The optimal mill is then selectedby matching the dominant mechanismswith qualitative ranks based on the ten-dency to induce fracture, fatigue, abra-sion or shear. This simple analysis canaid engineers in selecting the right mill

References1. Epstein, B., Logarithmico — Normal Distribu-

tion in Breakage of Solids, Ind. Eng. Chem.Vol 40, pp. 2,281-1,191,1948.

2. Sedlatschek, K. and Bass, L., Contributionto the Theory of Milling Processes, PowderMetal. Bull, 6: 148-153., 1953

3. Kapur, P.C. and Agrawal P.K., Approximate

Solutions to the Discretized Batch GrindingEquation, Chem. Eng. Science, Volume 25,Issue 6, pp. 1,111-1,113, 1970.

4. Bilgili, E. and Scarlett, B., Nonlinear Effectsin Particulate Processes, Nonlinear Anaiysis,Volume 63, Issues 5-7, pp. el,131-el,141,Nov. 30-Dec. 15, 2005.

5. Broadbent, S. and Calcott, T., J., Inst. Euel,Vol 30, pp. 13-15,1957.

for the job the first time. These criteriafor miU selection can be combined withother information about the bulk mate-rial, such as adhesive tendencies andparticle size, to help select a mill that isfree from troublesome operation. •

Edited by Mary Page Bailey

AuthorKerry Johanson is chiefoperations officer for Mate-rial Flow Solutions, Inc. (7010NW 23 Way, Suite A, Gaines-ville, Fla., 32653; Phone; 352-379-8879; Cell 352-303-9123;Email: matflowsol@bellsouth.net), the consulting firm hefounded in 2001. He alsospends time researching atthe University of Florida Par-ticle Engineering Research

Center. He began his career as a laboratory tech-nician with Jenike & Johanson, before movingto JR Johanson, Inc. in 1985, where he becamechief technical officer for the company. He hasauthored over 40 technical papers, which havebeen published in numerous technical journalsinternationally and has presented at many in-dustry seminars. He has also developed a gradu-ate course on powder flow and technology atthe University of Florida. Johanson holds a PElicense and has a Ph.D. in chemical engineeringfrom Brigham Young University.

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