Comparison of some different methods for measuring particle size using microscopically calibrated glass beads

Comparison of Some Dierent Methods for Measuring Particle Size Using Microscopically Calibrated Glass Beads C. M.

HUNT

AND A.

R. WOOLF

ZnsU~~fir Applied Technology. Narionol Bureau of Smndards.Boad&r. cokx (U_SA.) (R~vcd

No-k

SUMM_4RY Measurements of particle size distribution by the microscope and by a number of other methods -were cornpar& using samples of glass bends from a singIe blended batch as the reference material The other methods included a Coulter counter, electroformed sieves, the Andreasen pipette. and the Roller analyzer. Surface average particle size calculated from microscopic and L.ea-Nurse air-permeability measurements were also compared_ As an independent check of diameter measurements w3h the microscope, compmisons were made with an interferometer, using fibers drawn from a melt of the some glass_ These comparisons afiorded a? opportunity to assess some of the sources of error in each of themethods Dz@rences between the averages of results oh tained with the microscope and those obtained kth the Coulter counter, the Lea-Nurse apparatus, the Andreasen pipette as well as the interferometer were compar&le in magnitude with the normal statistical variations inherent in the methods themselves However, small systematic biases were observed_ Agreen?ent between results by the microscope and the Roller analyzer was satisfkctory, although the latter is subject to greater uncertainties than the other methods investigated_ Disagreements were obtained with jke electroformed siw which passed more material than predicted from the size distribution by the microscope Key words: air ehUriation, air permeabiiity, Andreasen pipette, calibrated glass bead& electroformed sieues. Couiter cowztm* microscopic size measuremen& par&le size measuremen& lNTRODUCTION are many me&ads of measuring particle size distriiution, and new ones continue to appear_ However- it is a common observation that methods There

12 196.8)

based on different physical principles do not always give closely agreeing results It is desirable, therefore, to compare results obtained by different methods in order to analyze differences and recognize some of the sources of error- Furthermore, some methods such as electtonic counters are usually calibrated with materials of known size distribution In order to carry out intercomparisons and calibrations it is necessary to have reference materials Polymer latexes have provided useFul reference materials in sixes below 2 fi and they are also available in larger sizes as polydisperse sample&- However, latexes have some limitations_ and additional reference materials are desirable, particularly in sixes above 2 F (*) The present paper describes the calibration and use of S-30 p glass beads as a reference material for the intercomparison of methods for measuring particle size-_ The use of glass beads as a reference material is not new’-“_ However. they are now available commercially in sixes below 30 F Some of the advantages of glass beads are that they are predominantly spherical, and the transformation of number data to volume or weight distriiutions is comparatively accurate Also_ compared with some particulate materials glass beads are relatively insoluble in most liquids Furthermore. since they are somewhat surface tempered and have no cleavage planes, they possess good impact strength and can withstand most mixing and dkpersion treatments without damage One of the disadvantages of these glassbeadsistheirsurfkereactivityinthepresence of atmospheric moisture Special precautions are requiredtoinsure their complete dispersion &so. some of the beads contain gas bubbles, and this requires density corrections if methods which

10

C. M.

HUNT,

measure distribution by weight, volume, or according to sedimentation rate are to be compared with data obtained with the microscope. Furthermore, a small fraction of the beads are not perfect spheres, and in these cases some approximations are required. Finally, the transparency of the beads may not be desirablefor use with certainoptical methods such as turbidimetry_However, the advantages of the use of glass beads outweigh the disadvantages in that they are us&l with many methods of measurement_ In the present work, the microscope was the primary means of determining particle size. However, the apparent diameter of a small sphere, as measured by the microscope, can vary somewhat depending upon the optical conditions under which it is mcasurcd4-s. Therefore,values obtained by the microscope were compared with those obtained with the interferometer using small glass fibers drawn from a melt of the same glass. Size distributions of the glass beads were then determined by a number of other methods. These included the Lea-Nurse apparatusg, Coulter counterlo, Andreasen pipette’ l, electrofo,%ed sievesr*, and Roller analyzerr3_ These determinations provided a basis for estimating the uncertaintyin particle sire values obtained by each of the methods and for examining some of the sources of error.

A.

R. WOOLF been previously described by Moore, Stark, and Cahnr S_ A Coulter counter (Model A) with a 140 p aperture was used. The supporting electrolyte was 4% sodium chloride. The Lea-Nurse apparatus has been previously describedg. The one used in these measurements was constructed in the laboratory, and had a sample cell 254 cm in diameter into which a sample bed 1.84 cm in depth was compacted Electroformed sieves (Buckbee-Mears) with nominal openings 5, IO, 20 and 30 p were used in the sieve measurements. Each sieve was 3 inches in diameter. pipette (Fisher Scientific Co. desAn Andreasen ignation 14-232) was used in the sedimentation analysis The sedimentation chamber had a volume of 550 ml and the sampling pipettea volume of 10 ml. The air elutriationanalysis was performed with a Roller analyzer (American Instrument Co_ designation zW%51). The interferometermeasurements of glass fibers were made with a Zeiss interferometer using a filteredhelium vapor light source having a dominant wavelength of 0.5876 p It had a PuIfrich viewing system so that light could be directed down upon the specimen between two optical flats and reflected back up to the observer. The principle of the method has been previously describedr4_

APPARATuSANDMATERiAL3 GLA!LSBEADSANDTHElRlXEATMENT

measurements were made with a Zeiss Standard PolarZng Microscope equipped with a 50 x objective of numerical aperture 0.85, a KZihler condenser with a nominal numerical aperture of 13 in suitable mounting medium or slightly l~thanunityinair.andanocularfittedwithafilar micrometer. Light was furnished by an auxihary sodium vapor lamp. The bead and bubble diameters were determined with the aid of a calibrated filar micrometer. The data were digital&d by means of a photoelectric pulse generator which was connected coaxially with the micrometer drum and converted angular drum movement to pulses These were fed to a counter and printer. The pulse generator has The

microscope

l cutainco Xenalsandmstrummtsareida&kd in this pqcr in order to spcci@ the expcrimmtal procedure adequately-Such idaxtificationdoes not imply recommmdation orindo rscsncntby the Nztional Bpnan of Sm nor does it im@y that the cquipmt or material idcntiliai is masarily thekstforthcpurpose.

According to the manufacturer, the glass beads (Minnesota Mining and Manufacturing Co. size 986) were of window glass composition. Most of the beads had diameters between 1 and 30 & They were treated in the laboratory to remove readily soluble matter and beads containing very large gas bubbles. To accomplish this, a dispersion of beads in water, containing 1% of a buffered phosphate detergent (Calgon) as a dispersingagent, was allowed to settle for several hours The concentration of beads was approximately 25% by weight. After settling, the supernat~tliquidandfloatingbeadswereremoved_ This prccess was repeated two more times. Most of the remaining water was removed by vacuum filtration and the beads were redispersedin 95% ethanol This was removed by filtration followed by vacuum drying All of the dried beads were passed through a U.S. No. 325 sieve, blended, and packaged in approximately 9ooo bottles Powder TechmL. 3 (1969) 9-23

11

PAFCTrcLE-srzE MEASUREMEKT ANALYSIS

MIcRosmPxc

Satnpling and ?neosurelnents One hundred bottles of beads were selected for microscopic meassements at intervals t-hroughout the bottling process_Beads were taken from several places in each bottle and mixed They were mounted

About 6% of the particles by number (or an estimated 4% by volume) were not spheres_ These ranged from nearly spherical particles to elongated particles and hagments of hollow beads Where these occurred, the volume was estimated, and for

purposes of computation. the estimated diameter of a sphere of equal volume was recorded

in clear epoxy (Shell Epon 828) resin into which

approximately 7% by volume of diethykne triamine

Computmio7ts

activator had been thoroughly mixed A drop of the mounting medium was sampled before addition of the beads as a check for spurious objects or other effects in the medium itself, and this blank together with a drop of the sample suspension, was mounted under separate cover glasses on the same slide. One hundred beads were measured per slide, selected from at least four fields making a total of lO,OCK_r beads. Each slide represented the beads in an individual bottle, and each bottle of beads is considered as a sample in the subsequent discussion. About 25% of the processed beads contained gas bubbles Of these, about half contained bubbles large enough to alter the density of the bead by an amount estimated to be 25% or more Where bubbles occurred, void diameters were measured and corrections applied as described in the next section. TABLE

1: MCRCSCOPICALLY OBTAISXD MJHBER DlsrRmbnos

Particle

otoc

5 s to < 10 loto c 15 15to t20 2010 c25 25to<30 >30

Filar micrometer measurements of each bead and its accompanying air voids, when present, were recorded_ From this data., volume distribution, weight distribution, two distributions accordmg to estimated sedimentation rates by Stokes’ law. and surface area values were calculated The data were procesz& with an electronic computer in ren groups of 1000 bea4 each group representing ten samples_ Data was pooled in this way because of the comparatively smzll number of beads measured per sample. Stokes. diameters were calculated from the relationship

where d, do and di are respectively the Stokes, void and bead diameters and p and p, are the specific OF ?Es

GROGPS

OF 1300

iE4Ds

BY CIASS

i?aEuvNs

Number of beads per riwusand

TOId

diamaer 01)

no_ of I

2

3

4

5

6

7

8

9

10

beads

Otoc 510 loto 15to zoto 25to Z-30

374 29$ 194 1!5 19 z 3

316 303 227 128 22 4 0

331 3x ‘19 125 16 3 1

325 312 223 112 24 3 1

350 321 _ms 93 24 4 0

277 317 2332 137 33 3 1

285 323 218 139 2s 6 1

275 306 2661 130 20 7 1

374 326 242 137 za a 0

294 326 2x 120 20 3 0

3.101 3.133 2.259 L236 227 36 a

5 c 10 c 15 c20 t25 CM

13 82 27.1 395 135 34 7-O

1.1 81 283 442 14.4

1.1 9.7 313 405 1l-7

l-1 87 312 369 164

1.4 102 303 37.1 152

1.0 7-4 262 39.0 2IIO

1.0 7-6 25.7 39.9 17-7 7-9 02

1.0 73 31.6 389 119 75 I.8

1.1 9.3 31.6 432 145 0.0 O_O

12 9J 320 392 14.6 35 00

1*1 S.6 29.6 39.8 15-o :5 13

Poxder TechnoL. 3 (I%9) 9-23

C. M. HUNT,

12

gravities of the solid glass and sedimentation medium respectively.

Resulis by microscope The results of microscopic measurements of ten groups of 1000 beads are given in Tables 1 and 2 The values have ‘been taken from the computer listing of each group of 1000 beads and are presented by 5-p class intervals. Table 1 shows the number of beads per thousand by 5-p diameter intervals up to 30 or.Table 2 shows percent by volume in the same class intervals. Error is introduced into the number distribution by uncertainty in the number of beads in the smallest size range, while the volume distribution is subject to uncertainty because of the small number of large beads measured2s. This latter deficiency is sometimes offset by subdividing the sample physically or selecting particles in such a way that more large particles are measured_ In the present case, this was not done because of the complication of gas bubble corrections. Observer bias was noted in the number of beads smaller than 5 k as may be noted in Table 1, where groups l-5 were measured by one observer and groups 610 by the other- Most of this difference was in beads smaller than 3 p which are not separately tabulated. Uncertainty in the number of beads smaller than 3 p introduced signilicent error into the number distribution, but on a percent by volume basis it represented about 0.1% of the sample. Tables 1 and 2 are designed to permit inspection of variations in data. However, cumulative distributions by volume or by weight are geI;erally more useful for comparisons between different methods. Table 3 shows cumulative distributions by volume, by weight, and as calculated by Stokes- law for rate of settling in water and air in 5-,u increments_ It TABLE

5 10 15

20 25 30

-

The indxacal

ontQ1groupsof

3: C”M”IATM

A. R. WOOLF

might be pointed out that in the absence of air bubbles all of these distributions would be identical. The measure of dispersion which has been selected is the standard error of the mean,

where x is the cumulative percent finer than the indicated diameter for any group of 1000 beads, X is the average value for the ten groups of 1000 beads, and n = 1Q This measure of dispersion has been selected for the microscope measurements because of the relatively small number of beads measured per sample. For all of the other methods reported here, standard deviation of individual samples about the group mean was selected as the measure of dispersion, because these methods measure many more beads per sample Standard deviation computed in this way provides a direct estimate of sample-ro-sample variation, while the standard error of the mean expresses the repeatability of the average of a large number of samples. The dispersion in Table 3 may be considered in another way by treating percent finer as an exact quantity and placing all of the uncertainty in the diameter measurement. Thus the variation of lo! finer by volume at 15 p falls on the steep part of the cumulative distribution curve and corresponds to an uncertainty of approximately 0.1 p in diameter, while the variation of O-9% at 25 ,Qcorresponds to an uncertainty of 0.7 p in diameter. Variation in percent by volume is greatest near the center of the distribution while variation in diameter is least. The opposite is true at the tails of the distribution curve. The foregoing analysis assesses the sampling errors and reproducibility of the microscopic measurements, but does not consider the accuracy PAR-,-K-

by oobme

by merght

1 l&O03 9.7*0 3 39.4* 1 0 5922 12 942kO.9 98.7kO.7

12k1-007 102+04 41.0~1.0 816kl.O 95.8507 99 3&O-4

SIZE DE-‘-RIB brnOU’

by Stokes’ Ian (warer) 1.7 kO.03 122_~0_6 47.0 + 1.0 87.4 f a9 98 4&Ow6 lax0

by Stokes’

hv (4 12+_007 105,03 435410 85.6+0_9 97-9 *0_7 lo&O

chc standard errors of the quantities rrportedLaascd lcm bcadq each group rep-ting Cal sampIcs

uucettsintiesare

Powder

i%chnoL.

3 (1969) S23

of the diameter measurements themselves. Bishop5 has shown that the apparent diameter of glass beads depended upon the comparative refractive indices of the mounting medium and the beads. There are also other uncertainties Saylor’ has reviewed the problem of size measurement with the microscope and presented evidence supporting the conclusion of Charman that it is possible to select more than one position of focus and obtain more than one apparent diameter for the same spherical particle_ In the present work fibers ranging from 11 to 22 p in diameter were drawn from a melt of the glass beads. They were measured with an interferometer, and then mounted in Epon 828 resin and measured microscopically by two observers. The results of this comparison are shown in Table 4. The difference in diameter as measured by two observers averaged 0.1 K but the microscopic measurements averaged 0.2 to 0.3 p smaller than those obtained with the interferometer_ The refractive index of the freshly mixed Epon resin was so close to 1.52, the refractive index of the glass, that it was difficult to see the fibers or beads, but the polymerized material had a refractive index approaching 1.59. The position of optimum focus for each bead or fiber was considered to be the one at which the Becke line, in this case a diffuse halo, just disappeared into the glass. According to Bishop’ the diameter values obtained when the refractive indices of the mounting medium and the glass are fairly close together are probably closest to the true values. However, Saylo? has suggested that total reflection within the glass occurs when the refractive index of the mounting medium is greater than that of the glass, and the apparent edge is a reflection image of the condenser diaphragm. Whatever the mechanism of image formation, the empirical evidence in Table 4 suggests that, in the measurements reported here, the error was not much greater than the limit of resolution of the microscope. However, because of the potential sources of error in microscopic measurements, it is always desirable to perform some kind of independent check of the accuracy of the diameter determination_ The effect of a systematic error in diameter measurement on the volume, weight, or Stokes’ law distributions was assessed by adding 0.3 p to all of the diameters and recomputing these distributions for a group of 1000 beads. It shifted the distribution towards larger particle sizes by an amount slightly less than 0.3 JL In other words, the linear error in

I

2

Frber no

Dr-er

4

3 (JZ)

MiUOSWjX

ItUl?+T0metc?Y

Ob13 7 3 10

lLs=O 1 11.6t04 19_4+0_3 224-c0.1 -

A

113=02 I I-4*03 19_4g2 zzo-0.3 -

Ob-

B

11_4,[LI 11.1 =iE 193IO2 21_9=02

diameter was not magnified in the conversion to a cumulative distribution by volume_ AG estimate of the accuracy of the _m bubble measurements which enter into the weight and Stokes’ law distributions was obtained by Calculating the density of the solid glass from the relationship

where ps is the density of the glass in g?m3. p is the average density of the beads, which had a value 01 2.39 g/cm3 by liquid displacement, di is the diameter of the i-th bead. and &< is the diameter of a solid bead having the same weight as the i-th bead. An average p, of 254 c/cm3 with a standard error of 0.01 g&m3 was obtained from eqn. (2) and the measured density of the beads_ The same value was obtained by weighing a solid prism of the same glass in water and in air_ The above measurements, plus recalculation of the data for 1000 beads with a simulated 10% error in the bubble diameter, indicated that ihe effect of any systematic error in bubble measurement was small compared with normal sampling variations-

COMPARISON

OF MICROSCOPE APPARATUS

Surface area measurements of the glass bead reference sample were made with a ‘Lea-Nurse apparatusg. The method is based upon the CarmanKozeny equationI and is related to other comPonder T.chmi,

3 (1969) 923

14

C. M. H-U-NT, A. R. WOOLF

TABLE

5: 03bSE’~XOFSURFA~ARUAND

.avmsAGE

DLedErBt

BY Mxaaux3pE

specik surface (CmVg) SurfaccaveragcdiameWrQ

sPElaFlcsuRFAcE AXD

LEA-h-

APR4RKms-

L&Z-NUT-

Microscope

17202 12 14.6&0X.@

1733k 16 14 520 13

* -Ihe indigtcd uarrainties in the k-Nurse ncasurrment are the standard dcv’.ationsof 12 samples about thclr mean. For the microscope standard errors are given based upon ten groups of loo0 bca& each group representingten samplu manly

used air permeabiIity

methods,

such

as the

Blaine apparatus”. and the Fisher Subsieve Sizer, which is a slight modification of a device described by Gooden and Smith’s. Comparison of specific surfaces obtained with the microscope and the Lea-Nurse apparatus is given in Table 5 The Lea-Nurse values are averages of twelve samples of beads. Surface average diameters, 4, were calculated from specific surfaces, S,, by the relationship,

and are given in the table. It is interesting to note that the standard deviation of the Lea-N-m-se data, which includes sample-to-sample variation. is of about the same magnitude as the standard error of the overall mean of 100 samples using the micro-

Complete dispersion of the particles in suspension is one of the elementary requirements for an accurate count by this method, as is true of most methods of particle size analysis- The glass beads presented a special problem in this respect due to their tendency to form aggregates in the presence of atmospheric moisture_ Some comparisons between the microscope and the co-enter which illustrate this behavior are shown in Fig. 1. The solid line represents cumulative percentage finer by volume calculated from the microscopic measurements, while the solid circles represent counter measurements of a sample taken shortly after bottling_ The circles are displaced toward larger sizes. This was due to the presence of undispersed agglomerates in the suspension which the normal stirring in the apparatus did not separate_ Some of these were present in the original material, and more were produced during wet processing and drying in the laboratory_ Agglomeration progressed still further during two years of storage in the presence of small amounts of moisture. This is shown by the open circles in the figure_ However, intensive mechanical shaking of the stored beads separated the agglomerates_ The erect triangles in Fig_ 1 represent the distribution obtained after 30 seconds of such shaking, and the inverted triangles were obtained after 30 minutes. The agreement

SCOpe. The Lea-Nurse

values in Table 5 were obtained with a particular instrument and particular cell. Instruments having different flowmeters and different cells may produce greater differences in values than those shown in the table Another source of error in the Lea-Nurse apparatus, as well as other methods based upon the Carman-Kozeny equation16, is that the porosity term ~~“/(l-e) does not adequately correct for changes in porosity_ Diffeient surface area values are normally obtained by varying the porosity of the bed. The values in Table 5 were obtained at a porosity of 0.45. The glass beads, being slightly coarser and less easily compacted than most powders which are measured by this method, offered less latitude for variation in porosity than most fine powders

COh¶PARISON

OF WCRCXSCOPE

AND

ELECIRONIC

COuLclER

Particle size distribution of the glass beads was determined with a Model “A” Coulter counterlo.

Fig 1. Comparison of size distribution of @ass beads obtained by electronic counter and by miu-~ show& the effects of agglomeration Distriintion obtained by mkroscops . sample obxaincd shortly after bottlins 0 sample after 2of trxzs of moisture. P stored sample YcarstoWFinpnsemr after 30 seconds of intcnsivc mechanical &akin& vscond sample after 30 minutes of intensive Rta&anical shaking

Powder

7.ahnoL.

3

(1969) 9-23

PARTICLI-SIZE

between the two sets of points, representing a 60/l ratio in the duration of shaking, indicates that the action separated agglomerates without undue attrition of the glass. Comparable dispersion was also obtained after shaking in a Wig-L-Bug or a Spex grinder (used without the usual grinding pellet) The need for such deagglomeration treatments was considerably reduced, however, if the beads were carefully dried ana stored in a dry state. No measurable change in the apparent size distribution of deagglomeratcd beads was observed after three months of exposure to air at 50% relative humidity, while signi&ant changes were observed within three days at 90% relative humidity_ In Table 6, the average size distribution by the counter, based on 25 samples of deagglomerated beads, is compared with the average obtained by the microscope_ The comparison is made in two ways. In the first, the diameters from the counter distribution are treated as exact quantities and the cumulative volume percentages by the counter and the microscope are compared in columns 2 and 3. In the second, volume percentages by the counter are treated as exact quantities and diameters by counter and microscope are compared in columns 1 and 4_ In these comparisons, the electronic counter does not offer an independent check of the microscope, because a calibration constant has been selected which gives best agreement Also. instead of using an extrapolation1g*20*” to estimate the amount of particles too small to be measured at

284 225

%_5&0.7 88_2& I-7

97.8&O-9 89.02 1.1

X6&0.8 223+06

17-9 143 IL4 9.1 73 6.0 10

6x?& 1.4 326+ 12 15_3&05 7_6+03 3_9&02 20+0.1 1.1**

6532 19 33.0 f O-9 15.0~0.3 7.1+0_3 3 8kO.1 2O+QO7 1.1 *CL1

17_8&02 143=0_2 115+0.1 9_3+0.2 7-4&O-l 5_9&cu 5_0=-

15

MEAsuREbENT

the lowest threshold, it was assumed that the volume of particles smaller than 5 p amounted to 1.1% of the distribution, the average value obtained by the microscope However, in Table 6 the electronic counter gives an independent check of the shape of the distribution because a single calibration wnstant has been used to convert threshold values to diameters for all sizes. The coincidence correction recommended in the Coulter manual”2 was used in Table 6. It has the form Ii?, = l&i-ah?

10-6

(4)

where A$ is the estimated real number of particles large enough to be counted at threshold x, n, is the actual number of particles counted, and c1 is a constant which may be calculated from the relationship Q = 25 (D/100)3 500/V

(5)

where D is the diameter of the aperture in _y and V is the volume of the metering manometer in ,A Calculations by others suggest that eqn. (4) gives wunts which are tco 10w~~-~‘_ Estimates of the total number of beads per milligram by microscope and by the counter further suggest that this may be the case Coincidence was also calculated by the relationship n,=

N,-CCN:

(6)

where n, and N, have the same signihcance as in eqn. (4), and C = A/21/. A is the volume of the sensing zone, and V is the manometer volume_ Equation (6) has been given by Princen and Kwolek” to correct for loss of count due to “ho_rizontal” interaction, the situation where only the largest of more than one coincidental partic!cs is registered, and Edmundson has used this equation as a starting point of an empirical method of coincidence correction which is of more general application2’. For a 140 p aperture and a 500 4 manometer at a total count of 10,009, eqn (6) gave an estimated real count nearly 17% higher *&an eqn. (4) while at 600Cl the estimated real count was 7.5% higher. The results in Table 6 were recalculated using coincidence corrections baaed on eqn. (6) Some wrrections were obtained for all but the largest sizes, but the greatest wrrections occurred in the smaller sixes which contributed the least POthe volume distributios so that the net effect of the increase in count was to shift the entire distribution to larger sixes by approximately 0.1 F For some purposes, the number

Pmder

Technd.

3 (1969) S23

16

C. hi_ HUIW,

of particles is the fundamental information which is needed In this case, the accura cy of the coincidence correction is of prime rmportance For many purposes, however, volume or weight distributions are required, and the contribution of the coincidence correction is smaller. However, many powders encountered in practice contain more line particles than these glass beads, so that the effect of errors in the coincidence correction may be greater than that obtained here, even on a volume basis. The Coulter counter is subject to a source of error which has been described by Kubitschek”. It arises from the fact that the apertures may be too short to ailow full integration of the electrical pulse in the brief time each particle is in the aperture_ Thus, particles of a given size could give a range of pulse amplitudes depending upon the velocity with which they passed through the aperture. This should result in some loss of resolution and broadening of the distribution. However, this effect does not seem to have a great influence on the volume distribution shown in Table 6, unless the deviation between results obtained with the microscope and the counter at the upper end of the distribution can be attributed to it In Fig. 2, incremental size distributions of the sample by the two methods are compared, considering only the portion of the distribution above 5 ,u_There is little evidence of broadening except at the larger sizes, and possibly broadening at the lower end of the distribution would be greater if the distribution were expressed on a number instead of a volume basis. Also. coincidence errors

FIN_ 2

Particle S& dmibmion of t-&m~ce glan beads plotted by 2-p intervals Microscope. - - - counter.

A. R. WOOLF

J 5

Fig. 3. Partick size distributions of tao samples of narrowly clasdicd beads plotted by 1-p intervals hiicroscoge,

---

czzmllltcr.

may be superimposed on resolution errors in this part of the distribution; otherwise the count might have been greater. Figure 3 shows comparisons obtained with two narrow size distributions of glass beads The left curves in the figure were obtained with a sample having an average diameter of about 11 cr, based upon microscopic measurement of 500 bea& while those on the right were obtained with a sample having an average diameter of about 27 k based upon microscopic measurement of 741 beads. The curves in Fig. 3 show greater broadening than were observed with the 5 to 30 p sample shown in Fig 2 It has been tacitly assumed that differences such as those shown in Figs 2 and 3 arise from the fact that the electronic counter measures more partides and is therefore more representativezs. Kubitschek’s analysis suggests another factor leading to this end result The effect of these differences also appears in calibration curves An example is shown in Fig. 4. This differs from the usual calibration curve in that the counter values on the ordinate are expressed as diameters instead of threshold values The circIes in the figure are a graphic representation cf column 4 us. column 1 in Table 6. The triangles are similar plots of data obtained from the two glass-bead samples of narrow size distribution from Fig 3. The experimental points describe a path of slightly greater slope than the line of 1: 1 correspondence over at least part of the range in each group of data_ This behavior has been observed repeatedly in caliPowder Tedmd.

3 (1969) +23

PARTlCLE-SIZE

17

MEASUREMENT

standard error of the mean The two measures of dispersion appear to be of approximately the same magnitude CohrPARrsoN OF

Fzg. 4. Comparison of diictns of &is bads by daxronic counter and microscope 0 Rcfcrcna glass bead sample (data from Table 6), A gIass bead sample with mean size of about 27 JI.,V glass bead sample with mean size of about 1 I JI_

bration plots with different samples It has also been observed in one intercomparison between the Andreasen pipette and the electronic counter. It would seem that if this were simply a sampling effect arising from the smaller number of particles measured with the microscope, the form of the disagreement between the two methods might be expected to exhibit a less consistent pattern The electrodes of the electronic counter reverse ‘ve count to minimize polarity with each successr polariznion. It is usually observed that alternate counts are higher (or lower) than the precedingones Rosentieldzg has suggested that this behavior is due to the fact that particlesof many materialsin suspension are charged. Thus, for example, more particles ofa negativelycharged suspension would be counted when the electrode inside the aperture tube is positive than when it is negative To minim& the effect of this behavior, averages were based on an equal number of counts at each polarity in the measnrements reported here. The foregoing discussion has stressed some of the potential sources of error in the electronic counting. On the other hand, counters have the advantage of measuring large numbers of particles, which is desirable from a statistical point of view_ The measure of dispersion of the Coulter counter values shown in Table 6 is the estimated standard deviation of the 25 samples about their mean, while the dispersion of microscopic data is again expressedas the

MlCROSCOPE

AXm

EiECTROFORMED

Samples of glass beads were sieved with fine electroformed sieves having nominal openings of 5,iO, 20 and 30 p Irani and Callis3” have briefly described a few procedures for use with electroformed sieves, and other methods have been described by Zwicke?, Ioos3’, Kravit~‘~. Nuckolls and Fulle?, Shel13’ and Daeschner et LzL~~_ In the present measurements. ultrasonic vibration was used ; the apparatus and procedure have been previously described38. The results of the sieve analysis are given in Table 7_ Column 1 in the table lists *he nominal sieve openings, while column 2 gives the average and estimated standard deviation of ten diameter measurements In every case, the measured values were larger than the nominal openings Columns 3 and 4 compare perceat finer by sieve analysis and by microscope corresponding to the microscopically measured sieve openings The fifth column in the table gives equivalent bead diameters corresponding to the amouut passing the sieve Twenty samples were used in the overall sieve analysis, two of which were used twice, resulting in a total of 22 sieve measurements It is often difficult to select a proper end point even with conventional sieves having comparatively Iarge ~perrings~~-~~_ This problem becomes greater

5 10 z

675z-s 11_9g_9 21-o= z-0 30_6_FlA

5.95 12 36.7 _L27 883k 1.6 993t0.3

3.1xQl 181 &cl9 858 = 1.0 993*03

8310.6 145&0_4 2IdsO.S 30X&1.1

- Unartaintia indicated in CoIumn 2 are standard &x&ioru of ten mcasnrcm ems In col3andSt?axcswndard deviationbaredonfivcorsixsmpIes.;tndincolamn4th~y standard crr0l-s of tat gronps of lalo IDcad& each lxprsncing ten SampIes

Powder 7kcJxnJL,3 !1%9) 9-23

18

C. M.

HUN&

as the size of the sieve openings becomes smaller The selection of ten minutes of ultrasonic sieving to obtain the data in Table 7 is an arbitrary procedure. Whether or not it represents a proper end point, it is to be seen by comparing columns 3 and 4 in Table 7

that with three out of four sieves, the amount passing was greater than that predicted from the particle size distribution of the sample_ Also, the equivalent bead diameters, corresponding to the percent passing, were larger than the average sieve openingsThe agreementwith microscopicmeasurements was poorest for the 5-p and 10-p sieves One possible cause of these differencesis enlargementof the sieve openings. There was little evidence of general wear based upon before-and-after measurement of several randomly selected openings even after a year of intermittent service. However, the average 3-inch sieve has more than I.5 million openings, so that if only a few oversized holes were present, the chance of missing them in a random selection would be great When the entire surface of each sieve was inspected under low power, one or two individual openings were often found which were noticeably larger than the average. Therefore, an inspectionwas made before and aftersievingeach sample- If any such oversized holes were found, they were filed with epoxy cement applied under the microscope with a fine needle, a procedure which has been previously described36. Oversized holes in the sieves were found in five of the 22 individual determinations averaged in Table 7, once with the 30-p sieve and twice each with the 10-p and 20-p sieves. However, the amount passing was greater than the amount predicted, whether or not enlarged holes were observed_ This suggests that other factors may also contribute to the differences between the measured sieve openings and the equivalent diameter of the beads passing the sieve. Attrition of the beads is a possibility_ However, there was no evidence of breakage or extraction of soluble matter. Also, beads as large as the equivalent bead diameters were observed in sieved fractions. There are factors arising from the microscopic measurements of the sieve openings to be considered Perhaps the average sieve opening is not the best vahre to use, because of the comparatively greater importance of the larger openings There may also be some unrecognized problems in measuring very fine holes with a microscope_ Charman reported that circularholes in aInminum film which were about 1 to 3 p in diameter and 0.05 p thick measured about 0.15 n larger by the

A. R. WOOLF

microscope than their estimated true diameters, but the present sieve measurements appear to be too smalL However. in the case of the 5-,u and l@p sieves, the depth of the holes may be a number of times as great as their diameter. The development of oversized holes may be the result of the ultrasonic treatment However, other procedures were not examined critically from the standpoint of sieve damage. Electroformed sieves are much newer than conventional sieves, and new methods of use are still beiig sought_ Ultrasonic vibration, whatever its potential hazard to the sieve, greatly accelerates the rate of particle separation

COMPARISON

OF MICROSCOPE

AND

AND-

PIPEl-l-E

Particle size distribution was determined with the Andreasen pipette‘r_ A 2% aqueous suspension of beads by weight was dispersedin a mixer of the type described in the ASTM method for the mechanical analysis of soils”. A buffered phosphate mixture (Calgon), in an amount equivalent to 1% of the weight of the beads, was used as a dispersing agent. After a minute of dispersion, the suspension was diluted to 1% in the Andreasen apparatus and brought to 25_O~O_l”C in a constant temperature bath The suspension was then thoroughly shaken, returned to the bath, and measured samples were withdrawn with the built-m pipette, each after a calculated settling period_ Reshaking and settling was repeated for each individual sample, instead of the more common practice of sampling sequentially after cne initial mixing This required longer for a particle size analysis, but eliminated any cumulative effect of disturbance of the suspension by sampling. It also permitted duplicate determinations of the same suspension with which to estimate variability arising from the procedure itself The summarized results of Andreasen pipette an&&s are compared with microscopic measurements in Table 8. The first column in the table gives the particle diameter used in the Andreasen analysis, while columns 2 and 3 compare the corresponding percent finer obtained by the two methods The measure of statistical variation given inthesecondcolumnistheestimateds~darddeviation of ten samples about their mean, and each of the ten values was an average of duplicates obtained with the same suspension. The pooled standard deviationsa2 of the duplicates are of approximately PowderTechmL.

3(1969)9-23

PAFtl-icLE-SIZE m TABLE

8:

OOWPARDON

BEAE6

OF PARTICLE SUE DlSlRIBLnOX

BY MK3DSCOF%

244 IV-4 14.2 98

97221.3 839i 1.5 41 St 1.1 135*0x5

46

2010-4

AND

AkDREAsEN

OF GLASS

PIPiXE-

97.8x 1 8 83-2127 39.8+28 114t1.8

238112 19_4=03 14420 1 103 50.2

1.4~0 8

531_0_4

2 and 4 arc standard deviations l -l-hcun azxaiotia in colbased on ten samples In column 3 they arc nandard errors based On tm

SOUpS

Of 1m

kads.

CiCh

~-tinj3

WI, ~PkS-

l*Tbhe miaoscopic vahcs arc obtain& from the Stokes’ distribution cakulatai for scdimcntationin water.

the same magnitude as the standard deviations shown in column 2, indicating that variability arising from the procedure itself contributed much to the total variability_ Columns 1 and 4 compare the diameters by the Andreasen pipette and the microscope corresponding to the percentages of beads given in column 2 From the standpoint of particle size, the closest agreement between the two methods occurred near the center of the distribution with a crossover at about 19-4 F A difference of 02 p between the sedimentation diameter and the equivalent microscopic diameter was obtained at 142 & but it was greater towards the ends of the distribution The comparison between the pipette and the

0

5

w: %rtlcle

15 20 d‘ometucp,

25

430

5. Parucle size tibmion of rcfcreoccgks beads plotted by 2-p intervals Microscope. - - - Andrrarcn pip&c

Fig

19

microscope is presented another way in Fig 5, where the weight of beads per 2-p class interval has been estimated from smoothed cumulative distribution curves and plotted as a function of particle diameter_ Considering the different physical principles involved in the two methods, the agreement is good, but the Andreasen pipette gave a slightly broader distribution and one which was displaced slightly towards smaller sizes One of the factors contributing to this latter effect is that about 4% of beads by volume were not perfect spheres These would tend to settle more slowly than the equivalent spheres estimated from microscopic measurementJ3=_ The sources of error in Andreasen pipette analysis have been reviewed elsewhere”-4s-J6, but some of the commonly reco_* oneS include inadequate sample dispersion, turbulence, and retention of solids in the pipette In the present measurements, one minute and ten minutes mechanical dispersion at ~0,000 r-p-m. led to essentially the same distribution. From this it is concluded that one minute was adequate, and there was no progressive attrition of the beads with longer dispersion time. This trcatment also overcame aggregation due to surface reactivity noted in Fig 1. Turbulence in tie suspension was minimized by temperature control, but a Certain amount of time is always required for random movements to subside after the original mixing This presents particular problems in the measurement of the larger siZes In Table 8 the largest size listed is 24.4 s This corresponds to a settling time of approximately six minutes in water_ To mmimize particle retention in the pipette, air bubbles were intermittently drawn back through the sampled suspension during transfer to the weighing container_ Also, the solids content of the original suspension was based upon values obtained from pipetted samples However, the fact that variations between duplicate samples from the same suspension were comparable in magnitude with those between different samples sueests that the effects of retention of solids. as well as their reintrainmenf were not eliminated_ Also. since the concentration of the suspension diminishes with time, any reintrainment of particles from an earlier sample withdrawal would contribute to an apparent shift of the distribution Howard smaller sizes This may be another factor contributing to the displacement observed in Fig 5 and Table S_ An electrical potential can develop when charged particles settle in a liquid&‘. This results in electroPowder Technol. 3 (1969) V-23

20

C. M. HUNT,

viscous resistance

to flow which can influence the rate of sedimentation_ The net effect of electroviscous effects may be somewhat compiex to evaluate in a polydisperse suspensi~n~~~*~‘. However, according to Elton and Hirschler4*, electroviscous effects are usually not observed in electrolyte solutions of ionic strength greater than 0.1 N- The electrolyte concentration in the present measurements was less than this. Thus, electroviscous effects may also have made a small contribution to the observed differences between the results of pipette and microscopic analysis_ Another potential source of error in pipette analysis is interaction between particles in suspension- This can result in sedimentation rates which deviate from Stokes’ lawJg. Experiments by Kaye and Boardman”, in which “marker” spheres were allowed to settle in suspensions containing varying concentrations of other particles, have shown that deviations from Stokes’ law are observable at lower concentrations than has previously been supposed For example, sedimentation rates approximately 1.5 times those calculated from Stokes’ law were observed when 9O@p marker spheres were allowed to settle with other spheres of similar size in concentrations comparable to those used in Andreasen pipette analysis_ Johne” has reported even greater settling velocities_ However, other data by Kaye and Boardmans suggest that somewhat higher concentration might bc reached before accelerated settling is observed, ifall of the particles are not approximately the same size_ The results in Fig. 5 and Table 8 do not show any evidence of accelerated settling. If anything, slightly the opposite effect may be observed_ Further investigation of particle interaction would be desirable, but the TABLE I

Sample no

1

2 3

l

Microscopic

9: CO.WARISONOF

PAFtTICLE

SEE

2

3

Diamerer ivy Rotter 01)

Roiter amtys~~ Percenr cottected

A. R. WO0L.F

present res?llts seem to confirm the earlier view that acceptable results may be obtained with particle concentrations up to O-So% by volume31b, but with perhaps the qualification that the suspension be polydisperse.

COb¶F’ARI!SON

OF MICRoscOPE

AND

ROLIBI

ANALYZER

Three samples of glass beads were analyzed with a Roller analyzer13*s2~s3. In the measurements described here, about 20 g of deagglomerated beads were placed in the apparatus and subjected to elutriation for successive 3&nin periods, until the amount collected in a given period was O-2 g or less, usually much less. In the process of elutriation, a certain amount of material was retained on the walls of the apparatus_ To correct for this loss, it was assumed that material which was not recovered in the elutriate or the residue had the same size distribution as the material in the sample compartment before elutriation. A comparison of results obtained with the Roller analyzer and microscope is given in Table 9, where the Roller diameters are given in column 2, and the corresponding cumulative percent finer by the two methods is compared in columns 5 and 6. Columns 2 and 7 compare diameters determined by the Roller analyzer and the microscope which correspond to percent finer obtained by Roller analysis. The amount of material collected with the Roller apparatus tended to be a little less than that predicted from microscopic measurements, but two exceptions are to be noted in Table 9. However, the amount of material estimated depends somewhat upon the compromises which have been made in

D 5I-RIBUllOpI’

BY btICROSCTX’E

AhD

ROLLEX

A~ALXZER

4

6 Mzcroscope-

Deposition tos.s

Percent

Equimtent’

fm

dmerer

by

7

weighr

f.4

10.5

123

49

129

21-l

830

59

87-9

124 900

10.7 20.5

150 25-O

3&I? 91-4

5.7 86

40-4 992

435 980

14.6 27-4

15-O 250

36J 93 3

I_5 3.5

37.1 96.6

43J 98.0

143 23.7

values arc obtained from the Stokes’ distribution cahdatal

for stdrmmtation

in air_

Powder

Technot.. 3 (1969) 9-23

PARTICLE-SIZE

dealing with the two important sources of error in the method, namely (1) the selection of an arbitrary end point, and (2) deposition of solids on the walls of the apparatus. The first of these, it has been suggested by R~lh+~~~~, arises from the fact that the axial velocity of the rising air column would be expected to be greater than the average velocity. Thus if elutriation is continued until no more material passes, particles larger than the calculated size will be included in the collected fraction. To compensate for this, an arbitrary end point is selected_ One end point tentatively suggested by Roller, is that elutriation be discontinued when the amount collected in an elutriation period is less than 10% of that collected in the initial period The end point which was used in the present measurements went beyond this point. However, in most of the examples given in Table 9, the estimated percent fmer by Roller analysk was less than that predicted from microscopis measurements_ Even if all the deposition loss were treated as part of the elutriate, as has bezn suggested by Roller, the agreement between the two methods would be reasonable. An alternate procedure suggested for the Roller analyzers4 is the use of 2-min elutriation periods. Two fractions were collected in this way, and the amounts obtained were much less than when 30min periods were used, resulting in much poorer agreement with the microscopically determined distribution. From this it is concluded that 3Ckmin elutriation periods are preferable to ~-II&I periods, a conclusion reached by Pollard” in the analysis of metal powders

CONCLUSION

Measurements of the Particle size distribution of samples from a single blended batch of glass beads were made with a microscope. Samples from the same batch were also measured by other methods of particle size analysis, and comparisons obtained by the di!Terent methods were made The repeatibility of the microscopic measurements was equivalent to 0.1 p near the center of the frequency distribution curve but was poorer than this towards the ends (particularly the upper end)Fibers of the same glass were measured with a microscope and an inte_z;rometer_ The systatic difference between diameters by the two methods did not appear to be greater than 0.2 to 0.3 ,u under

21

vi

the conditions of measurement used in the present

investigatioxL The glass beads were found to be reactive in the presence of atmospheric moisture which could lead to the formation of agglomerates_ Special treatment was required to separate these agglomerates However, storage in a dry atmosphere greatly reduced the rate and degree of aggregation The specific surface average diameter obtained with a Lea-Nurse apparatus was 14.6 ,u.,compared with 14~5 p by the microscope Accurate particle size distributions according to number were difficult to obtain by both the micro scope and the Coulter counter because of uncertainties in the number of the smallest particles present. These contributed very little to the total volume of the sample, so that the effect of this error was greatly reduced when results were expressed on a volume basis. The same was true of uncertainties in the coincidence correction for the Coulter counter. The agreement between values obtained with the microscope and the electronic counter was good, but some small systematic differences were observed- These may have arisen from imperfect resolution by the Coulter counter, but this view is based more on the systematic nature of the bias in a number of intercomparisons between the electronic counter and the microscope than on comparisons obtained with this particular reference sample Some disagreements were obtained between the microscope and 5-, lO- and 20-p electroformed sieves. More material passed the sieves than was predicted from the size distribution of the sample as determined by the microscope_ The differences were particularly great with the 5 and lO+ sieves. This may have been caused by enlargement of the sieve openings in the process of sieving, but there may also have been some problems in the measurement of very small sieve openings with a microscope_ The average diameter may not be the best value to represent the size of the sieve opening Also, in the case of S- and 10-~1 sieves, the depth of the openings may be a number of times as large as their diameter. which might present an optical problem iu measurement The difference between the average diameter obtained with the Anclreasen pipette and the microscope was equivalent to 2pproximately 02 p near the center of the distribution but was greater near the ends. The distribution obtained by the An-

C. M. HUNT,

22

dreasen method was slightly broader than that obtained with the microscope. However, the overall agreement between the two methods was much better than might have been predicted from recent published work on group settling vekxities of particles in suspension. Three samples were measured by air elutriation using a Roller analyzer. When SO-min elutriation periods were used, values were obtained which were in reasonable agreement with those obtained with the microscope. However, because material is retained on the walls of the apparatus, and because the elutriation process requires an arbitrary end point, the method is subject to greater uncertainties than the other methods used in the present investigation.

ACKKOWLED

GJZh5XN-r

authors are indebted to Miss Ruth Zucker for programming the data for the computer, to Mr. H. H. Ku for assistance in the statistical design of sample preparation and sampling, to Mr. Leonard Cahn for constructing the photoelectric pulse generator used in the digitalization of diameter measurements, to Mr. L. A. Tomes for the design and construction of accessory apparatus and to Mr. Karl Nefllen for suggesting the interferometric measurement of glass fibers, and providing the necessary technical assistance. The

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1965 2 A. M. G.+u~m

3

4

5

6

7

tin F. W. Bowmr. Surface m easureluem by vao da Waals Adsorpuon hfming TechnoL, 8 (3) (1944) l-6. F. G. C PER AhD V. R. DEB, Glass sphc_res for the measuremeot of the effectrve opemng of faring nc+es, J_ Res. Nar. Bw. Sran& 47 (3) (1951) 139-147. H. F. W- ~EDEKI-oPF. XIX--On the quality of the image and resolving powe-r in the microscope. J_ Roy. M~croscop. Sot., 49 (1929) 231-236. D. L. Blmop. A sedunenta~on method for the determination of fmely divided materials(such as hydrated lune), Bur_ Skmd_ J. Res_, 12 (1934) 173. W. N. U-. Some experiments concemiug the limitationsanderrorsinsizem easuraneut of small objects by vi&l microscopy. 1.Roy-Microscop. Sot_, 82 (1963)81-94. R. P. Low. Methods of pxticle-size analysis. ASTM Sump- on parri& size analysts. June 26 rmd 27.1958. Speuaf Technical publication No 234, p_ 78.

A. R. WOOLF SCP.SA~~~n,AshldYof~rr~~~iPth~m~atof microscopic spheres, Appr Opries, 4 (4) (1965) 477486. 9F_M.Lur~~~R.W.N~11~.Thespcdfic~~offinc Powders. J. Sot Chem. Ind [Lonabnl. 58 (1939) 278-283. 10 R. H. BERG. Electronic size analy5s of s&sieve particles by flowing through a small liquid resister. ASTM SJmp. on purzicIe size mensauement. June 26 wui 27, 195X S’cial Techmud Publvarum No. 234. pp. 245255. Zur Kcnmnis da Mahlgutes. Kolbih 11 A. H. M. Ahmm. them. Be&. 27 (1928) 349-X58. E E S-T oh?) E D. PmRs. AppliI2 H. W. D nz cation of elcetroformfxl micromesh sieves to the determination of particle size distribution, ASTM Symp. onpmzicL=size measurement. June 26 and 21.1958. Special Teck Publication No. 234. pp_ 26-47. 13 P. S. Rm Scparationand~~butionofrmcroscopic particles: an air aualyzer for fine paxtides. U.S. Bzu_ Mines i-e& Paper 490 (1931). Inrr&rion 10 Znrerjkoomer: Longmans 14 S. Tom. Green, London. 1955. pp_ 53-55. 15 R. T. MOOR& M. C. STARK AND L_ CAWN. Digitizing pictorial irkformation with a precision optical scanner. Phorogramme.‘ric Engng.. 30 (6) (1964). 16 P. c. CARUAX. Th; detamination of the speeitic surface of powders. J. Sot Chem. Znd (Lo&n). 57 (1938) 22!?-234_ 17 R. L. B-x A simplifxd air ~cruxability fineoess apparatus. ASTM Bull. No. 123 (1943) 51-55. 18 E. L. GOODEN AND C M. Shnmi. Measuring average particle diameter of powders, Znd Eng. Chcm.. Anal. Ed. 12 (1940) 47w2_ Size analysis in the sub-sieve 19 C. C. HARRIS ~?.m A. Jowm. range by electroniccounter. Nature. 208 (5006) (1965) 175-76. 20 0. I. %PP AhD J. MOU’X. SiZe aM&siS in the sub-sieve range by dectrouic counter, Nahrrc, 220 (5037) (1966) 72425. Dctermina tion of the solid volume percent21 R. K. E-o=. age below detectable size in a Couker couILtQ aoalysis, Narzcre. 210 (5037) (1966) 7’6M. 22 Ir&ruction manual. Coulter counter industrial model A, Coulter Electrooks Division. Chicago. 1963. 23 M. Wm Ahm J. N. Wnsoh. Theory of comcidence in Coulter particle counfers, Reu_ Sri. Znstr.. 32 (10) (1961) 1132-36. 24 L. H -cEN AhD W. F. KwoLEK, Coincidence corrections for particle size det erminations with the Coulter counter. Rec. Sci. Znsrr_.36 (5) 0965) -53. 25 1. C ED~_N. Coincidence error in Co&n counter parude size analysis. Nanrre. 212 (1966) 145&52 26 W. B-T AW G. HILBIG, Theotie dcs Koiuzidenzfehlers bei digital= Teilehengrosco-bestimmungeu. Sfa&. 27 (4) (1967) ls-90. 27 H. E. Kuanscmjc. Loss of resolution in Coulter coumers. Retx Scz. Znstr_.33 (5) (1%2) 575. 28 J.E.G~.E-J.CRos~~fi~W.R~Biasin particle size analysis by the count method. Znd &zg. Uzezn. Fkn&mU?nfak. 4 (2) (1965) 204-8. 29 Cmusnxcx Ras~rmo. Absrracts of paperspresenfed before rhe Dm. of Colloid and Surfs Chem. as the 151s mtg. of

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Znmerpretation. and Appiicatkm. Wiley. a pp. 119-21, b. p. 68.

New York.

Powder T&L.

1963.

3 (1969) +23

23 32 J_ D. ZWKXER, Si analysis below two microns. Technical Report &vida Work Aluminum Company of Canada. Ltd, Rpporr No- A W-~-1965. Sept 1965. 33 E. Ioar, Mikros5zbung mit Ultras&a& Srmrb,25 (12) (1965) -3. 34 J. H. KRAVXTZ,Using an ultrasonic disrupteras an aid to xvet sieving. J_ Se&me7u. PerroL. 36 (3) (1966) 811-12 35 M. J. NU~~OLUASDR K. Fuu~~,Sxveanalysisofpart~da ~arhan44micronsindiameta.SoilSci,102(5)(1966) 292-9s. 36 Dcxermination of particle size distribution of cracking caralysts, micromuh sieve method. dq swmg proadure, Shell Mellrod Senes 73IJ6.Z. Shell Development Co.. 1952. 37 H. W. DAEXHXX, E E. SEIBERT ASD E D. PmRs. Apphcation of clcstroformal prcdsion micromesh s-es to the detmnination of particle size distribution ASTM S_mp. on parxiciesizemeanu-l. No_ 234. pi_ 2ti7_

1958. Special TechnicaiPubhca~ion

38 C M. Huszr AX= A_ R WOW, Sieve techniquesfor obtaining small amomXs of narrowly chsificd pWt.iCks. ASTM Mater. Rec. Std. 4 (7) (1964) 3-S. 39 K. T. WHITBY. The mechanics of fine sieving, ASTM Symp.

on pad% size mensurement. 1958_ Speriar Technical Pad&cation No. 234. pp. 3-24. 40 B. H. KATZ Investigating the possibilities of dwclopmg a rate method of sieve analysis Powder Mel., (10) (1962)

199-217. 41 Standard method for grain size analye of soils, ASTM Designanon D 42263. 42 W. S. -YOUDEN. S~a;rskai Merho&for Chenm~. W&y. New York, 1951. pp_ 12, 16. 43 C. OR& JR_A?XD J. M. DAUAV~ Fm Pmrick hfeasmemenr. Macmillan. New York. 1960. a. p_ 48. b. pp_ 4-7. 44 G. B~aaorr. De bcpalmg van korrelgroo~tc \erdelingen. DC pipetmctbodc volgcns ~ndnxsen- Esenwzin, Chemisch

weekbZ,z& 56 (1960) 7-16. (Review of pipertc a=&= in &=h-) ysc van Kaolinm nacb 45 H. M. Kosnq Die Korn~oscnard dcm P~pcnavaf&rcn. Ber_ Dezzx. Keram. Gez. 39 (I%?) 432-38_ 46 B. H. KAY. Ponder stxncc for the paint tahnologh I. Ponder size analysis by the pipette method, Pain& 011 Colour L, Feb. 26. 1965.437-44-I 47 J_ T_ DA\AKD E K H~xE+.I_ hxerfaaizl Phmomenn. Academic Press. Kcw York, 1963. pp_ 137-39. Elalr0vncosl~ m 48 G. A. H. ELTOX AND F. G. HIRSCWLER. dltutc hcraodispux suspmsionr l-he physics of pas-ix& size an+&, i3rir L App?. Phys . Supplmezr Ii-o. 3. (1954) pp_ 60-63. 49 G. -AN. Smail-parrrcie Smrisrics, Butt~onhs. IKcxv York, 1960. pp_ 58.350. SO B. H_ KAYE A?GD R_ P. BoARDLUX. Cluster formaaon m dilurc s uspmsions. Proc_ s>mp. on inrerac1ion benceenfluids andpm&Zes. Inst Chem. En_London, 1962. pp_ 17-21. 51 R JonEmlluss da Konuntration cina monodispzsm Suspension ati dxe SinJcgeschwmdigkcitihrer Tcilchen. Forrschr_ Ber- VDI-Z, 3 (11) (1966). Reference from Srarrb, M (11) (1966) 499. 52 P. S. ROLLER,Measurcmmr of -de size v;ith an 2-IC analyzer: tic fmcness and panicle tic disuibution of Portland cement. Proc_ ASTM. 32 (II) (1932) 607-25. 53 P_ S. ROLLER,Si distnbution of ceramic poadcrs as dctermined by a particle-sue axranalyzer, J_ Am. Ceram. Sot. 20 (1937) 167-74. 54 Instructions for opcrat~on of the Roller Analyzer_ American Illstrumat co. 55 R. E. Pow, Subslwc parude-nzc m-remem of metal powders by au eluuianon. J_ Rex Nar. Bzu_ Szzi, 17 (3) (1951) 13947.

Powder TechnoL, 3 (1969) 9-23