M ETHODS
H . E. SCIIWEYER1, C olum bia U niversity, New York, N. Y.
'I’he hydrom eter, pipet, and W agner turbid im eter m eth od s for d eterm in in g particle size d istrib u tion in the subsieve size ranges were stud ied in d etail.
The resu lts ob tain ed on a variety o f ground m a terials in dicated th a t th e hydrom eter and pipet m eth od s give concordant data w h ich arc also in agreem en t w ith th ose ob tain ed by air elu triation . On th e basis o f these resu lts a special p ip et for rapid an alysis was designed. U sing a spccial tech n iq u e for size d istrib u tion s down to 1.25 m icrons, it was show n th a t th e W agner turbid im eter gives good re
su lts on ly for ground san d, silica, and certain cem en ts. T h e data ob tain ed w ith th e Wagner m ethod for oth er m aterials were u n satisfactory on a basis o f b oth specific surface and size d istrib u tion . T he poor resu lts by th e tu rb id im eter on certain m aterials were show n to be cau sed by th e lack o f validity o f th e em pirical conversion o f turbid ity data to w eigh t con cen tration ; th is is o f su ch m a g n itu d e th at it lim its th e u se o f th e apparatus to ground silica and certain ce m en ts.
A
LARGE number of methods have been proposed for evaluating the particle size distribution and the specific surface of pulverulent materials (35). M any of these methods have a limited use in industry because they require expensive equipment or complicated techniques, or because the principles upon which their operation is based have not been fully developed. The latter is especially true of methods th a t have been proposed for a particular purpose or those th a t measure relative size only. However, a number of methods have widespread industrial use because of their simplicity and speed. The purpose of this investigation was to make a critical study of certain methods in order to determine w hat theoretical and practical considerations limit their use.
The methods th a t have the greatest industrial use employ sedimentation or elutriation principles, and, accordingly, base particle size results on the
equivalent settling diam
eter. The principal a ttri
butes of such methods are simplicity of operation and relatively good precision, provided certain factors are given consideration.
Te m p e r a t u r e Co n t r o l.
A ll. analyses should be run under as nearly isothermal conditions as possible, es
pecially in methods which require 12 to 24 hours to complete the analysis. The im portant effect of slight variations in room tempera
ture is not the viscosity of the suspending medium but rather on the change of density which produces con
vection effects.
* P r e s e n t a d d r ess, T h e T e x a s C o m p a n y , P o r t N e c h e s , T e x a s.
Di s p e r s i o n. The necessity for good dispersion cannot be overemphasized, since in order to measure the size of particles they m ust be separated. This dispersion is best effected by mechanical means and no simple hand stirring can be considered suitable unless the material is larger than 20 to 30 microns.
Shaking devices are applicable where long periods of agitation are desired. High-speed stirrers having a rotor enclosed by a stator to give high shearing action without swirling are efficacious (34)■
In most cases agents m ust be added to aid the dispersion; a number of these have been described (15, IS, 20, 36). Considera
tion m ust be given to whether the agent merely lowers the sur
face tension—i. e., a wetting agent—or whether it actually sepa
rates the particles and prevents flocculation—i. e., a dispersing agent. For water dispersions a 0.08 per cent sodium metasilicate (Metso granular) has been found satisfactory for many materials.
For materials not easily wetted, such as coal, the same solution can be used if the m aterial is first wetted with a small amount of ethanol. For materials th a t react with or dissolve in water, noil- aqueous media (23) may be used. The difficulty with such media is to obtain good dispersions. In the case of elutriation the dis
persion is obtained by mechanical means, which m ust avoid ap
preciable attrition.
Co n c e n t r a t i o n. Consideration m ust be given to the concen
tration of the suspension in order to eliminate hindered settling and flocculation as much as possible. In general, sedimentation methods employ concentrations of less than 5 per cent, and hin
dered settling is not likely to occur (17).
Br o w n i a n Mo v e m e n t. While Brownian movement is un
doubtedly a factor in size determinations by gravity sedimentation of very fine materials, it probably is not im portant where most of the material is above 1 micron in size.
P h y s i c a l P r o p e r t i e s . The precision of sedimentation measurements is partly dependent upon the accurate determina
tion of the physical properties used in Stokes’ law. For this reason the densities of both liquid and solid and the viscQsity of the suspending medium should be determined by sound methods (2, 6).
Te s t Pr o c e d u r e. The sedimentation tim e should be meas
ured accurately, especially for the coarse sizes, since the precision is lowest in th a t size range. The sedimentation should be carried out in a constant-tem perature bath free from appreciable agita
tion and the sedimentation vessels should be placed in a vertical position to prevent convection currents produced by nonuniform density changes.
S i z e L i m i t s . The upper lim it of sedimentation methods is controlled by the applicability of Stokes’ law up to Reynolds numbers equal to 1, and also by the practicability of tim ing the coarse sizesjthat the particular method allows. The upper limit
Fi g u r e 1 . Pi p e t An a l y s e s
622
August 15, 1942 A N A L Y T I C A L E D I T I O N 623
• T U R B ID IM E T E R O H Y D R O M E T E R A A I R A N A L Y Z E R
* • S P E C IA L P I P E T
2 0 - 4 0 ^ FRACTION
196
X , V SPECIAL P I P E T
■ TURBIDIMETER-A
□ TURBIOIMETER- B Fi g u r e 2 . Sp e c i a l Pi p e t
is, in general, about 75 to 90 microns. The lower limit is con
trolled by the speed with which the results are desired, but is in general about 0.5 to 1 micron. . . . .
Ca l c u l a t i o n s. T he calculations are similar in all methods and are described in detail in another publication (34), which also gives the complete procedure employed in the present study.
S t u d y o f I n d iv id u a l M e th o d s
All methods studied in this investigation are of the incre
ment type (35)—i. e., the size distribution is determined directly in increments rather than indirectly by graphical differentiation of a sedimentation curve as is necessary for cumulative methods (35).
P i p e t M e t h o d . The pipet method employing the appara
tus designed by Andreasen (6) when used under the pioper conditions has been found
satisfactory for determining particle size distribution.
The weight of particles of a given size remaining in suspension is determined directly, the height of fall is determined by direct meas
urement, the proper tech
n iq u e c a n b e le a r n e d quickly, and the apparatus is relatively inexpensive.
On the basis of comparative studies, the pipet method is recommended as the best for the determination of particle size distribution based on the sedimentation diameter if complete dis
persion of the particles can be obtained.
The results of a number of analyses on ground Ottawa
sand, F-14, using the technique described elsewhere (34) are shown in Figure 1 along with data obtained by other methods used in the present study. These data and studies of a large number of other materials, show th a t an average deviation of less than 2 per cent by weight a t any given size can be a t
tained by the pipet method.
The principal disadvantage of the Andreasen pipet method is the time required to run the analysis to very small sizes, since in many cases the elapsed time to reach 1.25 microns is 24 hours. As shown in Figure 1, using a cylinder half full, the time can be shortened by reducing the height of fall with
out greatly affecting the precision. Stokes’ law states th at the time required to separate a given particle diameter is directly proportional to the height of fall and the viscosity of the medium and inversely proportional to the difference in density of the suspending medium and of the suspended solid.
I t is, therefore, possible to reduce somewhat the time of test by using liquid media other than water, if good dispersion can be obtained. In an effort to reduce the time of test in the pipet method, a special pipet was designed (Figure 2). Its dimensions and the procedure for use are given elsewhere (34).
Such a pipet allows an analysis to be made in one fourth the time required for the Andreasen pipet by utilizing shorter distances of fall for the small sizes; the precision in the coarse size range is not affected since a long distance of fall is used for the large sizes. Results shown in Figure 3 indicate th a t it yields particle size data in good agreement with those from other methods.
Since the pipet method is based on no assumptions other than the validity of Stokes’ law, it offers a precise method of particle size analysis to which other methods may be com
pared and as such serves a calibration method. In the devel
opment of other rapid methods the results m ay be compared with those from the pipet method to prove, their validity for the particular problem involved. The pipet method has been used by Hogentogler and Wills (21) for soils, by Loomis (24) for settling periods of 96 hours on clays, by Andreasen (7) in studies on the grinding of iron oxide and barytes, and by Lea and Nurse (23) in studies on cement.
The manipulations required in the pipet method are numerous and limit to a certain extent the number of points on the curve th a t can be determined where a large number of tests are being run by a single person. The use of a cumula
tive per cent undersize versus log diameter plot of the data where the points are judiciously selected allows interpolation for the intermediate points.
D I A M t T t R , I V l l C R O N S
F i g u r e 3 . S i z e D i s t r i b u t i o n o f S i l i c a s
624 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 14, No. 8 analysis, first described by Bouyoucos (12), the concentration a t some level, a t a distance h from the surface, is measured and described hydrometers, but the streamlined Bouyoucos hydrometer type now m anufactured gives results in good agreement with other methods as is shown in Figure 4 for silica, using the author’s technique (34). For this hydrome
ter the height of fall, h, is computed as 0.42 times the dis
tance from the surface of the liquid to the bottom of the hydrometer. This factor, which was determined empirically by Thoreen for the old type of Bouyoucos hydrometer, may vary with different hydrometers and for best results should be determined by calibration. The alternative specific gravity type of hydrometer might be used, although there appears to be no necessity for having two types for the same purpos3.
For this type the height of fall is equal to the distance from the surface to the center of volume. The results obtained with this instrum ent are shown in Figure 4; because it m ay give low results, the streamlined Bouyoucos type is preferred.
The hydrometer method has been criticized on the basis of certain theoretical aspects, such as the fact noted by Puri (28) th a t there is a density gradient from the top to the bottom of the suspension. However, these objections have not proved to be critical, since the experimental data indicate th a t the hydrometer gives results as precise as the pipet method if the possible sources of error are eliminated. Bouyoucos (13, 14) studied the density gradient aspect and showed th a t in spite of it the hydrometer gives the proper result. Certain in
vestigators have proposed a correction factor for the variation in displacement resulting from the use of containers of differ
ent diameters. The experimental data illustrated in Figure 5 show th a t even a 50 per cent variation in diameter has a relatively small effect on the results and th a t it is not necessary to make any correction when using ordinary 1000-cc. gradu particular solid-water system as is done a t present.
Since the determination of concentration depends on density difference and a small difference may not be recorded on the hydrometer, Bouyoucos (11) has suggested using a special hydrometer for the small size ranges when most of the suspended material has settled out (concentrations of less than 10 grams per liter). The use of this hydrometer does not complicate the method unduly if high precision is desired.
The precision with the hydrometer method is equal to that of the pipet, with deviations of less than =t 2 per cent. The method has been used extensively for soils on which Thoreen (38) has shown th a t for up to 40 per cent of less than 1 micron the results agree w ith a pipet method. The precision is best for very fine materials since the larger density differences are evaluated more accurately by the hydrometer. The precision in the coarse ranges depends upon how accurately the particles can be timed. The range of sizes covered is about the same as w ith the Andreasen pipet, b u t since the distance of fall decreases w ith decrease in concentration in the hydrometer and is never as great as in the Andreasen pipet method, the former requires about one half the time for measurements down to 1 micron.
T he chief advantages of the hydrometer method over the pipet method are in the more simple operations required since the concentrations are read directly (16). I n addition, one hy
drometer can be used to make a num ber of analyses simultane
ously if they are staggered to allow for the dispersing and 30-minute initial starting period.
Ap p l i c a t i o n s o p Hy d r o m e t e r Me t h o d. Reimers (29) has used the hydrometer method for clays. Bauer (9) has used it for evaluating the relative value of deflocculating agents._ Biddle and Klein (10) have compared the results on cements with those obtained by the Klein turbidim eter. They doubt the use of the hydrometer for cements having surfaces greater than 2000 sq.
cm. per gram, because the results did not agree with the turbi
dimeter. A similar conclusion was reached by Gran (19) for results based on the hydrometer and Wagner turbidim eter. In reaching these conclusions all these authors apparently overlooked the fact th a t the turbidim eters m ay not be giving the correct result, which is shown below to be the cause of lack of agreement.
The data developed in this study show th a t the h y d r o m e t e r
has yielded results as precise as the pipet method and may be
considered a sound method.
A i r A n a l y z e r . The air analyzer developed by Roller
(30, 31) is one of several types of elutriators that have been
discussed elsewhere (35). I t has been used successfully by a number of investigators and, as is the case with all elutriators, the size analysis yields fractions of the whole powder th at can be studied individually. A number of materials used in this investigation have been analyzed in this apparatus, and the results compared w ith those from other methods. The apparatus gives good results down to about 2 microns if the material is not subject to attrition effects, but the time per analysis is greater than for other methods and the instrument is considerably more expensive.
W a g n e r T u r b i d i m e t e r M e t h o d . In general, turbidi- metric methods for determining particle size distribution have not proved satisfactory, although they have been widely used in various industries and are useful in evaluating relative size.
The fact th a t the fundamental relations for converting tur
bidity data to weight distribution have not been rigorously established for these methods has resulted in conflicting statements in the literature regarding their accuracy com
pared to other methods. Turbidimetric methods offer ad
vantages in the small sample required, simplicity of operation, and saving of time; for these reasons a rather comprehensive study was made of one particular method (4, 40), and the results obtained were compared with those from other meth
ods.
The Wagner turbidimeter method is essentially a sedimen
tation method of the increment (35) type in which the change in weight concentration a t a given depth and time of sedi
mentation is computed from the change in turbidity as measured by a photoelectric cell. (The weight concentra
tions, however, are computed directly to surface in the Wagner equations.) As has been pointed out (35), the turbidity relations are very complex, and while the Wagner method was proved valid for one type of material—cements of certain specific surfaces and certain size distributions (1)—
it appears to be rather limited in its application.
The surface of the particles (assumed as spheres) is computed from the following form of the Beer-Lambert law:
- l o g T = E = kW l/d (1) where T = fractional transmission
E = extinction
W = concentration in grams per liter of suspension I = thickness of the suspension, cm.
d — diameter of the particles, microns
k = optical constant which includes the density of the particle
August 15, 1942
If the transmission of suspensions of particles exhibiting similar optical effects is obtained, it should be possible to convert the turbidity data to weight and thereby determine the size distri
bution. However, the general applicability of Equation 1 has not been proved. Wagner (40) has stated th a t the relation is invalid above 60 microns. Since the size a t which a No. 325 sieve separates may be considered as 53 microns on a sedimentation basis, this serves as a convenient datum for the application of Equation 1. If Equation 1 is applied to polydisperse powders, W m ust be the weight smaller than 53 microns and d must be the mean diameter for th a t material.
In practice Equation 1 is used in the following form by Wagner:
E, = log ( /,,//,,) = S j/C (2) where E/ — extinction for the fraction between diameters <ii
and
I j i = intensity of light just as the last particles of size di are settling out of the light beam
Id. = intensity of light just as the last particles of the next smaller size, di, are settling out of the light beam
S/ = total surface of all particles and larger, but smaller than dt
C = optical constant which is determined empirically based on the assumption th a t C is a constant for all sizes, regardless of the am ount and size of other particles th a t are present
Equation 2 is a special form of Equation 1, since the surface of the particles is proportional to W /d, which permits the calcu
lation of the weight distribution from the values of S/ for the indi
vidual fractions. The equation for this computation as derived from Equation 1 is:
W, J Ef d ,/K " (3)
where W/ = weight (grams per liter of suspension) between size limits di and di
d; = arithmetic mean size of the fraction, microns K ’ = optical constant which also includes the density
of the particles and the thickness of the suspension In order to use Equation 3 it is necessary to know the value of A'*, which is obtained by assuming it is constant for all sizes.
Thus it may be computed from Equation 5, wherein all unknowns are evaluated from the experimental data.
W P = SIT, = 2(E ,d,/K ") ( 4 )
or,
K " = Z (E ,d ,)/W r (5) where Wf is the total weight in the size ranges for which E qua
tion 3 is valid—below 53 microns (No. 325 sieve)—
and is determined by sieve analysis.
Since the property usu
ally evaluated is surface, the particles in the small size ranges are the most im portant. This is appa
rent from a consideration of the equations, since a relatively large error in the coarse size ranges (which affects the weight distribution considerably) does not greatly affect the total specific surface if the surface data in the smaller size ranges are essentially correct.
In order to minimize certain serious criticisms of the apparatus and tech
nique, a number of modi
fications of the method were necessary.
625
Fi g u r e 5 . Hy d r o m e t e r An a l y s e si n Gr a d u a t e s o f Di f f e r e n t Di a m e t e r
A N A L Y T I C A L E D I T I O N
626 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y VoL 14, No. 8
Apparatus Considerations. The slit opening in the apparatus is 1.59 cm. which is not a serious consideration for large sizes,
Apparatus Considerations. The slit opening in the apparatus is 1.59 cm. which is not a serious consideration for large sizes,