Particle Size Studies METHODS H. E. SCHWEYER’, Columbia Uni\ersity, New York, S . 1.
DISPERSION.The necessity for good dispersion cannot be overemphasized, since in order to measure the size of particles they must 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 t o 30 microns. Shaking devices are applicable where long periods of agitation are desired. High-speed stirrers having a rotor enclosed by a stator t o give high shearing action without swirling are efficacious (34) In most cases agents must be added to aid the dispersion; a number of these have been described (15,18,20 36). Consideration must be given to whether the agent mereiy lowers the surface tension-i. e., a wetting agent-or whether it actually separates 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 material is first wetted with a small amount of ethanol. For materials that react with or dissolve in water, nonaqueous media (23) may be used. The difficulty with such media is to obtain good dispersions. In the case of elutriation the dispersion is obtained by mechanical meam, which must avoid appreciable attrition. COKCESTRATIOK. Consideration must be given to the concentration 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 hindered settling is not likely to occur (17 ) . BROWNIAX MOVEMEKT. While Brownian movement is undoubtedly a factor in size determinations by gravity sedimentation of very fine materials, it probably is not important where most of the material is above 1 micron in size. PHYSICAL PRoPERTIEs. The precision of sedimentation measurements is partly dependent upon the accurate determination of the physical properties used in Stokes’ law. For this reason the densities of both liquid and solid and the viscosity of the suspending medium should be determined by sound methods
The hydrometer, pipet, and Wagner turbidimeter methods for determining particle size distribution in the subsieve size ranges were studied in detail. The results obtained on a variety of ground materials indicated that the hydrometer and pipet methods give concordant data which are also in agreement with those obtained by air elutriation. On the basis of these results a special pipet for rapid analysis was designed. Using a special technique for size distributions down to 1.25 microns, it was shown that the Wagner turbidimeter gives good results only for ground sand, silica, and certain cements. The data obtained with the Wagner method for other materials were unsatisfactory on a basis of both specific surface and size distribution. The poor results by the turbidimeter on certain materials were shown to be caused by the lack of validity of the empirical conversion of turbidity data to weight concentration; this is of such magnitude that it limits the use of the apparatus to ground silica and certain cements.
A
LARGE number of methods have been proposed for
evaluating the particle size distribution and the specific surface of pulverulent materials (35). Many 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 that have been proposed for a particular purpose or those that 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 what theoretical and practical considerations limit their use. The methods that have the greatest industrial use employ sedimentation or elutriation principles, and, accordingly, base particle size results on the equivalent settling diameter. The principal attributes of such methods are simplicity of operation and relatively good precision, provided certain factors are given consideration.
(2, 5).
TESTPRocEDuRE. The sedimentation time should be measured accurately, especially for the coarse sizes, since the precision is lowest in that size range. The sedimentation should be carried out in a constant-temperature bath free from appreciable agitation and the sedimentation vessels should be placed in a vertical position to prevent convection currents produced by nonuniform density changes. SIZELIMITS. The upper limit of sedimentation methods is controlled by the applicability of Stokes’ law up to Reynolds numbers equal to 1, and also by the practicability of timing the coarse sizes that the particular method allows. The upper limit
TEMPERATURE CONTROL. All analyses should be run under as nearly isothermal conditions as possible, especially in methods which require 12 to 24 hours to complete the analysis. The important effect of slight variations in room temperature is not the viscosity of the suspending medium but rather on the change of density which produces convection effects. DIAMETER, M I C R O N S Present address. The Texas Company, Port Nechea, Texas. 1
FIGURE 1. PIPETANALYSES 622
August 15, 1942
ANALYTICAL EDITION
FIGURE
2.
SPECIAL PIPET
is, in general, about 75 to 90 microns. The lower limit is controlled by the speed with which the results are desired, but is in general about 0.5 to 1 micron. CALCULATIONS. The calculations are similar in all methods and are described in detail in another publication (S4), which also gives the complete procedure employed in the present study.
Study of Individual Methods All methods studied in this investigation are of the increment type (55)-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 (55). PIPETMETHon. The pipet method employing the apparatus designed by Andreasen (6) when used under the proper conditions bas 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 measurement, the proper technique can be learned 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 dispersion of the particles can he obtained. The results of a number of analyses on ground Ottawa
623
sand, F-14, using the technique described elsewhere (54) are shown in Figure 1along with data obtained by other methods used in the present study. These data and studies of a large number of other materials, show that an average deviation of less than 2 per cent by weight a t any given size can be attained 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 t i e can be shortened by reducing the height of fall without greatly affecting the piecision. Stokes’ law states that 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. It is, therefore, possible to reduce somewhat the time of test by using liquid media other than water, if good dispersion can he obtained. I n 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 (54). 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 that 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, i t offers a precise method of particle size analysis to which other methods may be compared and as such serves a calibration method. In the development of other rapid methods the results may he 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 (9f) for soils, by Loomis ($4) 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 (95) 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 that can be determined where a large number of tests are being run by a single person. The use of a cumulative per cent undersize versus log diameter plot of the data where the points are judiciously selected allows interpolation for the intermediate points.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 14, No. 8
calibrating temperatures and materials) to per cent remaining in suspension a t the temperature of test. Since t h e hydrometer method for determining concentration depends on the difference in density of the medium and suspension, and since these differences are generally small in numerical value, it is imperative that such densities should be known accurately. The best means of making these corrections is by calibration in a manner which makes one hydrometer universally applicable for any solid-liquid DIAMETER, MICRONS system used ($4). I n this respect a streamFIGURE4. SIZEDISTRIBUTIOX BY HYDROMETER lined Bouyoucos hydrometer would be more satisHYDROMETER METHOD. I n the hydrometer method for size factory if calibrated in true density than if calibrated for one particular solid-water system as is done a t present. analysis, first described by Bouyoucos (1,9), the concmtration Since the determination of concentration depends on a t some level, a t a distance h from the surface, is measured directly, thus eliminating the necessity of taking samples as density difference and a small difference may not be recorded on the hydrometer, Bouyoucos (11) has suggested using a in the pipet method. h varies with the concentration and special hydrometer for the small size ranges when most of the has been found to be a function of the type of hydrometer used. suspended material has settled out (concentrations of less than 10 grams per liter). The use of this hydrometer does The best discussion of this method was given by Thoreen not complicate the method unduly if high precision is desired. (38),whose work formed the basis for the A. S. T. hf. method The precision with the hydrometer method is equal to that of test (3). Other investigators have discussed this method of the pipet, with deviations of less than *2 per cent. The and described hydrometers, but the streamlined Bouyoucos hydrometer type now manufactured gives results in good method has been used extensively for soils on which Thoreen (98) has shown that for up to 40 per cent of less than 1micron agreement with other methods as is shown in Figure 4 for the results agree with a pipet method. The precision is best silica, using the author’s technique (34). For this hydromefor very fine materials since the larger density differences are ter the height of fall, h, is computed as 0.42 times the disevaluated more accurately by the hydrometer. The precision tance from the surface of the liquid to the bottom of the hydrometer. This factor, which was determined empirically in the coarse ranges depends upon how accurately the particles can be timed. The range of sizes covered is about the same by Thoreen for the old type of Bouyoucos hydrometer, may vary with different hydrometers and for best results should be as with the Andreasen pipet, but since the distance of fall decreases with decrease in concentration in the hydrometer determined by calibration. The alternative specific gravity and is never as great as in the Andreasen pipet method, the type of hydrometer might be used, although there appears to former requires about one half the time for measurements be no necessity for having two types for the same purpos.. down to 1 micron. For this type the height of fall is equal to the distance from the surface to the center of volume. The results obtained The chief advantages of the hydrometer method over the with this instrument are shown in Figure 4; because it may pipet method are in the more simple operations required since give low results, the strramlined Bouyoucos type is preferred. the concentrations are read directly (16). I n addition, one hyThe hydrometer method has been criticized on the basis of drometer can be used to make a number of analyses simultanecertain theoretical aspects, such as the fact noted by Puri (28) ously if they are staggered to allow for the dispersing and that there is a density gradient from the top to the bottom of 30-minute initial starting period. the suspension. However, these objections have not proved to be critical, since the experimental data indicate that the APPLICATIONSOF HYDROMETER METHOD. Reimers (29) has used the hydrometer method for cla s. Bauer (9) has used it hydrometer gives results as precise as the pipet method if the for evaluating the relative value of deffocculating agents. Biddle possible sources of error are eliminated. Bouyoucos ( I S , 14) and Klein (10) have compared the results on cements with those studied the density gradient aspect and showed that in spite obtained by the Klein turbidimeter. They doubt the use of the of it the hydrometer gives the proper result. Certain inhydrometer for cements having surfaces greater than 2000 sq. cm. per gram, because the results did not agree with the turbivestigators have proposed a correction factor for the variation dimeter. A similar conclusion was reached by Gran (19) for results in displacement resulting from the use of containers of differbased on the hydrometer and Wagner turbidimeter. In reaching ent diameters. The experimental data illustrated in Figure these conclusions all these authors apparently overlooked the 5 show that even a 50 per cent variation in diameter has a fact that the turbidimeters may not be giving the correct result, which is shown below t o be the cause of lack of agreement.. relatively small effect on the results and that it is not necessary to make any correction when using ordinary 1000-cc. graduThe data developed in this study show that the hydrometer ates. has yielded results as precise as the pipet method and may be Among the sources of error, which can be eliminated by considered a sound method. proper technique, are the lack of maintaining a constant AIR ANALYZER.The air analyzer developed by Roller temperature and the indiscriminate use of formulas for (30,91) is one of several types of elutriators that have been correcting the observed readings (which are based on the
August 15, 1942
discussed elsewhere (36). It 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 that can be studied individually. A number of materials used in this investigation have been analyzed in this apparatus, and the results compared with those from other methods. The apparatus gives good results down t o 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. WAGNERTURBID~METER METHOD. In general, turbidimetric 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 that t h e fundamental relations for converting turbidity data t o weight distribution have not been rigorously established for these methods has resulted in conflicting statements in the literature regarding their accuracy compared to other methods. Turbidimetric methods offer advantages 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 methods. The Wagner turbidimeter method is essentially a sedimentation method of the increment (35) type in which the change in weight concentration at a given depth and time of sedimentation is computed from the change in turbidity as measured by a photoelectric cell. (The weight concentrations, however, are computed directly t o surface in the Wagner equations.) As has been pointed out (56), 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.
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 distribution. However, the general applicability of Equation 1 has not been proved. Wagner (40) has stated that the relation is invalid above 60 microns. Since the size at which a No. 325 sieve separates may be considered as53 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 must be the weight smaller than 53 microns and d must, be the mean diameter for that material. In practice Equation 1is used in the following form by Wagner:
where El
extinction for the fraction between diameters dl and dZ Z d , = intensity of light just as the last particles of sire dl are settling out of the light beam I d 2 = intensity of light just as the last particles of the next smaller size, d2, are settling out of the light beam S, = total surface of all particles dp and larger, but smaller than dl C = optical constant which is determined empirically based on the assumption that C is a constant for all sizes, regardless of the amount and size of other particles that are present
-log T = = = = = =
=
E
=
kWl/d
=
Equation 2 is a special form of Equation 1, since the surface of the particles is proportional to W / d , which permits the calculation of the weight distribution from the values of S, for the individual fractions. The equation for this computation as derived from Equation 1 is: W, where W,
The surface of the particles (assumed as spheres) is computed from the following form of the Beer-Lambert law:
where T E W I d k
625
ANALYTICAL EDITION
df = K" =
(3)
weight (grams per liter of suspension) between size limits dl and dt arithmetic mean size of the fraction microns 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 K " , 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.
(1)
fractional transmission extinction concentration in grams per liter of suspension thickness of the suspension, cm. diameter of the particles, microns optical constant which includes the density of the particle
=
E/df/K"
W F = ZWl = X(Eld//K")
(1)
K" = Z ( E / d f ) / w F
(5)
or, where W Fis the total weight in the size ranges for which Equation 3 is valid-below 53 microns (No. 325 sieve)and is determined by sieve analysis. Since the DroDertv usually evaluated is surface, the particles in the small size ranges are the most important. This is apparent 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 technique, a number of modifications of the method were necessary. I
DIAMETER, MICRONS
FIGURE 5. HYDROMETER ANALYSESI N GRADVATES O F DIFFEREST DIAMETER
.
"
INDUSTRIAL AND ENGINEERING CHEMISTRY
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TABLE I. COMPARISON OF DATAFOR AMOUNT PASSING A No. 325 SIEVE Material
B y Nozzle0
70
B y Dispersionb
Remarks
%
Min.
74.9 2 73.5 Very flaky 74.9 5 79.1 78.8 2 75.2 Normal Silica D-2 29.7 1 25.3 Very coarse Silica W-1 0 1-gram sample a t 10 pounds per s q . inch water pressure for 1 minute. b 0.5-gram sample dispersed with mechanical stirrer and washed through sieve with light spray from wash bottle. Silica 4-168
TABLE 11. VARIATIOK IN PROPERTIES OF CEMENT114c UPON EKDPOINT DEPENDIXG Sample Weight Gram
a
E n d Point Mzcrons
