Particle Size Distribution of Particles from 10 to 2000 Microns by Sedimentation Analysis L. C. Bate and F. F. Dyer Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.
THE PARTICLE SIZE distribution
of large particles is usually determined by means of sieves. The use of sieves is possible except where the bulk of the material has a particle size of 5 microns or smaller, the large particles are fragile and the action of the sieves would cause them to disintegrate, the particles are radioactive, and a finer resolution of particle sizes than can be obtained with sieves is required. This method was developed for two applications: to determine the concentration of nonfragile clinkers (particles larger than 10 microns in diameter) in thoria particles fired to high temperatures, and to measure particle-size distributions of fragile particles that were radioactive and too large to be studied by the conventional sedimentation methods (1-4). PRINCIPLES OF SEDIMENTATION
This method is a modification of other sedimentation methods (1-4) in which the particles are dispersed throughout the medium before the start of sedimentation. In this method the particles are released at the top of the column to begin sedimentation. This technique is necessary for particles that are too large to be kept dispersed throughout the medium for any significant time. In addition, this technique prevents large fragile particles from being broken, and eliminates the entrainment of air bubbles in viscous sedimentation media. The viscosity and density of the supporting medium are adjusted so that the particles settle according to Stoke’s law (Equation 1).
ds = diameter of particle, cm 1 micron = cm h = sedimentation distance, cm 7 = viscosity of supporting medium, poise Dz = density of particles, gram/cm3 D1 = density of supporting medium, gram/cm3 g = acceleration due to gravity, cm/sec2 t = sedimentation time, sec
In a single system where the same medium and density of particles are used, the constants in Equation 1 can be combined so that the equation can be reduced to
K
ds = -
dT
(1) G . W. Leddicotte, H. H. Miller, R. E. Druschel, M. T. Kelly, and L. C . Bate, “Particle Size Distribution Analysis of Radioactive Materials,” 1958 National Symposium on Instrumental Methods of Analysis, Vol. 4, Houston, Texas, May 12-14, 1958, p 117-27. (2) E. H. Arnstein and B. A. Scott, J. Appl. Chem. (London), 1, Suppl. No. 1 , 510 (1951). (3) L. C. Bate and G. W. Leddicotte, “Particle-Size Distribution in Thorium Oxide, Neutron Activation-Sedimentation Method,” ORNL Master Manual Method No. 5, 10200. (4) C. P. Ross, “Particle Size Analysis by Gamma-Ray Absorption,” ANAL.CHEM., 31, 337-9 (1959).
468
ANALYTICAL CHEMISTRY
Figure 1. Photograph of sedimentation tubes where K denotes the combination of the constants in Equation l. As seen from Equation 1, the time required for a particle to fall through the medium depends on its size-(Le., the larger particles fall faster). Thus by removing the settled particles from the bottom of the column at appropriate time intervals, all the particles of a specific size range are obtained in each fraction. EXPERIMENTAL Apparatus. The sedimentation apparatus consists of a water-jacketed glass tube with a borosilicate glass stopcock (T 10) on each end. Several columns are pictured in Figure 1. The sample fractions are collected at the bottom in a samplecollecting vial. The top is funnel shaped to aid sample introduction. Before the stopcocks were installed, their bores were precision ground to the size of the sedimentation tube (11-mm i.d.). This eliminated small ledges within the stopcocks on which particles could settle. The sedimentation tube was 14-mm 0.d. with a 1.5-mm wall. The total sedimentation distance (including the bores of the stopcocks) was 100 cm. A male ground glass joint (SjT, 14/10) was installed 2 inches below the bottom stopcock. The sample collector (15 X 80 mm tall form weighing bottle) was connected by means of this ground glass joint. A water jacket
was welded between the two stopcocks to minimize thermal convection caused by air currents. Radioactivity Measurements. The radioactivity of the collected fractions was measured by a gamma-ray spectrometer to integrate photopeak areas. Thoria samples were measured by using their natural radioactivity. When received the samples of ZrOz, A1203, and MgO contained about lo7 dpsigram. The radioactivity produced and measured in each material was as follows: 94Zr(n, y)94Zr (0.72, 0.75 MeV y), 27Al(n,a)24Na(1.37 MeV y), and 24Mg(n, p)24Na (1.37 MeV y). The glass beads were neutronirradiated to form lo7 dps of 24Naper gram of sample. The radioactivity of the sample fractions was counted until about 104 counts were accumulated in the appropriate photopeak areas. Counting errors were therefore about k 1.0%. The Clinker Test. The fine fraction of thoria samples forms clinkers when fired above 1000” C. These larger particles which are not easily broken into smaller ones interfere in reactor loop tests (in pumping operations, settling out, etc.) to an extent depending on their concentration (5). To measure the quantity of clinkers in fired thoria, a 0.5gram sample was weighed in a weighing vial (15 X 80 mm) and an aliquot of an aqueous solution of 0.005M Na4P207 (dispersant) ( I , 3) was added to the vial. After being dispersed, the particles were allowed to settle for 4 minutes to permit the clinkers to settle. The supernate slurry was syphoned off, to remove a fraction of the fine particles. This process was repeated until essentially all the fine particles were removed. If the fines were not preseparated before the slurry was added to thetop of the column, the slurry did not settle as individual particles but flowed down the supporting medium in a turbulent manner. The coarse particle fraction was transferred to the top of the column which was filled with supporting medium. During this transfer, the top stopcock was closed. The supporting medium in this analysis was 0.005M Na4P207water solution. Sedimentation was begun when the top stopcock was opened. A sedimentation of 31 minutes and 5 seconds measured from the time this stopcock was opened was sufficient for particles of 10 micron or larger to fall past the bottom stopcock. The bottom stopcock was closed, the collector containing the clinkers was removed, and their radioactivity was measured. Three small aliquots from the original sample were weighed and their radioactivity was counted to obtain the counts per milligram of Tho2. This permitted the per cent clinkers in the sample to be calculated. Results of Clinker Tests. Typical results obtained by this procedure are tabulated in Table I as the weight per cent of particles with diameter of 10 microns or greater. Deviathe range of tions of measurements are expressed as =t1/2 values obtained for the several measurements on each sample. It should be noted that the clinker concentration of these samples varies from 0.012 to 64.3 %. DISCUSSION
The clinker analysis was shown to be a reliable method to evaluate the product thoria prior to loop tests and relate the clinker content with the wear of slurry pumps and piping (5). On certain samples containing appreciable amounts of clinkers, particle size distribution curves were obtained by the method previously described (3). The fraction of the particles, found by this method, to have diameters of 10 microns or greater agreed closely with the results of the clinker test. The sedimentation procedure developed in these studies was subsequently applied in pilot plant operations to separate the undesirable coarse particles from thoria product. (5) K . 0. Johnson and R. H. Winget, “Pilot Plant Preparation of
Thorium and Thorium-Uranium Oxide,” ORNL 2853, Dec. 8, 1959.
Table I. Typical Data Obtained in “Clinker” Test (Particle Size: 10 Microns or Greater)
Sample 1
4
Average
2 Greater
2 greater
2.56 2.52 2.55 2.58 2.51 2.53 0.21 0.24 0.22 0.25 55.8 54.0 57.8 55.3
2.54
Deviation f0.04
0.23
f 0.02
55.7
f2.1
0.010
0.010 0.014 0.011 0.011 0.014 0.21 0.17
0.012
f0.002
0.19
f0.04
0.47
f0.02
0.15
0.22 0.49 0.45 0.45
7
0.48 63.4 62.4 62.6 66.4 65.5 65.6
64.3
f2.1
Choice of Supporting Media for Particle Size Distribution Studies. The rate of sedimentation of particles in a supporting medium is determined by the viscosity and to a lesser extent by the densities of the medium and the particles. The only media found to have suitable physical properties were aqueous glycerol solutions wherein the viscosity could be varied from 0.893 centipoise (value for water) to 945 centipoise (value for glycerol) at 25 O C (6). The particle size distribution of the materials studied ranged from 10 microns to 2000 microns. Because of the wide variation of particle sizes in some materials, several compositions of glycerolwater solutions were found to be necessary to define the various distribution curves. Particle Size Distribution Analysis. Particle size distribution curves were determined on sieve-size (10-2000 micron) particles of MgO, ZrOz, Thoz, AlzO2, and glass beads. The sedimentation procedure used was similar to that of the clinker test. Two opposing factors determine the quantity of sample taken for analysis. The sample must be small enough to ensure that particles will fall individually and yet large enough to provide a reliable resolution of the distribution curve. In most instances samples of about 0.5 gram were found to be optimum. The radioactivity of the samples was measured before sedimentation to permit calculation of the mass of each fraction collected. Supporting media of suitable viscosities (6) “Handbook of Chemistry and Physics,” 36 Ed., p 2015, Chemical Rubber Publishing Co., Akron, Ohio, 1954. VOL 40, NO. 2, FEBRUARY 1968
469
>-1
500 ---___ .......5
........ .......... Li
N cn
................
......
100
u
SAMPLE^ METHOD
*.*.a.
I
\MEDIUM [CENTIPOISE SEDIMENTATION
F
a
8 IO0
0.01
Medium, 45.86 C.P. Glycerol-Water Sedimentation Distance, (00 cm
101 2
I
5
I
I
l
l
l
l
l
I
I
I
1 1
Figure 2. Particle size distribution of MgO, Thot, A l t o , and ZrOz
were prepared by mixing appropriate amounts of glycerol with water. Because the density of the particles was approximately known and the sizes of the particles could be visually estimated, it was possible to use Stoke’s law so that particles of predetermined size range were collected. The radioactivity of each fraction collected was measured to determine the concentration (per cent of total weight) of each fraction. The size range of particles collected in each fraction was calculated from the sedimentation times using Stoke’s law (Equation 2). RESULTS
The data for most systems were plotted on Log-Normal Probability paper to determine if the particles obeyed the Hatch-Choate distribution (7). Data for some typical samples of MgO, Thon,A1203,and ZrOz are plotted in Figure 2 as particle size 6s. the cumulative percentage of particles larger than that indicated. The curves in Figure 3 represent the size distributions of five different glass bead samples. The glass beads were supplied by the manufacturer with specified size ranges for use in distillation columns. Because the columns did not operate as expected (the number of theoretical plates disagreed with experimental), the size distribution of the beads was measured. The average diameters of the beads obtained by this method permitted values for the number of theoretical plates of the col(7) C. Orr, Jr., and J. M. Dallavalle, “Fine Particle Measurement,” Macmillan, New York, 1959.
ANALYTICAL CHEMISTRY
I 5
I
I
I
20
50
80
I I 95 99.5 99.99
PARTICLES OF SIZE LARGER THAN THAT INDICATED, %
10 20 30 4 0 506070 80 90 95 98 PARTICLES OF SIZE L A R G E R T H A N THAT INDICATED, %
470
I 0.5
--
Figure 3. Particle size distribution of glass beads
umn to be calculated; these agreed with the experiment (8). The curves in Figure 3 were obtained by the method reported here. The particle size distribution curves shown for MgO, Alz03, and glass beads in Figures 2 and 3 are representative of the samples studied. The data, which could be approximately fitted by a straight line (on log-normal probability paper), were indicative of a Hatch-Choate distribution. Distribution curves for other samples exemplified by the results for the T h o z and ZrOs in Figure 2 seemed to be described by two intersecting straight lines. This was interpreted by assuming that these materials consisted of two particle size distributions, each obeying the Hatch-Choate logarithmic function but with different mean and dispersion indices. CONCLUSION
The sedimentation method described has proved useful not only for clinker analysis but also for particle size distribution measurements of particles in the range 10-2000 microns in diameter. The particle size resolution of the method can be increased to any degree desired by increasing the number of fractions taken and/or by using longer columns. The technique of measuring the mass of the collected particle fractions provides much greater sensitivities than conventional procedures. In addition, the technique is rapid because the radioactivity is measured without separating the particles from the sedimentation medium. The 45.86 centipoise glycerol-water solution was found to be the most useful medium but other media from pure glycerol to water can be used depending on particle size range and density of the particles. RECEIVED for review July 19, 1967. Accepted November 24, 1967. Research sponsored by U. S. Atomic Energy Commission under contract with Union Carbide Corp. (8) J. W. Snyder, ORNL, private communication, November 1959.
