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An experimental investigation of particle size analysis by a modified andreasen pipet
Powder
Technology,
48 (1986) 23 - 29
23
An Experimental Investigation of Particle Size Analysis by a Modified Andreasen Pipet YE-MON CHEN and SHAN-WON DO0 Department (Taiwan)
of Chemical
Engineering
(Received December 2,1985;
and Technology,
National
Taiwan Institute
of Technology,
Taipei 107
in revised form May 19,1986)
SUMMARY
The Andreasen pipet is very commonly used for particle size analysis; however, due to its improper method of vertical sampling, a powder sample with a logarithmic-normal distribution cannot be reproduced by the pipet method. The induced error is rather serious, particularly for the mnge of smaller particles. Instead of vertical sampling, the present experiment introduces the modification of a stem of tubing extending from the bottom of the vessel to form a sampling slot. Two powder samples are tested and analysis by a micron photo sizer is chosen as the standard for comparison. The results show that powder samples with logarithmic-normal distributions are very well reproduced, and the analysis by the modified pipet is almost as good as that by the photo sizer.
INTRODUCTION
Among many methods for analyzing particle size distribution, the Andreasen pipet is a relatively simple, inexpensive but reliable apparatus for obtaining reproducible data. Due to these merits, the Andreasen pipet has enjoyed wide application in laboratories as well as in industry since its early introduction in the thirties [l]. The pipet most commonly used today is essentially the same as the earliest model. It consists of two major parts, the settling vessel with a height scale outside and the sampling pipet extending to the lowest mark of the scale, as shown in Fig. 1. During analysis, the representative sample of the powder to be 0032-5910/86/$3.50
0
0
Settlq
IOcm3
vessel
@ Sampling
pipet
Fig. 1. Schematic diagram of a vertical sampling Andreasen pipet.
analyzed is diluted to 1 to 2 wt.%, well agitated and poured into the vessel. Initially, the solution is homogeneous in the vessel, as represented by Fig. 2(a) [2]. As time goes by, the particles in the solution start to segregate, since larger particles descend at greater speeds. If a small amount of sample is taken from the vessel through the pipet at time tl , corresponding to the point when particles of sizes larger than D1 have all descended below the sampling level, as shown in Fig. 2(b), the sample contains particles of sizes smaller than Di only. By periodical sampling at ti, samples containing particles of sizes smaller than Di are obtained. The largest particle in each sample can be determined by the Stokes’ equation with a terminal velocity of hilti, and by drying each sample and weighing the solid contents, the cumulative weight undersize distribution, the D curve, can be obtained. @ Elsevier Sequoia/Printed
in The Netherlands
24
Thz
1
C <
c c C
a
(b)
(a)
(Cl
Fig. 2. Schematic diagrams of particles descending the settling vessel.
,,,I , ” 01
05
2
,
;
10
30 cl
Aybeayn
50
70
, 90
in
1 98
%
Fig. 3. Experimental investigation analysis by Peters [ 81.
<-. ,1. .II ‘1 4’ \ ._I’
of particle size
Schweter [3] suggested the modification of using multiple, parallel pipets inside the vessel for faster sampling; however, the sampling method remained the same. Berg [4] suggested another modification using a horizontal sampling tube through which samples were taken horizontally from the side wall of the vessel. Johnson [ 51 studied both the horizontal and vertical pipets and found that the horizontal pipet gave a coarser analysis. Similar experiments were also conducted by Allen [6] but somewhat contradictory results of insignificant difference between the two sampling methods were reported. Leschonski [7] suggested an improvement of horizontal sampling by extending the sampling pipet to the bottom of the vessel and samples were taken from four horizontally drilled holes around the pipet. In other studies [ 8,9], the optical microscopy method was used in comparison with the analysis by the Andreasen pipet and quite obvious deviation was observed, as shown in Fig. 3. Samples that were well represented by the logarithmic-normal distribution, indicated by straight lines in the figure, did not reproduce
(b)
._
(cl
--\ Samplh ___I _____. .__’ Level
(d)
Fig. 4. Schematic diagrams of sampling volumes taken by different sampling methods. (a), Vertical sampling [l]; (b), single, horizontal sampling [4]; (c), multiple, horizontal sampling [ 7 ] ; (d), present sampling.
similar results by the pipet method. The deviation of results from the Andreasen pipet may be attributed to an improper sampling method. In the pipet method, it is assumed that the sample taken from the pipet is exactly at the level of the pipet tip; however, this cannot be achieved in practice. The sample taken has a finite volume and it must be represented by a finite thickness of solution originally in the vessel before sampling. For the first approximation, the sample taken from each sampling hole, either vertically [l] or horizontally [ 4,7], can be considered as a spherical volume, as shown in Figs. 4(a), 4(b) and 4(c). In the vertical sampling, not all the solution taken is at the sampling level but some is actually below it. Since the solution taken at a lower level contains particles larger than the analyzed size, referring to Fig. 2(b), but is regarded to be the analyzed size, the weight percentage of the fine is overestimated. In the single, horizontal sampling, Fig. 4(b), the volume taken is symmetric to the sampling level and the analysis is somewhat balanced by averaging. Still, the single, horizontal sampling is not an ideal method since the sample contains solution in a wide spread of levels. The solutions at different levels have different particle contents and it is very difficult to justify what the average should represent. The span of sampling level is reduced by the multiple, horizontal sampling [ 71 since the volume of the individual sphere becomes smaller, compared with that of the single sampling. Intuitively, an even better sampling method can be achieved by using a stem of tubing of exactly the same size as the pipet extending
25
from the bottom of the vessel. The stem is aligned with the pipet and together with the pipet forms a sampling slot, as shown in Fig. 4(d). For the first approximation, the sampling volume of the presently modified pipet can be considered as a disk. The sampling level is not taken to be at the tip of the pipet but at the center of the slot. This is a much more ideal sampling volume since not only is the volume circumferentially symmetric to the sampling level, but it also contains a very narrow spread of level. Intuitively, this is better than the multiple, horizontal sampling suggested by Leschonski
[71.
The present pipet has some other minor advantages over Leschonski’s [7] pipet. Since the sampling pipet is removable from the vessel, instead of being attached to the vessel as suggested by Leschonski, it is more convenient for cleaning purposes, and an existing Andreasen pipet can easily be converted to the present pipet by simply attaching a stem of tubing to the bottom of the vessel. The objective of the present study is to verify, by some experimental tests, whether the vertical sampling pipet indeed induces sizable errors. If so, can the errors be eliminated by the present modification? Two different samples of powder were tested in both the Andreasen and the modified pipets and analysis by a micron photo sizer (model SKN-1000, manufactured by SEI-SHIN Co., Japan) was chosen as the standard for comparison. EXPERIMENT
Two sets of glass pipets are used in the experiment. The vertical sampling pipet, also called the unmodified pipet, is the one shown in Fig. 1. The settling vessel is 6 cm in outside diameter and has a 23 cm height scale on the side. It holds 770 ml of solution when filled to the upper mark. The sampling pipet within the vessel is 0.75 cm in outside diameter and extends to the lower mark of the scale. At the top of the pipet is a three-way stopcock, which leads to a 10 ml sampling chamber. The other pipet, called the modified pipet, is essentially the same as the unmodified pipet except for the modification of a small stem of tubing fixed at the bottom of the vessel. The width of the sampling slot, which is the
distance between the top of the stem and the tip of the pipet, is 0.2 cm. Two different samples of powder, CaFz and diatomaceous earth, are used in both of the pipets. The densities of the samples are 3.18 and 2.2 g/cm3, respectively. For both samples, distilled water is used as the dispersing phase and a few drops of sodium hexametaphosphate are added as the dispersing agent. The experimental procedures are exactly the same for the two pipets. Predetermined amounts of powder sample, distilled water and dispersing agent are weighed and poured into the vessel, filling it to the upper mark. The stopcock is then closed and the solution is mixed thoroughly by alternately reversing the vessel for a period of time [lo]. The whole apparatus is set vertical for sedimentation and solution samples are taken at different periods of time until the solution at the sampling level becomes clear. When sampling, pressure is applied to the vessel by pressing a rubber ball connected through the side vent, and’the solution is forced into the sampling chamber. When the chamber is full, the stopcock is turned and the solution is drained into a beaker. Excess distilled water is run through the chamber to wash off the particles sticking to the wall. Each solution sample is filtered and dried, and the solid contents are weighed. To compare the results of the two pipets, an analysis of the same powder sample using the micron photo sizer is also carried out. The principle of this apparatus is to project a narrow, horizontal beam of parallel light through the suspension on to a photo cell at a predetermined depth. Due to the presence of particles in the suspension, some of the light source is blocked and the intensity of the light received by the photo cell is reduced. Hence, there exists a direct relationship between the solid contents in the solution and the intensity of the received light. The photo cell is located at a certain fixed depth in each experiment. As time goes by, larger particles eventually descend below the observation point and the intensity of the light increases. By recording the light intensity change, a similar measurement of the D-curve can be deduced. The apparatus is also equipped with a centrifuge for use with slow sedimentation; however, this feature is not used in the present tests.
26
It must be emphasized that the particle size distribution measured by the photo sizer is basically projection area-based but that by the pipet method is weight-based. However, an area-based distribution can be converted to a weight-based distribution without much difficulty [ 111. The conversion is particularly simple for a logarithmic-normal distribution since the standard geometric deviation is the same regardless of the basis. On a typical logarithmic-probability plot, a logarithmicnormal distribution retains its linear nature, irrespective of the different bases, and the area- and weight-based distributions are just two parallel lines on the plot. In the present study, the distribution measured by the photo sizer is converted to the weight-based distribution, by assuming that the particles are perfectly spherical, so that the comparison is on the same basis. The reason for choosing analysis by a micron photo sizer as the standard is that both the photo sizer and the pipets apply the same principle of sedimentation. The only differences between the two are their analyzing methods. For the sizer, a very narrow beam of light at a very precise level is observed so that there is no doubt about which part of the solution is analyzed. Moreover, the analyzed sample is observed directly in the settling vessel and need not be taken out, as in the pipet method. This minimizes the disturbance to sedimentation. Thus, the analysis of the photo sizer is an ideal standard for
comparing the errors induced in sampling by the pipets.
RESULTS AND DISCUSSION
Periodic measurements for each of the pipets using the two powder samples are listed in Tables 1 and 2. For the CaFz sample, the deduced cumulative undersize distribution curve of the unmodified pipet alongside the measurements of the micron photo sizer are plotted in Fig. 5. In the figure, it is seen that the deviation of D% by the unmodified pipet is rather small for larger particles but steadily increases for smaller particles. At the lower range of very small particles, the overestimation of D% by the unmodified pipet is about 100%. This phenomenon of increasing error for smaller particles with the vertical sampling pipet results from its inaccurate sampling volume, as shown in Fig. 4(a). Table 1 shows a sample with a high solid weight percentage, which corresponds to the D% of a large particle, is taken from the settling vessel at an earlier stage of sedimentation. Since the solution is homogeneous at first and segregates continuously, the degree of segregation is rather small at an earlier stage and there is only limited accumulation of large particles at the lower end of the vessel, as represented by Fig. 2(b). When a sample is taken at this stage, the error induced
TABLE 1 Experimental data of two pipets for CaF? Unmodified pipet Initial concentration
Modified pipet Initial concentration
0.0164 g/ml
0.0167 g/ml
ti
hi (cm)
Mi (&!I
D%
Di (PI
G
hi (4
Mi (fa
D%
Di (wd
2’46” 6’30” 8’36” 10’32” 12’47” 16’21” 21’33” 30’20” 35’ 41’40” 49’25” 55’10”
23.0 22.6 22.1 21.7 21.3 20.9 20.3 19.8 19.4 19.0 18.6 18.2
0.1313 0.1169 0.0941 0.0653 0.0497 0.0471 0.0390 0.0244 0.0225 0.0213 0.0211 0.0197
80.07 71.30 57.39 39.79 30.28 28.74 23.78 14.90 13.70 13.01 12.85 12.04
34.1 22.1 19.0 17.0 15.3 13.4 11.5 9.6 9.0 8.0 7.3 6.8
2’35” 4’31” 7’23” 11’01” 14’ 19’ 24’36” 30’23” 34’26” 40’36” 43’07” 50’40”
24.0 23.6 23.2 22.8 22.4 22.0 21.6 21.2 20.8 20.4 20.0 19.6
0.1348 0.1136 0.0988 0.0761 0.0591 0.0447 0.0335 0.0171 0.0150 0.0143 0.0135 0.0128
80.74 68.0 59.18 40.78 35.41 26.74 20.04 10.24 9.01 8.54 8.07 7.68
36.1 27.1 21.0 17.1 15.0 12.8 11.0 9.9 9.2 8.4 8.0 7.4
27 TABLE 2 Experimental
data of two pipets for diatomaceous earth
Unmodified pipet Initial concentration
0.0189
Modified pipet Initial concentration
g/ml
0.0186
g/ml
ti
hi (cm)
Mi (g)
D%
Di (Pm)
ti
4 (cm)
Mi (Id
D%
Di 0-W
5’ 10’ 15’ 20’ 25’ 30’ 40’ 50’ 55’ 60’ 65’ 70’
22.2 21.8 21.3 21.0 20.5 20.1 18.9 18.4 17.9 17.2 16.8 16.4
0.1510 0.1047 0.0773 0.0553 0.05.05 0.0449 0.0286 0.0263 0.0259 0.0250 0.0242 0.0190
79.91 55.39 38.79 29.28 26.74 23.78 15.12 13.90 13.70 13.21 12.79 10.04
33.7 23.6 19.0 16.3 14.5 13.1 11.0 9.7 9.0 8.6 8.1 7.7
5’ 10’ 15’ 20’ 25’ 30’ 40’ 52’ 57’ 62’ 67’ 72’
24.7 24.3 23.9 23.5 23.1 22.7 22.3 21.9 21.5 21.1 20.7 19.9
0.1520 0.1082 0.0817 0.0675 0.0495 0.0353 0.0239 0.0153 0.0149 0.0140 0.0099 0.0083
81.74 58.18 43.93 36.28 26.62 18.96 12.84 8.24 8.01 7.54 5.30 4.48
35.5 24.9 20.2 17.3 15.4 13.9 11.9 10.4 9.8 9.3 8.9 8.4
60
‘oo*oor----l
40 -
som-
30g
60.00 -
20-
\
\: *
CT
0
lo-
4o.ou -
8-
*
Micron
o
Unmodified
photo
sizer
-
pipet
620.00 -
5II
4 1
5
,I 10
20
30
50 D
0.m
0.08
0.16
0.32
0.24
Dp x 10e2
0.40
0.4 8
(pm)
70
80
90
95
99
%
Fig. 6. Comparison of the logarithmic-normal distribution plot of the unmodified pipet for CaF2.
Fig. 5. Comparison of experimental results from the unmodified pipet for CaFz.
by the improper sampling volume of the unmodified pipet is small. On the other hand, when a sample corresponding to the D% of a small particle is taken after a long period of sedimentation, the degree of segregation is very extensive. The solution at the sampling level is rather clean but a lot of large particles have accumulated at the lower end of the vessel, as represented by Fig. 2(c). The sample taken at this stage contains a very small weight percentage of particles and any inaccurate volume taken below the sampling level will result in a considerable increase in the particle contents. This is why vertical sampling is an improper method for smaller particles.
In Fig. 6, data of particle size us. D% are plotted on a logarithmic-probability scale. It is seen that the data of the micron photo sizer are well represented by a straight line, which indicates that the particle size distribution of the CaF, sample can be described as a logarithmic-normal distribution. However, the data points of the unmodified pipet do not reproduce a similar result of a straight line. The present experiments reproduce the same results observed by Peters [ 81, as shown in Fig. 3, and the data of the unmodified pipet also show a very similar tendency to convexity on the logarithmic-probability plot. In Fig. 7, the D-curve measured by the modified pipet is plotted against that of the photo sizer. The two curves almost coincide.
28
60.00
l
Micron
o
Unmoditled
photo
x
Moditwd
sizer pipet
pipet
0.00 0.00
0.16
0.08
0.24 Dpx
0.32
IO-’
0.40
0.01
0.43
Fig. 7. Comparison of experimental results from the modified pipet for CaFa. 60
I
0.08
0.15
(,uum)
Fig. 9. Comparison diatomaceous earth.
0.22
0.29
Dp x IO-’
C,um)
0.36
of experimental
0.43
results for
I
60,
/
40 30
-
20
-
l
Micron
o
Unmoditled
photo
X
Modified
wer plpet
PIPet
8’
65-
::
4 1
5
10
20
30
50
70
80
90
95
99
1
I
I
I
I
I
5
10
20
30
50
II 80
90
95
99
D %
rJ %
Fig. 8. Comparison of the logarithmic-normal tribution plot of the modified pipet for CaFa.
,I 70
dis-
This suggests that the present modification of the sampling method successfully eliminates the error induced by the vertical sampling. In Fig. 8, data of the modified pipet are plotted on the logarithmic-probability scale, alongside data of the photo sizer. It is seen that the data of the modified pipet are also well represented by a straight line and the logarithmic-normal distribution of the sample is reproduced. The two parameters of the logarithmic-normal distribution can easily be determined from the figure. The median size Ds,, is directly read from the particle size of 50% and the geometric standard deviation us is the ratio of particle sizes of 84.13% and 50%. In Fig. 8, Dso determined by the photo sizer is 21.2 pm, and by the modified pipet, 20 pm. ug is 1.80 by the photo sizer and 1.88 by the modified pipet. In Fig. 9, all the data for the powder sample of diatomaceous earth are plotted together. The data points of the unmodified
Fig. 10. Comparison of the logarithmic-normal tribution plot for diatomaceous earth.
dis-
pipet again show increasing deviations for smaller particles, but those of the modified pipet follow quite well with the photo sizer measurements. In Fig. 10, the straight line representing the measurements of the photo sizer suggests a logarithmic-normal distribution for the sample. This distribution is well reproduced by the modified pipet but not by the unmodified pipet. The median size and geometric standard deviation determined by the modified pipet are 21.5 I.tmand 1.77, respectively, compared with 22 pm and 1.73, respectively, by the photo sizer.
CONCLUSION
The present experimental investigation confirms Peters’ observation [8] that a powder sample with a logarithmic-normal distribution cannot be reproduced by a vertical sampling Andreasen pipet. The error
29
is induced by the improper sampling method of taking solution from below the sampling level. This error becomes rather serious, particularly in the range of smaller particles. The present investigation indicates that the result of particle size analysis by a pipet can be seriously affected by different sampling methods. This supports Johnson’s [5] observation but is in contrast to Allen’s [6] or Leschonski’s [ 71 investigations. Comparison of the results from the modified pipet and the micron photo sizer verifies the validity of the present modification. Powder samples with the logarithmicnormal distribution are well reproduced and the analysis by the modified pipet is almost as good as that by the photo, sizer. Another significance of the present modification is that it is very simple. The modification will not change the simplicity and inexpansivity of the pipet method, but only improve its accuracy. An existing, vertical sampling pipet can be changed to the presently suggested form without any difficulty. LIST OF SYMBOLS
D D1, Di
cumulative undersize weight per cent, the largest particles in the samples taken at times tl , ti, pm
ho
4
hl,hi
Mi
tl, ti %
median size of a powder sample, pm particle size, I.tm descending heights corresponding to particle sizes D1, Di, m solid content corresponding to ith sample, kg first and ith sampling times, s geometric standard deviation of a powder sample, -
REFERENCES 1 A. H. M. Andreasen and J. J. V. Lundberg, Ber. Deut. Keram. Ges., 11 (1930) 312. 2 C. C. Chen, W. M. Lu and L. P. Leu, Unit Operation Experiments, National Taiwan University (1973) 124. 3 H. E. Schweyer, Eng. Progr., Univ. Florida, 6 (1952). 4 S. Berg,ASTM Sp. Publ. 234 (1958) 143. 5 R. Johnson, Trans. B. Ceram. Sot., 55 (1956) 237. 6 T. Allen, Particle Size Measurement, Chapman and Hall, London, 2nd edn., 1975, p. 198. 7 K. Leschonski, Staub, 22 (1962) 475. 8 L. K. Peters, Ph.D. Thesis, Univ. Pittsburgh (1971). 9 G. E. Klinzing, Gas-Solid Transport, McGrawHill, New York, 1981, p. 19. 10 L. Silverman, C. E. Billengs and M. W. First, Particle Size Analysis in Industrial Hygiene, Academic Press, 1971, p. 166. 11 T. Allen, Particle Size Measurement, Chapman and Hall, London, 2nd edn., 1975, p. 202.
Technology,
48 (1986) 23 - 29
23
An Experimental Investigation of Particle Size Analysis by a Modified Andreasen Pipet YE-MON CHEN and SHAN-WON DO0 Department (Taiwan)
of Chemical
Engineering
(Received December 2,1985;
and Technology,
National
Taiwan Institute
of Technology,
Taipei 107
in revised form May 19,1986)
SUMMARY
The Andreasen pipet is very commonly used for particle size analysis; however, due to its improper method of vertical sampling, a powder sample with a logarithmic-normal distribution cannot be reproduced by the pipet method. The induced error is rather serious, particularly for the mnge of smaller particles. Instead of vertical sampling, the present experiment introduces the modification of a stem of tubing extending from the bottom of the vessel to form a sampling slot. Two powder samples are tested and analysis by a micron photo sizer is chosen as the standard for comparison. The results show that powder samples with logarithmic-normal distributions are very well reproduced, and the analysis by the modified pipet is almost as good as that by the photo sizer.
INTRODUCTION
Among many methods for analyzing particle size distribution, the Andreasen pipet is a relatively simple, inexpensive but reliable apparatus for obtaining reproducible data. Due to these merits, the Andreasen pipet has enjoyed wide application in laboratories as well as in industry since its early introduction in the thirties [l]. The pipet most commonly used today is essentially the same as the earliest model. It consists of two major parts, the settling vessel with a height scale outside and the sampling pipet extending to the lowest mark of the scale, as shown in Fig. 1. During analysis, the representative sample of the powder to be 0032-5910/86/$3.50
0
0
Settlq
IOcm3
vessel
@ Sampling
pipet
Fig. 1. Schematic diagram of a vertical sampling Andreasen pipet.
analyzed is diluted to 1 to 2 wt.%, well agitated and poured into the vessel. Initially, the solution is homogeneous in the vessel, as represented by Fig. 2(a) [2]. As time goes by, the particles in the solution start to segregate, since larger particles descend at greater speeds. If a small amount of sample is taken from the vessel through the pipet at time tl , corresponding to the point when particles of sizes larger than D1 have all descended below the sampling level, as shown in Fig. 2(b), the sample contains particles of sizes smaller than Di only. By periodical sampling at ti, samples containing particles of sizes smaller than Di are obtained. The largest particle in each sample can be determined by the Stokes’ equation with a terminal velocity of hilti, and by drying each sample and weighing the solid contents, the cumulative weight undersize distribution, the D curve, can be obtained. @ Elsevier Sequoia/Printed
in The Netherlands
24
Thz
1
C <
c c C
a
(b)
(a)
(Cl
Fig. 2. Schematic diagrams of particles descending the settling vessel.
,,,I , ” 01
05
2
,
;
10
30 cl
Aybeayn
50
70
, 90
in
1 98
%
Fig. 3. Experimental investigation analysis by Peters [ 81.
<-. ,1. .II ‘1 4’ \ ._I’
of particle size
Schweter [3] suggested the modification of using multiple, parallel pipets inside the vessel for faster sampling; however, the sampling method remained the same. Berg [4] suggested another modification using a horizontal sampling tube through which samples were taken horizontally from the side wall of the vessel. Johnson [ 51 studied both the horizontal and vertical pipets and found that the horizontal pipet gave a coarser analysis. Similar experiments were also conducted by Allen [6] but somewhat contradictory results of insignificant difference between the two sampling methods were reported. Leschonski [7] suggested an improvement of horizontal sampling by extending the sampling pipet to the bottom of the vessel and samples were taken from four horizontally drilled holes around the pipet. In other studies [ 8,9], the optical microscopy method was used in comparison with the analysis by the Andreasen pipet and quite obvious deviation was observed, as shown in Fig. 3. Samples that were well represented by the logarithmic-normal distribution, indicated by straight lines in the figure, did not reproduce
(b)
._
(cl
--\ Samplh ___I _____. .__’ Level
(d)
Fig. 4. Schematic diagrams of sampling volumes taken by different sampling methods. (a), Vertical sampling [l]; (b), single, horizontal sampling [4]; (c), multiple, horizontal sampling [ 7 ] ; (d), present sampling.
similar results by the pipet method. The deviation of results from the Andreasen pipet may be attributed to an improper sampling method. In the pipet method, it is assumed that the sample taken from the pipet is exactly at the level of the pipet tip; however, this cannot be achieved in practice. The sample taken has a finite volume and it must be represented by a finite thickness of solution originally in the vessel before sampling. For the first approximation, the sample taken from each sampling hole, either vertically [l] or horizontally [ 4,7], can be considered as a spherical volume, as shown in Figs. 4(a), 4(b) and 4(c). In the vertical sampling, not all the solution taken is at the sampling level but some is actually below it. Since the solution taken at a lower level contains particles larger than the analyzed size, referring to Fig. 2(b), but is regarded to be the analyzed size, the weight percentage of the fine is overestimated. In the single, horizontal sampling, Fig. 4(b), the volume taken is symmetric to the sampling level and the analysis is somewhat balanced by averaging. Still, the single, horizontal sampling is not an ideal method since the sample contains solution in a wide spread of levels. The solutions at different levels have different particle contents and it is very difficult to justify what the average should represent. The span of sampling level is reduced by the multiple, horizontal sampling [ 71 since the volume of the individual sphere becomes smaller, compared with that of the single sampling. Intuitively, an even better sampling method can be achieved by using a stem of tubing of exactly the same size as the pipet extending
25
from the bottom of the vessel. The stem is aligned with the pipet and together with the pipet forms a sampling slot, as shown in Fig. 4(d). For the first approximation, the sampling volume of the presently modified pipet can be considered as a disk. The sampling level is not taken to be at the tip of the pipet but at the center of the slot. This is a much more ideal sampling volume since not only is the volume circumferentially symmetric to the sampling level, but it also contains a very narrow spread of level. Intuitively, this is better than the multiple, horizontal sampling suggested by Leschonski
[71.
The present pipet has some other minor advantages over Leschonski’s [7] pipet. Since the sampling pipet is removable from the vessel, instead of being attached to the vessel as suggested by Leschonski, it is more convenient for cleaning purposes, and an existing Andreasen pipet can easily be converted to the present pipet by simply attaching a stem of tubing to the bottom of the vessel. The objective of the present study is to verify, by some experimental tests, whether the vertical sampling pipet indeed induces sizable errors. If so, can the errors be eliminated by the present modification? Two different samples of powder were tested in both the Andreasen and the modified pipets and analysis by a micron photo sizer (model SKN-1000, manufactured by SEI-SHIN Co., Japan) was chosen as the standard for comparison. EXPERIMENT
Two sets of glass pipets are used in the experiment. The vertical sampling pipet, also called the unmodified pipet, is the one shown in Fig. 1. The settling vessel is 6 cm in outside diameter and has a 23 cm height scale on the side. It holds 770 ml of solution when filled to the upper mark. The sampling pipet within the vessel is 0.75 cm in outside diameter and extends to the lower mark of the scale. At the top of the pipet is a three-way stopcock, which leads to a 10 ml sampling chamber. The other pipet, called the modified pipet, is essentially the same as the unmodified pipet except for the modification of a small stem of tubing fixed at the bottom of the vessel. The width of the sampling slot, which is the
distance between the top of the stem and the tip of the pipet, is 0.2 cm. Two different samples of powder, CaFz and diatomaceous earth, are used in both of the pipets. The densities of the samples are 3.18 and 2.2 g/cm3, respectively. For both samples, distilled water is used as the dispersing phase and a few drops of sodium hexametaphosphate are added as the dispersing agent. The experimental procedures are exactly the same for the two pipets. Predetermined amounts of powder sample, distilled water and dispersing agent are weighed and poured into the vessel, filling it to the upper mark. The stopcock is then closed and the solution is mixed thoroughly by alternately reversing the vessel for a period of time [lo]. The whole apparatus is set vertical for sedimentation and solution samples are taken at different periods of time until the solution at the sampling level becomes clear. When sampling, pressure is applied to the vessel by pressing a rubber ball connected through the side vent, and’the solution is forced into the sampling chamber. When the chamber is full, the stopcock is turned and the solution is drained into a beaker. Excess distilled water is run through the chamber to wash off the particles sticking to the wall. Each solution sample is filtered and dried, and the solid contents are weighed. To compare the results of the two pipets, an analysis of the same powder sample using the micron photo sizer is also carried out. The principle of this apparatus is to project a narrow, horizontal beam of parallel light through the suspension on to a photo cell at a predetermined depth. Due to the presence of particles in the suspension, some of the light source is blocked and the intensity of the light received by the photo cell is reduced. Hence, there exists a direct relationship between the solid contents in the solution and the intensity of the received light. The photo cell is located at a certain fixed depth in each experiment. As time goes by, larger particles eventually descend below the observation point and the intensity of the light increases. By recording the light intensity change, a similar measurement of the D-curve can be deduced. The apparatus is also equipped with a centrifuge for use with slow sedimentation; however, this feature is not used in the present tests.
26
It must be emphasized that the particle size distribution measured by the photo sizer is basically projection area-based but that by the pipet method is weight-based. However, an area-based distribution can be converted to a weight-based distribution without much difficulty [ 111. The conversion is particularly simple for a logarithmic-normal distribution since the standard geometric deviation is the same regardless of the basis. On a typical logarithmic-probability plot, a logarithmicnormal distribution retains its linear nature, irrespective of the different bases, and the area- and weight-based distributions are just two parallel lines on the plot. In the present study, the distribution measured by the photo sizer is converted to the weight-based distribution, by assuming that the particles are perfectly spherical, so that the comparison is on the same basis. The reason for choosing analysis by a micron photo sizer as the standard is that both the photo sizer and the pipets apply the same principle of sedimentation. The only differences between the two are their analyzing methods. For the sizer, a very narrow beam of light at a very precise level is observed so that there is no doubt about which part of the solution is analyzed. Moreover, the analyzed sample is observed directly in the settling vessel and need not be taken out, as in the pipet method. This minimizes the disturbance to sedimentation. Thus, the analysis of the photo sizer is an ideal standard for
comparing the errors induced in sampling by the pipets.
RESULTS AND DISCUSSION
Periodic measurements for each of the pipets using the two powder samples are listed in Tables 1 and 2. For the CaFz sample, the deduced cumulative undersize distribution curve of the unmodified pipet alongside the measurements of the micron photo sizer are plotted in Fig. 5. In the figure, it is seen that the deviation of D% by the unmodified pipet is rather small for larger particles but steadily increases for smaller particles. At the lower range of very small particles, the overestimation of D% by the unmodified pipet is about 100%. This phenomenon of increasing error for smaller particles with the vertical sampling pipet results from its inaccurate sampling volume, as shown in Fig. 4(a). Table 1 shows a sample with a high solid weight percentage, which corresponds to the D% of a large particle, is taken from the settling vessel at an earlier stage of sedimentation. Since the solution is homogeneous at first and segregates continuously, the degree of segregation is rather small at an earlier stage and there is only limited accumulation of large particles at the lower end of the vessel, as represented by Fig. 2(b). When a sample is taken at this stage, the error induced
TABLE 1 Experimental data of two pipets for CaF? Unmodified pipet Initial concentration
Modified pipet Initial concentration
0.0164 g/ml
0.0167 g/ml
ti
hi (cm)
Mi (&!I
D%
Di (PI
G
hi (4
Mi (fa
D%
Di (wd
2’46” 6’30” 8’36” 10’32” 12’47” 16’21” 21’33” 30’20” 35’ 41’40” 49’25” 55’10”
23.0 22.6 22.1 21.7 21.3 20.9 20.3 19.8 19.4 19.0 18.6 18.2
0.1313 0.1169 0.0941 0.0653 0.0497 0.0471 0.0390 0.0244 0.0225 0.0213 0.0211 0.0197
80.07 71.30 57.39 39.79 30.28 28.74 23.78 14.90 13.70 13.01 12.85 12.04
34.1 22.1 19.0 17.0 15.3 13.4 11.5 9.6 9.0 8.0 7.3 6.8
2’35” 4’31” 7’23” 11’01” 14’ 19’ 24’36” 30’23” 34’26” 40’36” 43’07” 50’40”
24.0 23.6 23.2 22.8 22.4 22.0 21.6 21.2 20.8 20.4 20.0 19.6
0.1348 0.1136 0.0988 0.0761 0.0591 0.0447 0.0335 0.0171 0.0150 0.0143 0.0135 0.0128
80.74 68.0 59.18 40.78 35.41 26.74 20.04 10.24 9.01 8.54 8.07 7.68
36.1 27.1 21.0 17.1 15.0 12.8 11.0 9.9 9.2 8.4 8.0 7.4
27 TABLE 2 Experimental
data of two pipets for diatomaceous earth
Unmodified pipet Initial concentration
0.0189
Modified pipet Initial concentration
g/ml
0.0186
g/ml
ti
hi (cm)
Mi (g)
D%
Di (Pm)
ti
4 (cm)
Mi (Id
D%
Di 0-W
5’ 10’ 15’ 20’ 25’ 30’ 40’ 50’ 55’ 60’ 65’ 70’
22.2 21.8 21.3 21.0 20.5 20.1 18.9 18.4 17.9 17.2 16.8 16.4
0.1510 0.1047 0.0773 0.0553 0.05.05 0.0449 0.0286 0.0263 0.0259 0.0250 0.0242 0.0190
79.91 55.39 38.79 29.28 26.74 23.78 15.12 13.90 13.70 13.21 12.79 10.04
33.7 23.6 19.0 16.3 14.5 13.1 11.0 9.7 9.0 8.6 8.1 7.7
5’ 10’ 15’ 20’ 25’ 30’ 40’ 52’ 57’ 62’ 67’ 72’
24.7 24.3 23.9 23.5 23.1 22.7 22.3 21.9 21.5 21.1 20.7 19.9
0.1520 0.1082 0.0817 0.0675 0.0495 0.0353 0.0239 0.0153 0.0149 0.0140 0.0099 0.0083
81.74 58.18 43.93 36.28 26.62 18.96 12.84 8.24 8.01 7.54 5.30 4.48
35.5 24.9 20.2 17.3 15.4 13.9 11.9 10.4 9.8 9.3 8.9 8.4
60
‘oo*oor----l
40 -
som-
30g
60.00 -
20-
\
\: *
CT
0
lo-
4o.ou -
8-
*
Micron
o
Unmodified
photo
sizer
-
pipet
620.00 -
5II
4 1
5
,I 10
20
30
50 D
0.m
0.08
0.16
0.32
0.24
Dp x 10e2
0.40
0.4 8
(pm)
70
80
90
95
99
%
Fig. 6. Comparison of the logarithmic-normal distribution plot of the unmodified pipet for CaF2.
Fig. 5. Comparison of experimental results from the unmodified pipet for CaFz.
by the improper sampling volume of the unmodified pipet is small. On the other hand, when a sample corresponding to the D% of a small particle is taken after a long period of sedimentation, the degree of segregation is very extensive. The solution at the sampling level is rather clean but a lot of large particles have accumulated at the lower end of the vessel, as represented by Fig. 2(c). The sample taken at this stage contains a very small weight percentage of particles and any inaccurate volume taken below the sampling level will result in a considerable increase in the particle contents. This is why vertical sampling is an improper method for smaller particles.
In Fig. 6, data of particle size us. D% are plotted on a logarithmic-probability scale. It is seen that the data of the micron photo sizer are well represented by a straight line, which indicates that the particle size distribution of the CaF, sample can be described as a logarithmic-normal distribution. However, the data points of the unmodified pipet do not reproduce a similar result of a straight line. The present experiments reproduce the same results observed by Peters [ 81, as shown in Fig. 3, and the data of the unmodified pipet also show a very similar tendency to convexity on the logarithmic-probability plot. In Fig. 7, the D-curve measured by the modified pipet is plotted against that of the photo sizer. The two curves almost coincide.
28
60.00
l
Micron
o
Unmoditled
photo
x
Moditwd
sizer pipet
pipet
0.00 0.00
0.16
0.08
0.24 Dpx
0.32
IO-’
0.40
0.01
0.43
Fig. 7. Comparison of experimental results from the modified pipet for CaFa. 60
I
0.08
0.15
(,uum)
Fig. 9. Comparison diatomaceous earth.
0.22
0.29
Dp x IO-’
C,um)
0.36
of experimental
0.43
results for
I
60,
/
40 30
-
20
-
l
Micron
o
Unmoditled
photo
X
Modified
wer plpet
PIPet
8’
65-
::
4 1
5
10
20
30
50
70
80
90
95
99
1
I
I
I
I
I
5
10
20
30
50
II 80
90
95
99
D %
rJ %
Fig. 8. Comparison of the logarithmic-normal tribution plot of the modified pipet for CaFa.
,I 70
dis-
This suggests that the present modification of the sampling method successfully eliminates the error induced by the vertical sampling. In Fig. 8, data of the modified pipet are plotted on the logarithmic-probability scale, alongside data of the photo sizer. It is seen that the data of the modified pipet are also well represented by a straight line and the logarithmic-normal distribution of the sample is reproduced. The two parameters of the logarithmic-normal distribution can easily be determined from the figure. The median size Ds,, is directly read from the particle size of 50% and the geometric standard deviation us is the ratio of particle sizes of 84.13% and 50%. In Fig. 8, Dso determined by the photo sizer is 21.2 pm, and by the modified pipet, 20 pm. ug is 1.80 by the photo sizer and 1.88 by the modified pipet. In Fig. 9, all the data for the powder sample of diatomaceous earth are plotted together. The data points of the unmodified
Fig. 10. Comparison of the logarithmic-normal tribution plot for diatomaceous earth.
dis-
pipet again show increasing deviations for smaller particles, but those of the modified pipet follow quite well with the photo sizer measurements. In Fig. 10, the straight line representing the measurements of the photo sizer suggests a logarithmic-normal distribution for the sample. This distribution is well reproduced by the modified pipet but not by the unmodified pipet. The median size and geometric standard deviation determined by the modified pipet are 21.5 I.tmand 1.77, respectively, compared with 22 pm and 1.73, respectively, by the photo sizer.
CONCLUSION
The present experimental investigation confirms Peters’ observation [8] that a powder sample with a logarithmic-normal distribution cannot be reproduced by a vertical sampling Andreasen pipet. The error
29
is induced by the improper sampling method of taking solution from below the sampling level. This error becomes rather serious, particularly in the range of smaller particles. The present investigation indicates that the result of particle size analysis by a pipet can be seriously affected by different sampling methods. This supports Johnson’s [5] observation but is in contrast to Allen’s [6] or Leschonski’s [ 71 investigations. Comparison of the results from the modified pipet and the micron photo sizer verifies the validity of the present modification. Powder samples with the logarithmicnormal distribution are well reproduced and the analysis by the modified pipet is almost as good as that by the photo, sizer. Another significance of the present modification is that it is very simple. The modification will not change the simplicity and inexpansivity of the pipet method, but only improve its accuracy. An existing, vertical sampling pipet can be changed to the presently suggested form without any difficulty. LIST OF SYMBOLS
D D1, Di
cumulative undersize weight per cent, the largest particles in the samples taken at times tl , ti, pm
ho
4
hl,hi
Mi
tl, ti %
median size of a powder sample, pm particle size, I.tm descending heights corresponding to particle sizes D1, Di, m solid content corresponding to ith sample, kg first and ith sampling times, s geometric standard deviation of a powder sample, -
REFERENCES 1 A. H. M. Andreasen and J. J. V. Lundberg, Ber. Deut. Keram. Ges., 11 (1930) 312. 2 C. C. Chen, W. M. Lu and L. P. Leu, Unit Operation Experiments, National Taiwan University (1973) 124. 3 H. E. Schweyer, Eng. Progr., Univ. Florida, 6 (1952). 4 S. Berg,ASTM Sp. Publ. 234 (1958) 143. 5 R. Johnson, Trans. B. Ceram. Sot., 55 (1956) 237. 6 T. Allen, Particle Size Measurement, Chapman and Hall, London, 2nd edn., 1975, p. 198. 7 K. Leschonski, Staub, 22 (1962) 475. 8 L. K. Peters, Ph.D. Thesis, Univ. Pittsburgh (1971). 9 G. E. Klinzing, Gas-Solid Transport, McGrawHill, New York, 1981, p. 19. 10 L. Silverman, C. E. Billengs and M. W. First, Particle Size Analysis in Industrial Hygiene, Academic Press, 1971, p. 166. 11 T. Allen, Particle Size Measurement, Chapman and Hall, London, 2nd edn., 1975, p. 202.