A New Technique of Particle Size Analysis of Aerosols and Fine Powders Using an Ultramicroscope Tetsuo Yoshida, Yasuo Kousaka,* and Kikuo Okuyarna faculty of Engineering, University of Osaka Prefecture, Osaka, Japan
A new technique to determine t h e particle size distribution of fine powders and aerosols including those of fine liquid droplets was developed. T h e technique is in principle somewhat similar to t h e Andreasen pipet method, but has some distinctive features as follows: (1) sedimentation is m a d e in air a s well as in water according to t h e particle size; (2) sedimentation depth is extremely shallow; (3) particle concentration at a given d e p t h in a sedimentation cell is detected by an ultramicroscope on the number basis. The lower limit of t h e measurable particle size is several t e n t h s of a micron in diameter and the upper more than several tens of microns. By sedimentation mostly in air at depths less than a few millimeters, very quick measurement was possible even for submicron particles. It is desirable for t h e particle n u m b e r concentration to b e high.
Introduction In recent years an increasing interest in the size analysis of aerosols has arisen in connection with air pollution control. In existing ultramicroscopic techniques of particle size analysis (Richardson, et al., 1956; Mukaibo et al., 1962), the settling velocities of hundreds of individual particles h u s t be observed by an ultramicroscope to determine the size distribution, and thus the techniques require much time. The technique developed in this study is quite different from the existing ones and, above all, has the distinctive feature of quick analysis of size distribution for particles, including water droplets, of more than several tenths of a micron in diameter. The technique is also applied to the determination of the particle number concentration of aerosols and, by some additional devices, the density of particles. Although the technique described below is limited to aerosols of small particles dispersed in air, for the powders of larger particles the technique can be applied when they are dispersed in water.
sedimentation continues until the particles disappear from sight. The terminal settling velocity of a particle is represented by the equation
ut
=
gb, -
pf)Du2C, 18P
(1)
Ut in this equation is replaced by h l t , where h is the depth of sedimentation preliminarily set; then the particle diameter Dp is determined in accordance with the sedimentation time t, that is 0, = F ( h / t )
The particle with the diameter Dp calculated by eq 2 a t time t is the maximum one which can be recognized at the depth h; that is, the particles larger than it have already passed below the depth h. Thus the particle number in sight at time t after the start of sedimentation is given by the equation
Principle The principle of the method is almost same as that of the Andreasen pipet method, but the concentrations of particles at a given depth as sedimentation progresses are detected by an ultramicroscope on the number basis. Sedimentation in air or in water with shallow sedimentation lengths makes it possible to analyze smaller particles in a short time, whereas in the Andreasen pipet method sedimentation is usually made in water with a deep sedimentation length. The sedimentation length is from about 0.5 to a few millimeters, so that, for example, a water droplet 1 p in diameter is measured within several tens of seconds. The detection of particle number concentrations by ultramicroscope and then the analysis of particle size distribution is made by the following procedure: aerosol is introduced into a small cell having valves at both inlet and outlet sides, the flow of the aerosol is instantaneously stopped by closing the valves, and then sedimentation is started. When the focus of the ultramicroscope is preliminarily set a t depth h shown in Figure 1, the aerosol particles existing in the volume urn are recognized because of their shining at the depth of the focus but they are as yet unknown in sizes. The particles appearing in the microscope are photographed or recorded by a video recorder as
(3) The integral term of this equation indicates cumulative fraction undersize, then
(4) N(O),the particle number in the volume U r n in Figure 1 at the beginning of sedimentation, and N ( t ) ,the numbers at various elapsed times, are counted by slow video. Then the size distribution is determined by eq 4. Table I shows the analysis procedur,e. In the procedure, to prevent photophoresis, thermophoresis, and thermal convection, the lighting of the microscope must be extinguished during the intervals between successive observations. Another method may also be true in principle. If the sedimentation depth h is varied instantaneously a t constant elapsed time, the particle size distribution can be determined by almost the same procedure described above. The particle number concentration, no, is given as follows, when the volumes urn or U h shown in Figure 1 are predetermined Ind. Eng. Chem., Fundam., Vol. 14, No. 1, 1975
47
a
glass wall
6 thick vinyl
---L
inlet
/
aerosol out ~,,=KO?(h*dh/2)/4 Figure 1. Illustration of observation cell.
in mm
b
---L
inkt
in m
Figure 3. (a) Observation cell for fog particle. (b) Observation cell for small particle.
o b s e r v a t i o n cell Figure 2. Arrangement of ultramicroscope.
Table I. Procedure of Analysis SO), 1,
time elapsed
number of particle in
I,,
D,,
F,
particle diameter
cumulative undersize
The estimation of Ah in Figure 1, the depth in focus, is made as follows. Small numbers of particles to be analysed are first deposited on a glass in some way. The glass is mounted on the stage of the ultramicroscope and the deposited particles are observed while shifting the stage up and down. Then Ah is given as the total displacement of the stage over which the images of the particles are in sight with a certain ciearness. When the particle number concentration is thus obtained, and when the particle weight concentration is separately determined by another appropriate way such as filtering, the particle density is, in principle, obtainable by means of the above technique of size analysis. In the principle described here Brownian coagulation and diffusion are neglected. When the particle number concentration exceeds lo7 particles per cubic centimeter, the effect of the Brownian coagulation will not be negligible (Fuchs, 1964), and when'there are particles less than about 0.4 p in diameter, diffusion influences the gravitational settling (Davies, 1949). The development of some devices to remove these effects by forced sedimentation, such as by thermophoretic or centrifugal forces, or theoretical methods to compute the effects will be desirable in order to extend the application of this technique. Apparatus
where Ait,t,l is the particle number in the volume u h which is obtained by counting all the particles passing through the volume urn during sedimentation. Equation 5' is especially useful when the' particle number concentration is small. In this procedure, however, since the microscope must be kept lighted during the measurement, it is not suitable to measure the size distribution of particles smaller than about 1 p in diameter, where thermophoresis and thermal convection affect sedimentation. 48
Ind. Eng. Chern., Fundarn., Vol. 14, No. 1 , 1975
The ultramicroscope used in this study is shown in Figure 2. It has a 150-W halogen lamp and an observation cell on its stage. The magnification of the objective and the eyepiece were selected according to the particle size and the particle number concentration. Two typical types of the observation cell are shown in Figure 3. The cell shown in Figure 3a consists of a double cell. The outer cell is provided for temperature control of the aerosol to be observed in the inner one. This type is useful for the analysis of fog particles or other volatile particles which can vary their size by evaporation or condensation with change of temperature. The cell shown in Figure 3b has a small sectional area so that the effect of convection is removed. The aerosol particles tested in this study were generated
u orifice
4
compTessor
I heat exchanger
Figure 4. Arrangement of tobacco aerosol generator
C
filter I
e
U
heat*
Figure 5. Stearic acid aerosol generator.
Figure 7. Change of particle number with the lapse of time (stea. ric acid aerosol): (a) t = 0 sec after the start of sedimentation; (b) t = 40 sec; ( e ) t = 50 sec: (d) t = 60 sec; ( e ) t = IO see. Table 11. Characteristics of the Ultramicroscope Used
__
Eye. piec X
hot
ob
jective
Ah,w
vm,cm3
10 X 1 0
125 40 15
1.9 X l O - ' 1.4 x10-5 1.2X10-6
O I XZO
10x40
Figure 6. Fog particle generator. as shown in Figures 4, 5, and 6. Figure 4 shows a tobacco aerosol generator. The particle number concentration of tobacco aerosol was controlled from 106 to 10s particles per cubic centimeter by air flow rate through tobacco and the rate of the by-pass. The particle size was controlled by residence time in the aging chamber from 0.7 to 2 fi in geometrical mean diameter. The stearic acid particles were generated by a La Mer generator shown in Figure 5, but because of the rough control of temperature they were not monodisperse. Figure 6 shows a fog generator. The fog particles were formed around the tobacco particles as condensation nuclei, and the particle number concentration and the particle size as well were controlled by changing the number of the condensation nuclei. The controlled size was from 1 to 10 p and the concentration was from l@ to 106 particles/cm3. Experimental Section Some characteristics regarding the ultramicroscope used were predetermined hefore experiments. Table Il shows the results. The last column gives a criterion of the
no[particles/ cm3] equiv Visible to over 50 particle particles in diam,p volume,u,
22 20.2 20.05
23 X 105 2 4 x 106 >4X107
particle number concentration to be required for analysis. When the concentration is less than the criterion, ohservation must be repeated until a sufficiently large number is obtained. Otherwise the whole number in the volume ut, must be counted for the analysis, which is accomplished by slow video. For aerosols with lower concentrations, the visual field of the microscope or the volume urn may he enlarged by giving a horizontal sweep to the observation cell. In any case the more dense the particle number concentration is, the easier is the analysis in this method. A series of the photos which illustrate the change of the particle number as time elapses is shown in photos (a) to (e) in Figure 7. These pictures are only for illustration and the most of the size analysis were made by the slow video system because of the more rapid analysis than the photographic one. Figure 8 shows the result of the analysis. No differences in the size distribution are found for various depths of sedimentation. This agreement indicates that the aerosol introduced into the cell is homogeneously dispersed and also indicates almost no effect of diffusion or thermophoresis, which probably appears at the vicinities of the upper or the lower wall of a cell because of the larger gradients Ind. Eng. Chem., Fundam., Vol. 14,
No. 1.1975
49
,
Table 111. Representative Experimental Data
stearic acid particle
95 90
No. of par-
Time elapsed, f, sec
$80 U
70
particles/cc
#
1
Q
-
ticles in by sight, eq 2, Ar(t)
Cumulative undersize,
D,,
(Run 1;stearic acid, h 0 20 40 50 60 70 80 90 100 110 120
47 46 42 32 24 12 7 8 4 1 1
1.31 0.90 0.80 0.73 0.67 0.62 0.58 0.55 0.51 0.48
F = Ar(t)/Ar(0) =
Remarks
1000 p in Figure 8)
0.98 0.89 0.68 0.51 0.26 0.15 0.17 0.085 0.021 0.021
eyepiece Xobjective X
X 10 X 20 P p = 0.84 g/
cm3
(Run 2; tobacco, left side in Figure 10)
I
’&
Particle diam
0.4 0.60.6 1
0.2
D,/2
Cpl
Figure 8. Particle size distribution of stearic acid aerosol for various sedimentation depths.
0 15 30 45 55 70 80 90 100 120 140 160 180
145 144 124 110 89 68 52 37 29 13 8 6 2
1.64 1.12 0.92 0.82 0.72 0.66 0.63 0.59 0.53 0.49 0.45 0.42
0.99 0.86 0.76 0.61 0.47 0.36 0.26 0.20 0.083 0.055 0.041 0.014
10 X 20 p p = 0.75 g/ X
c1n3 12
= 1000 !J
(Run 3; iron oxide pigment in Figure 11)
hot saturated air
V
0 2 6 8 10 16 20 30 40 50
31 31 1.74 1.00 X 10 X 2 0 30 0.98 0.97 p, = 0.52 g/ 27 0.84 0.87 cm3 21 0.74 0.68 /Z = 1000 p 0.36 11 0.56 0.50 0.36 11 0.29 9 0.40 0.34 0.13 4 0.28 0.13 4 (Run 4;fog, right side in Figure 8)
old saturated air 20”c , 6 I/min
0.60.8 1
2
4
6
DP/~ Figure 9. Particle size distribution of fog.
of concentration and temperature, respectively. The agreement, moreover, indicates that Brownian coagulation, which must progress with the lapse of time or with the depth of sedimentation, has no effect on the size analysis below 107 particles/cm3. Figure 9 shows the result of the analysis of fog particles or water droplets, which have been thought difficult to analyze without any disturbance as they are in suspension in air. In these cases the particle number concentrations were so small that the size analyses were made by counting the whole number in the volume Uh. Figure 10 shows the two kinds of size distributions of tobacco aerosols (“Cherry” made by the Japan Monopoly Corp.). One is that obtained for low concentration and the 50
Ind. Eng. Chem., Fundarn..Vol. 14, No. 1, 1975
0-0.5 0.5-1.0 1.0-1.5 1. 5-2.0 2.0-2.5 2. 5-3.0 3.0-3.5 3.54.0 4.04.5 4,. 5-5.0 5.0-5.5 5. 5-6.0
111 107 95 84 61 65 39 37 25 9 6 6
9.5 7.4 6.2 5.5 5. 0 4.6 4.3 4.0 3.8 3.6 3.4
0.97 0.86 0.76 0.55 0. 59 0.35 0.33 0.23 0.081 0.054 0.054
x 10 x 10 P p = 1.0 g/
cm3 12
= 2000 !J
A\rtot(t)is the sum of 7 observations
other is that for particles grown by Brownian coagulation after sufficient aging time. The wide size distribution of the latter indicates a typical feature when coagulation oc-
991 95. n
0'O
I
I
iron oxide pigment
1
I
=
I
90-
U
80 Q,
7 P. ' io
"30-
0
c
.> 20c 0
-510E
35-
-
-
-
y
6-
? no= 2.58 x 1 0 partileslcc
0
-
40-
.5 30-
-
-
3
01
V
L O
10 - po+ectron
miulxcope
0
1-
,
I
I
I
I 1
i
I .
5 0.1
DdPCpI F i g u r e 10. Particle size distribution of tobacco aerosol.
I
1
I
1
0.4 0.6 0.8 1
0.2
4 / 2 b.3 Figure 11. Particle size distribution of powder of iron oxide pigment.
curs. Although the sizes of tobacco particles reported by other investigators (Sano, et al., 1954; Keith and Derrick, 1960; Porstendorfer and Schraub, 1972) are smaller than those in Figure 10, such difference is thought to be caused by the existence of water, which is expected to adhere to the particle surface. Figure 11 shows one of the results of analysis of fine powders. In this analysis iron oxide pigment powder was dispersed into air by a mixer-type disperser. It probably takes a few days to measure by the Andreasen pipet method while only a few minutes was required by this method. The result of size analysis by an electron microscope for the same powder is also plotted in the figure. They agree fairly well. Some of the representative data are shown in Table 111. Conclusion The technique developed in this study was found to be useful for the particle size analysis of fine powders and aerosols, including those of fine water droplets. The technique has the advantage of sedimentation methods in which particles are observed while they are suspended. Moreover, the usual disadvantage of sedimentation procedures, that much time is needed for the fall of small particles, was overcome by air sedimentation with an extremely shallow sedimentation depth. As a result, the size analysis of particles, including water droplets, which are larger than several tenths micron in diameter, was possible in a short time. The ultramicroscopic detection of the particle concentration on a number basis and its recording by a video system served for quick analysis without disturbing the aerosols during observation. The particle number concentration, however, must be rather high, a fact which is both an advantage and a disadvantage of the method.
Acknowledgment
T. Miyazaki was very helpful in the experimental work. Nomenclature Cm = Cunningham's correction factor F = cumulative fraction undersize De = effective diameter of microscopic sight shown in Figure 1, cm D p = particle diameter, p or cm f(D,) = particle size distribution function h, Ah = values shown in Figure 1, cm N ( t ) = particle number observed by microscope at t sec after the start of sedimentation Nt,t(t) = particle number observed by microscope during a certain period of observation at t sec after the start of sedimentation Ntotal = total particle number in volume u h RO = particle number concentration, particles/cm3 t = time elapsed, sec Ut = terminal settling velocity, cm/sec u h , urn = volumes shown in Figure 1, cm3
Greek Letters 1 = viscosity, g/(cm sec) pp = density of particle, g/cm3 p f = density of fluid, g/cm3
Literature Cited Davies, C. N., Proc. Roy. Soc., Ser. A , 200, 100 (1949). Fuchs, N. A., "The Mechanics of Aerosols," Pergamon Press, 1964. Keith, C. H.. Derrick, J. C., J. ColloidSci., 15, 340 (1960). Mukaibo, T., et a/., Sogo Shikensho Nempo, 20, No. 2 (1962). Porstendorfer, J., Schraub, A , , Staub, 32 (10). 33 (1972). Richardson, J. F., Wooding, E. R . , J. Photogr. Sci., 4, 75 (1956). Sano, K.. Fujiya, Y., Sakata, S.. J. Chem. SOC.Jap., 74, 664 (1954).
Received for review April 1,1974 Accepted September 6, 1974 Presented at the Chemical Engineering Meeting in Japan.
Ind. Eng. Chem., Fundam., Vol. 14, No. 1, 1975
51
