Electrical Precipitation and anical Dust Collection WALTER A. SCHMIDT Western Precipitation Corporation, Los Angeles, Calif. After reviewing some of the fundamentals of the Cottrell electrical precipitation process, such as the meaning of the precipitation constant, the effect of acid and basic conditioning, the occurrence of “back discharge,” and the significance of dust resistivity, this paper discusses the dependence of resistivity upon temperature, humidity, and chemical composition. Following this, the importance of good gas distribution in the precipitator is emphasized, and by gas flow diagrams it is shown that proper dis-
tribution may be obtained by carefully chosen corrective devices. Next, the rating of centrifugal dust collectors is considered, and their tendency to collect particles selectively depending upon size is discussed. After describing recent trends in the theory and construction of centrifugal collectors, it is concluded that present theories are adequate for a general understanding of the centrifugal collection process, but that many details of the design still are evolved empirically.
T
Horne (3, 7 ) conducted an extensive investigation of this problem many years ago and developed a precipitation equation which in its simplest form can be written as 1 - E = K‘, in which E represents the precipitator efficiency, t the time of treatment, and K a constant that numerically expresses the precipitation characteristics of the gas and fume combination under conditions of treatment. This equation can be derived mathematically from the assumption that, in a Cottrell precipitator, the dust
HE process of electrical precipitation of suspended par-
ticles from gases, generally called the Cottrell process, is well known. Figure 1 is a diagrammatic sketch of a simple fype of precipitator and its basic electrical connections. More complete information is given in earlier publications (6, I d , IS). It has been known for a long time that the rate of precipitation differs widely with different fumes and dusts, but no wholly satisfactory explanation has been worked out, Anderson and ti@
iensloniine carrying
/ Recttfied Current
Q
H,ghT/eysion Lines Discharge Electrode
Tension tine
Collecting Electrode
SwltchbOard
Rectifier PRECIPITATOR
Figure 1. Schematic Diagram of Cottrell Precipitator 2428
INDUSTRIAL AND
November 1949
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2429
combination having a K of 0.7 will require a precipitator twice as large as one with a K of 0.48 for a given efficiency. ELECTRICAL RESISTIVITY OF DUST AND ITS SIGNIFICANCE
Figure 2.
Apparatus for Measuring Resistivity of Deposit
concentration is reduced a t a rate proportional to the concentration. The data obtained by Anderson and Horne conformed to this equation, and during the intervening years the accumulation of test data from commercial installations has strongly substantiated the correctness of this early work. In the Anderson and Horne equation given above, a constant with a numerical value of 1 would correspond to a precipitator of 0 efficiency, whereas a constant of 0 would correspond to B precipitator of infinite capacity within the limits of permissible gas velocity. All other things being the same, a gas and fume
Fume and dust concentrations have a bearing upon the rate of precipitation, possibly because of a space charge effect. Gas composition also has a marked effect upon the rate of precipitation, which is usually attributed to the fact that gas composition affects the electrica1,resistivity of the suspended dust, and this resistivity in turn must be maintained below a certain critical value in order to avoid the adverse sparking and arcing conditions commonly designated as “back discharge.” Wolcott (19) showed in 1918 that moisture and free acid were excellent conditioning agents for establishing the necessary conductivity in the deposit. Chittum (4) showed that basic secondary conditioning agents, such as ammonia and triethylamine, are effective with acidic materials whose surfaces are not readily wetted with moisture, such as the catalysts used in the fluid catalyst process in the petroleum industry, whereas with such basic materials as lime dust these basic secondary conditioning agents are noneffective, but certain salts and free acids are effective. These secondary conditioning agents probably form a monomolecular film upon the particles to which the moisture can then attach itself to establish the necessary conductivity in the deposit. White and Anderson (18)investigated the relationship between back discharge and the electrical resistance of the deposit, and White developed the technique of measuring this resistance. He precipitated a la er‘of the dust or fume on a circular disk and guard ring, the J s k being grounded through appropriate measuring instruments. Then the discharge electrode was replaced by a disk slightly smaller than that on which the dust
?
21
IO’
TEMPERATURE
Figure 3.
IN
DEG. FAHRENHEIT
Apparent Resistivity of Precipitated Cement Dusts
Approximately 1.3% moisture by volume, five different cements
\
I
I
1
I
I
1
I
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below this narrow temperature range, but there is no sharp break in the curve. This coincides with extensive field test data obtained from commercial installations, where i t has been found that the efficiency of a dry process cement plant precipitator falls rapidly as the temperature of the gases is lowered from around 700’ to around 400’ F. For this reason, a precipitator operating on dry process cement mill gases behind a waste heat boiler must be proportionately much larger than R precipitator operating on hot gases a t temperatures around 700’ F. if it is to handle the same gas volume, a t operating conditions, and give the same efficiency of collection. Of course, there is a compensating factor in that, with a waste heat boiler, infiltration of outside air is held at a minimum and the volume of gas is further reduced by the reduction in temperature. Nevertheless, the precipitator must be much larger proportionately, as is shown from the following table, calculated for a rod curtain precipitator on the basis of experience: Gas Volume
Efficiency,
Cu. Feet/&.
%
100,000 100,000
90
Temperature,
F. 700
O
No. of Unit Ducts
350
90
28
53
Similarly, the efficiency of a given precipitator varies with the temperature, as is shown from the following data obtained at a plant collecting dust from a rotary dolomite calcining furnace: Temperature,
Gas Volume Approximately constant
114,000
TEMPERATURE
IN
DEG. FAHRENHEIT
Figure 5. Effect of Moisture Content on Apparent Resistivity of Precipitated Cement Dust
was precipitated. This second disk was lowered until its full weight rested on the upper surface of the deposit. Knowing the area of the disks and the applied voltage between them, and measuring the thickness of the dust layer and the current passing through it, the resistivity of the deposited material could be calculated.
at
CU.
%
400
75
540
fcet/min.
Efficiency,
F. 700
95 86
On the other hand, such materials as cement dust or lime dust can be easily precipitated a t room temperatures. Unfortunately, no plant data are available for this low temperature range, as all cement and lime kiln gases are handled at elevated temperatures. There is one precipitator operating on the vent gases of a cement packing room, and although this is not a comparable problem, i t is interesting to note that this small precipitator handles a disproportionately large gas volume at a very high efficiency. Putting all these laboratory and fieId data together, it appears rather definite that there is a correlation between the dust resis-
T h e resistance of the dust layer depends upon the degree of compacting, because it is a noncontinuous medium, and so the resistivity measured in this way has been designated as the “apparent” resistivity. The apparatus developed by White was further improved by Chittum and is shown in Figure 2. White showed rather conclusively that when the apparent resistivity is more than 2 X 10’0 ohm-cm., back discharge is apt to occur and that above this value the normal precipitation equation no longer applies. RECENT DEVELOPMENTS RELATED TO DUST RESISTIVITY
This work has now been carried considerably further by Sproull and Nakada ( l 7 ) , who have shown that the resistivity factor is closely associated with the rate o f normal precipitation and that the apparent resistivity is dependent upon a number of factorsfor example, temperature is an important factor, as i t is in the resistance of a solid conductor; humidity is also an important factor. Figure 3 gives the apparent resistivity of cement kiln dust from five different factories, when the dust is exposed to air containing approximately l.3yowater vapor by volume. The curves closely Follow each other, even though the chemical analyses of the various dusts differ considerably. The lime, silica, and alkali content of the five dusts is given at the bottom of Figure 3. The apparent resistivity reaches a very high peak in the temperature zone of 250 to 350’ F., and falls rapidly both above and O
TEMPERATURE
IN
DEG. FAHRENHEIT
Figure 6. Effect of Moisture Content on Apparent Resistivity of Precipitated Synthetic Catalyst
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Table 1. Apparent Resistivity and Precipitability of Dusts Speoifio Planta Powdered coal flp ash Cement kiln dust Lead fume, heavily humidified Lead fume, lightly humidified Lead fume not humidified Flash calcined gypsum
Apparent Resistivity, Ohm-Cm. 8 x 10s 2 x 100
Precipitability Satisfactory Satisfactory
3
x
109
Satisfactorv
2
x x x
10'0
Fair
10'8 1012
Difficult Very difficult
1 0
that conditions within the precipitator be so controlled that low resistivity of the deposit is maintained. Table I shows the relationship of several types of dusts and fumes to their apparent resistivity and their rate of precipitation. I
I
Figure 7. Cross-Sectional Air Flow Diagram Showing Poor Cas Distribution i n Experimental Wind Tunnel Diameter of circles represents gas veloclty. Arrows indicate direction of transverse flow. Open circles, forward flow. Shaded circles, turbulent flow. Solid circles, reverse flow
IMPORTANCE OF PROPER GAS DISTRIBUTION
The erosion factor frequently is overlooked in the operation of electrical precipitators. As the collected material accumulates upon the electrodes, it is expbsed to the sweeping effect of the moving gas stream, and may be dislodged and re-entrained in the gas, particularly if the material is dry and noncoherent. Most deposited materials hold tightly to the electrode up to a critical gas velocity. Beyond this critical velocity, the deposit starts to move, first forming dunes, like the sands of the desert; at still higher velocities, material is torn loose and then must be reprecipitated, or it will be carried out of the precipitator with the exit gases. With plain electrodes, this critical velocity varies with the material over a rather wide range. Carbon black is eroded a t a velocity of less than 2 feet per second. Fly ash from powdered coal-fired furnaces will usually hold on up to a velocity of 8 feet per second. Cement kiln dust is more cohesive, and will stand up to 10 or 12 feet per second, but at 20 feet per second even a liquid film, such as sulfuric acid, will start to be reentrained by the gases. Obviously, the better the gas distribution, the less danger of excess gas velocity in any part of the precipitator. However, precipitators offer very little resistance to the gas flow and at these low velocities i t is difficult to establish uniform gas flow,
Figure 8. Cross-Sectional Air Flow Diagram Showing Conditions with Corrective Devices installed Diameter of circles represents gas velocfty. Arrows indicate direction of transverse flow
tivity and the rate of precipitation, and that there is no marked break between precipitability and nonprecipitability. Work is now in progress, aimed a t establishing this correlation more accurately. Similarly, gas composition has a marked effect upon the resistivity of the deposit. Figure 4 shows the effect of moisture on cement kiln dust at five different temperature levels. That the effect of moisture is most pronounced a t lower temperatures is explainable, on the assumption that moisture adsorption increases the conductivity of the surface of the dust particles, that a t higher temperatures the moisture is driven off the dust particles, and that a t these higher temperatures the mass conductivity, previously discussed, comes into play. At any rate, if we plot moisture in the gases against temperature and resistivity as coordinates, we get a series of curves for cement kiln dust as shown in Figure 5. Similar curves for synthetic catalyst dust from a petroleum fluid catalytic plant are shown in Figure 6. The rate of precipitation obviously determines the size of the precipitator for any given job. Consequently, it is desirable
f Figure 9.
Four Types of Pocket Electrodes
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of radius r. Most manufacturers of cyclonic dust collectors have since followed their lead. However, certain confusion has also followed, as this centrifugal force equation might lead one t o assume that under any definite set of conditions there would be a clean-cut cleavage in the size of particles t h a t would be collected and lost. I n other words, if we should ignore the surface configuration of the particles, it might be assumed that all particles above a certain size should be collected and all particles bclon this size should be cagried out of the apparatus with the exit gascs. I t has been shown that this is not the case. There is always considerable tux bulence within a cyclone, as n o d d be eupected, because the outer vortex travels downJvard hile the inner vortex travels upward. It is less easily explainable that there is usually a certain amount of bouncing of the. laiger particles and i t is not unusual to find some large particles in the loss from all types of cyclones. On the other hand, there appears to be a drag effect, particularly with high dust coiicentration, as a result of which much of the very fine material is trapped and collectrd along with the coarse material. Because of these various factors, thcre is always a considerable overlapping of particle size, both in the collection and in the loss. Table I1 illustrates this point.
Table 11. Particle size
Figure 10.
Multiple Cyclonic Dust Collector Multiclone type
Distribution, Afirrons 0-10 10-20 20-40 $44
particularly as the electrodes and bus bars tend to set up eddy currents. Available space also usually determines the flue connections, and sharp turns at inlet and outlet cause serious difficulties, unless proper devices are installed to establish good gas distribution. Correcting means include directing vanes, perforated resistance grids, arid chain curtains of various types, used singly or in combination. Figures 7 and 8 illustrate the effectiveness of proper gas distribution means. These data were obtained by Oberman (IO) in an open rectangular wind tunnel having no internal members. This presented a more difficult gas distribution problem than a commercial precipitator, which has some, even though little, internal resistance. Another way to meet the erosion factor is to sweep or drop the collected material out of the gas stream into pockets or dead spaces, and many types of so-called pocket electrodes have found limited application in specific fields. Several types which have been used for many years are illustrated in Figure 9.
Specific Cement Kiln Dust Catch, Loss,
%
%
34.3 17.8 20.6 27.3
87.0 10.6 1.9 0.5
Particle Size Analyses Cases (Quantity Distribution Omitted) Pulverized Fuel Soda Ash Clay Rock Dryer D u s t Boiler Fly Ash Dryer D u s t Catch, Loss, Catch, Loss, Catch, Lori,
%
%
%
% '
%
%
35.1 23.5 22.7 18.7
86.8 9.0
11.7 12.6 20.4 55.3
91.5
61.9 33.3
93.9
PARTICLE
3.3 0.9
SIZE
-
1
1
6.2 1.5 0.8
4.2
2,ij 2.6
0.6
0.9
MICRONS
RECENT TRENDS IN CYCLONIC DUST COLLECTORS
All dry mechanical dust collectors, except settling chambers and filteis, operate on the principle that a change in direction of the gas flow brings about a segregation of the dust particles, because of their greater density and consequent greater momentum. There are innumerable types of baffle chambers, skimmers, and cyclonic devices, each with its specific field of application. Only the cyclonic type, which is most efficient, is discussed here. For high collection efficiency, i t is now customary to use a multiplicity of small-diameter cyclones in parallel. One of this type is the Multiclone illustrated in Figure 10. The design was based on the pioneer studies of Lissman and Horne in 1930 ( 9 ) , who showed that a small-diameter cyclone will operate a t a higher separating efficiency than a large-diameter cyclone at a given pressure drop, as could be expected from the centrifugal force equation, F = mVZ/r, where F is the centrifugal force acting upon a dust particle of mass m, moving with a velocity V in a circle
1-
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D
November 1949
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INDUSTRIAL AND ENGINEERING CHEMISTRY
I n view of this overlapping of fractions, it would appear erroneous to rate the dust collection efficiency of a cyclonic device on the basis of percentages for the various particle size fractions, as is sometimes done. On the other hand, we know that the efficiency of a cyclonic collector decreases as the average fineness Qf the material increases. However, the average fineness does not mean very much, as a small amount of coarse material will shift the average considerably on a weight basis. After much study of this perplexing rating problem, this company has adopted the policy of rating the efficiency on the basis of the - 10-micron fraction contained in the incoming dust. Although this is an arbitrary rating, it works out satisfactorily in practice, as most dusts that are dealt with are the result of fine grinding, and in the comminution of rock or coal the 10-micron fraction increases as the average fineness increases, and the particle size distribution of the ground material follows the usual probability pattern. This also appears to be true with selective suspensions. Figure 11illustrates the validity of this assumption. Of course, each type of dust and each cyclonic apparatus has its own rating. Figure 12 shows the expectancy curve that this company uses on fly ash from pulverized coal-fired boilers for a 9-VG-12 Multiclone, where V designates the vane as the means for establishing the vortex, 9 gives the diameter of the cyclone tube in inches, G designates the shape and arrangement of the cyclone tubes, and 12 designates the relative tube capacity. I n contrast to the nearly unanimous trend to build cyclonic collectors with a larger number of smaller tubes, there are widely divergent trends regarding other features of construction. Some manufacturers are building straight-through types, in which the dust-laden gas enters a t one end of the collector and the cleaned gas leaves a t the other. Others cling to the older construction in which the gas enters and leaves the collector a t the same end, so that the gas spirals in an “outer vortex” and then spirals out in the reverse direction in an “inner vortex.” I n this case, there is a reversal of the axial motion, but not of the rotary motion. Some manufacturers impart the rotary motion to the gas by passing it through a “vane,” which is essentially a stationary axial flow fan, while others cling to the older principle in which the rotary motion is set up by simply admitting the air through a tangential duct or ducts. Some manufacturers build their tubes of aluminum, some fabricate them from steel sheets or plates, and others use cast iron. There is widespread disagreement regarding the merits of these various types as regards their freedom from clogging and their ability t o withstand high temperature and the wear of abrasive dusts and corrosive gases.
-
rl
’
RECENT CONTRIBUTIONS TO THE THEORY OF CENTRIFUGAL COLLECTORS
Following the early work of Lissman and Horne (9) the theory of the motion of a particle in a cyclone was further developed, as reported by Anderson (9),Rosin, Rammler, and Intelmann (If), Lapple and Shepherd (8, 16),and others. The following formula for the minimum sized particle to be wholly separated in a cyclone is in wide use:
where D is in feet, 1) is the viscosity of the gas in pounds per foot per second, b is the width of the gas stream in feet (obtained by subtracting the radius of the outlet pipe from the radius of the collecting tube), N is the number of revolutions made by the gas stream in the collector, V is the tangential velocity of the dust particles in feet per second (assumed constant across width b ) , p a is the density of the particles in pounds per cubic foot, and p is the density of the gas in pounds per cubic foot. Rosin, Rammler, and Intelmann replace V in the above formula by V,, which is the inlet velocity of the gas, implying that the inlet conditions persist through the outer vortex of the cyclone. Lapple and
2433
!-
I
ga a W n
I
>m V 2
w
P 75
z 0
I-
v
w
70
-1
i
69
€0
40
PERCENT
OF MATERIAL
60
Bo
IW
UNDER 10 MICRONS
Figure 12. Expected Efficiencies of 9-VC-12 Multiclone for Fly Ash Collection
Shepherd replace b by the radius of the outlet pipe, and Lissman replaces b by half the radius of the collecting tube. Since Shepherd and Lapple (16)measured the gas velocity within a cyclone and concluded that it varied inversely as the square root of the radius, Gardiner ( 6 ) has attempted to simplify the theory by making use of this observation, and has arrived at the conclusion that the tangential inlet duct of a vanelesa cyclone should not be narrower than the annular width, b, of the cyclone. Gardiner also derived a formula for the pressure losses, F , in a vaneless cyclone, having an inlet duct of height h and width w, and an outlet pipe of diameter e:
where a is the diameter of the cyclone, R is Reynolds’ number, B, CY, 8, and y are constants, and F is measured in terms of inlet velocity heads. INADEQUACYOFTHETHEORY Although theories such as those mentioned above are helpful in selecting the proper proportions of individual cyclone tubes, many questions facing the designer of modern cyclones remain unanswered: What is the most practical way of equalizing the gas flow between tubes in multiple operation, and what features of the design control this equalization? What should be the exact shape of the blades of the vane or stationary fan used t o impart the spiral motion to the gas in some cyclones, and should there be five blades, or six or seven or eight? What is the best way to prevent clogging, and t o reduce abrasion without sacrificing efficiency or volume capacity? These and many other questions facing the designer of cyclones must be answered today by a careful analysis of systematic laboratory experiments and wide experience with cyclones in actual industrial service. ACKNOWLEDGMENT The author wishes to express his thanks to Harry V. Welch, Norman McGrane, Wayne Sproull, and Anna Frey, of the Western Precipitation Corporation, for assistance in preparing the data and illustrations used in this paper.
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BIBLIOGRAPHY Anderson, Evald, Chem. &Met. Eng., 26,151 (1922). Anderson, Evald, “Separation of Dusts and Mists,” in J. H. Perry’s “Chemical Engineers’ Handbook,” 2nd ed., p. 1850, New York, McGraw-Hill Book Co., 1941. Anderson, Evald, Trans. Am. Inst. Chem. Engrs., 16, 69 (1925). Chittum, J. F.. unpublished laboratory report. CottrelI, F. G., Smithsonian Institution Report for 1913, Pub. 2307, 653-885 (1914).
Gardiner, J. E., Shell Petroleum Co., Ltd., Tech. Rept. I.C.T./lS (1948).
Horne, G. H., J. Am. Inst. Elec. Engrs., 41, 552 (1922). Lapple, C. E., and Shepherd, C. B., IND. ENG.CHEM.,32, 605 (1940).
Lissman, M., Chem. & Met. Eng., 37, 630 (1930).
(10) (11)
Vol. 41, No. 11
Oberman, Carl, unpublished laboratory reports. Rosin, P., Rammler, E., and Intelmann, R. E., Ver. deut. Iny
,
76, 443 (1932). (12) Schmidt, W. A., 8th Int. Congress Applied Chem., 5 , 117 (1912). (13) Schmidt, W.A., IND. ENC.CHEM.,16, 1038 (1924). (14) Schmidt, W. A., J.Inst. Elec. Engrs., 41, 547 (1922). (15) Schmidt, W. A., and Anderson, Evald, Elec. Eng., 57, 332 (1938).
(16) Shepherd, C. B., and Lapple, C. E., IND.ENG. CHEM.,33, 972 (1939); 32, 1246 (1940). (17) Sproull, W. J., and Xakada, Y., unpublished laboratory reports. (18) TVhite, H. J., and Anderson, E., unpublished laboratory reports. (19) Wolcott, E. R., Phys. Reo., 12 (N.S.), 284 (1918).
E L W O IMarch V ~ D 7, 1949.
Agglomeration of Smoke, Fog, or Particles by Sonic Waves HILLARY W. ST. CLAIR Bureau of Mines, College Park, M d .
1t has been observed by several investigators that aerosols may be rapidly agglomerated by intense high frequency sound waves. The recent development of powerful sound generators opens the way for industrial utilization of this effect as another means of removing suspended matter from smoke and fumes. The forces acting to cause sonic agglomeration are complex. The more important factors seem to be a combination of the following: (1) covibration of particles in a vibrating gas; (2) attractive and repulsive hydrodynamic forces between neighboring particles; and (3) radiation pressure.
T
HE agglomeration of suspended particles is one of the many
interesting phenomena exhibited by high frequency sound waves. This interesting effect was observed independently by Brandt, Freund, and Hiedemann (9) in Germany, by Andrade and his co-workers in Great Britain (e) and by the author (9). A demonstration of sonic agglomeration was made hefore a meeting of the American Institute of Mining and Metallurgical Engineers in New York City, 12 years ago. Since then there has been widespread interest concerning its practical application in agglomerating smokes and other aerosols produced in industrial operations. At the same time, there have been new developments in generating high frequency sound waves on a large scale. There is good reason to expect that sonic agglomeration will find a place as another tool for removing suspended matter from aerosols. The experimental work by the Bureau of Mines has dealt chiefly with the more basic problems of the physical causes of sonic agglomeration and generation of high frequency sound fields of great intensity. N o serious attempt has been made to try the process on a large scale. The flow of smoke in laboratory tests has been of the order of only 2 to 5 cubic feet per minute. THEORY OF SMOKE AGGLOMERATION It is well known that smoke, fogs, and other dispersions of liquids or solids in gases are unstable and undergo spontaneous flocculation with a lapse of time. Under certain conditions, this flocculation can proceed with appreciable rapidity as in the first stages of the formation of highly dispersed metallic smokes, such as zinc oxide. The theory of collisions between suspended particles was studied by Smoluchowski (11). According t o Smoluchomki’s collision theory the reciprocal of the number of par-
ticles per unit volume varies as a linear function of time. It is evident that spontaneous flocculation or agglomeration will be rapid when the number of particles is very large but will proceed a t a decreasing rate as the number of particles decreases. The only forces acting on the particles under these conditions are those molecular forces that produce Brownian movement. The rate of spontaneous flocculation for most industrial smokes is measurable only after a lapse of minutes. Under the influence of intense high frequency sound, new forces are brought into action which cause rapid agglomeration of smokes that would otherwise remain fairly stable for a long period. These forces are manifold and complex and do not permit any simple explanation. The agglomeration is due only in part to vibrations of the particles induced by the vibrating gas. Other important forces acting on the particles are associated only with the vibration of the gas-that is, they are hydrodynamic or acoustic forces. It was concluded from some of the earlier experiment8 that the explanation lay in the vibratory motion of the particles. but further study has revealed that the causes of agglomeiation of smoke particles are much the same as those responsible for the striations in the lvcopodium powder observed in the classic Kundt dust tube experiment. The behavior of suspended particles under the influence of sonic vibrations in the enveloping gas may be considered as a, combination of the following effects: covibrations of particles in B vibrating gas; attractive and repulsive hydrodynamic forces between neighboring particles; and radiation pressure. Covibration of Suspended Particles. Because of the viscous reaction of the gas in which a particle is suspended, the particle will participate to a certain extent in vibration of the gas. When the particles are very small or when the vibration frequency is low, the particles will vibrate with virtually the same amplitude as the gas, so that the only effect of the particles is to increase the effective density of the gas, thereby decreasing the velocity of sound through it, At higher frequencies of vibration, the inertia of the suspended particles becomes relatively larger with respect to the viscous forceR exerted by the gas, so the redative amplitude of the particles becomes less, until eventually a frequency is reached at which t,he particle will remain virtually stationary while the gas vibrates past it. A t intermediate frequencies, the particles participate in the vibration to variable degrees, d~pending on the particle &e. I n this range, particles of different sizes vihrate with different phases as well as different amplitudes. The
