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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 unpublished laboratory report.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).
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(10) Oberman, Carl, unpublished laboratory reports. (11) 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 (17) Sproull, W. J., and Xakada, Y., unpublished laboratory reports. (18) TVhite, H. J., and Anderson, E., unpublished laboratory reports.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
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relative amplitude or phase of a particle is determined by the product of the frequency and the square of the diameter; the relation may be expressed mathematically as follows:
*
a
where X,, X, = amplitude of particle and gas, respectively; 4 = difference in phase of particle and gas; p = density of particle; d = diameter of particle; and p = viscosity of gas. At a frequency of 5000 cycles per second, water droplets less than 1 micron in diameter will vibrate with virtually the same amplitude as the gas, whereas particles 10 microns in diameter have an amplitude of only about 6% of that of the gm. If the frequency is increased t o 25,000 cycles per second, 1-micron droplets have an amplitude of about 90% of t h a t of the gas. The frequency must be increased to about 90,000 cycles per second to reduce the relative amplitude of 1-micron droplets to one half. However, owing to the difference in phase, even when the relative amplitude of the droplet is only one half, the maximum relative velocity of the gas with respect t o the droplet is nearly 87% of what it would be if the particle remained stationary. Brandt, Freund, and Hiedemann have proposed a theory to explain agglomeration on the basis of the variation in phase and amplitude of particles differing in size in the critical size range. They suggest that sonic agglomeration is a result of the increased rate of collision occurring when smaller particles having a relatively large amplitude come in contact with the larger stationary particles. However, it is difficult to explain any great increase in rate of agglomeration on the basis of this factor alone, a s collisions of this type must occur only between neighboring particles aligned in the direction of vibration. Without going into a detailed discussion, the so-called orthokinetic coagulation proposed by Brandt, Freund, and Hiedemann will be dismissed a s only one contributing cause of sonic agglomeration.
HYDRODYNAMIC FORCES OF ATTRACTION AND
REPULSION The hydrodynamic forces between particles are effective only when two particles are separated by distances equal t o a few particle diameters, They arise as a result of the constricted flow of the gas between two adjacent particles. These forces do not require vibration of the gas and would apply in principle to unidirectional gas flow. However, it is only when the gas is vibrating a t a high frequency that high relative velocity can be maintained between the suspended particles and the fluid surrounding them. The hydrodynamic forces between spherical particles in a vibrating gas were calculated by Koenig (8) in a mathematical analysis of the formation of the Kundtrtube striations. The forces are a result of the well-known Bernoulli effect or the phenomenon that explains the curving of a baseball. These forces can be given a simple qualitative explanation. If two spherical particles relatively close together and having their line of centers transverse to the direction of vibration are considered, the crosssectional area through which the gas must flow may be considered as constricted in the region between the two particles. As a result, there will be a slightly greater velocity of flow in this region. The well-known Bernoulli principle of hydrodynamics tells us that under such conditions there will be a drop in static pressure in this region, and the spheres will behave as though they are being attracted to each other. ConverRely, there will be a sheltered zone on the leeward side of a particle so that particles having their line of centers in the direction of vibration will be repelled from each other. Consequently, the effect of the sound
2435
A VIBBOR
m
REFLECTOR
-
Figure 1. S t a n d i n g Waves i n a Cylindrical Enclosure field on suspended particles is to give rise to repulsive forces between particles in the direction of vibration and attractive forces in the transverse directions. It is evident that these forces will be important only when the particles are very close together. They are in fact inversely proportional t o the fourth power of the distance between centers. Hydrodynamic forces like the covibration of particles are inadequate t o account by themselves for the observed increase ioi rate of coagulation, but they are important in increasing the effective particle diameter and in causing the formation of thin, waferlike flocs made up of particles that cling tenaciously together and set themselves a t right angles to the direction of vibration. I n a stable standing wave field of plane waves, sucb flocs may reach a diameter of several centimeters. Standing Waves. Before discussing the effect of radiation pressure on suspended particles, some of the pertinent characteristics of standing waves or of gases vibrating in resonant enclosures will be reviewed:
If two plane waves of the same frequency and amplitude b u t opposite in direction are superposed upon each other, they will reinforce each other in certain regions and cancel each other i n others. As a consequence the gas is broken up into stationary vibrating segments in which the amplitude of each segment is a maximum in the center and diminishes in either direction. The amplitude varies the same in each segment but adjacent segments vibrate with opposite phase. Such a system of standing waves may be set up by coupling a closed-end tube t o a vibrating piston, as shown in Figure 1. The standing waves are the regultant of the incident and reflected waves. The condition for resonance is that the distance from the vibrator t o the reflector be an integral number of half wave lengths. (This is not exactly true. According to an exact mathematiral treatment taking into account the dissipation of sound energy, the vibrator will be slightly displaced from the nodal position a t resonance.) The positions of minimum amplitude are known as nodes, and those of maximum amplitude, loops or antinodes. The variation in amplitude along the tube is shown by B in Figure 1. Positive values of the amplitude mean that the vibration is in phase with the vibrator; negative values indicate vibration of o posite phase. Therefore, a standing wave field may be considere$ as a attern of vibration in which the amplitude varies as a periodic Punction of location and the phase is either the same or opposite that of the vibrator. The standing wave field in a cylindrical tube is the simplest case of standing waves in a resonant enclosure. Any enclosure will re-
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Figure 2.
Coin Suspended by Radiation Pressure
spond in the kame way to vibrations a t one of its resonant frequencies, forming a pattern of nodal and antinodal regions in three dimensions. As the dimensions of the enclosure become large with respect to the wave length, the frequency becomes less and less critical owing to the greater number of modes of vibration that become possible. Radiation Pressure. It is usually surprising t o learn that sound waves exert a pressure against an obstacle in their path, because at ordinary sound intensities this pressure is too small to be measured. However, at high intensities, such as those required for sonic agglomeration, the pressure is great enough to be felt against one's hand if it is placed in the beam of sound; or, it is possible to suspend metal spheres or coins in mid-air by radiation pressure, as shown in Figure 2. The effect of radiation pressure depends on the size of the surface relative to the wave length of the sound. Two different cases will be considered: (1) the pressure exerted against a large reflecting surface, and ( 2 ) the pressure exerted against a small obstacle suspended in a standing wave field. The radiation pressure against a large reflecting surface is given by: PR
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has been possible to support lead shot by a sound field set up between a reflection plate and an electromagnetic vibrator having a frequency of 10 kc. On the basis of pure sinusoidal vibration at 10 kc. this would indicate an energy density of 4800 ergs per cubic cm. or an intensity of lG watts per sq. cm. However, the intensity may not have actually reached this level. Owing to distortion of the sound field, harmonics are introduced, so that the effective wave length to be used in the above equation is much less than that corresponding to 20 kc. (A = 1.73 cm.). Were i t not for the nonlinear distortion a t high intensities, absolute measurements of sound of great intensities could be made by determining the sphere of greatest density that could be supported by the sound field. The radiation pressure against a large plane reflecting surface is independent of frequency and so i t provides a more satisfactory measure of energy density or intensity a t any intensity that will produce a measurable radiation pressure. Now consider the effect of radiation pressure on a large number of suspended particles in a standing wave. It is evident that, under the influence of forces of this nature, the particles will drift toward and become concentrated in the antinodal regions, I t has been shown that the equation for a particle under the influence of radiation pressure is given by: a: = -tan-' I
k
(tan kxOeBA)
where zo = position of particle at t = 0; z = position of particle at t = t; k = 2x/X; B = 20/9 + u 2 E / h 2 y ; a = radius of particle; and y = viscosity of gas. The progressive changes of concentration of particles initially distributed uniformly are shown in Figure 3, These distribution curves were calculated by a graphic method based on the above equation of motion, as described in a previous paper (10). The progressive changes in concentration are given for t = 0, 27, and 43 seconds for a sound field having an energy density, E = 1000 ergs per cubic cm., and a frequency of 10 kc. It is not actually possible to produce a pure sinusoidal standing wave without harmonics at this intensity on-ing to the nonlinear distortion. At the intensities attained for rapid agglomeration,
l+rs 2
~
where E is the energy density and y the ratio of specific heats of the medium. The force against a reflector 6 inches in diameter exerted by plane waves of sound having a frequency of 20 kc. and an amplitude of 50 microns cm.) equals about 50 grams. It is the radiation pressure on a small obstacle in a standing wave that is important in sonic agglomeration. It may be shown (7') that a spherical obstacle in a standing wave will be acted on b y a force that urges it toward the antinode or the position of maximum amplitude. This force is periodic with respect to position, having a period equal to one half wave length. The force is zero at the nodal and antinodal positions and reaches a maximum midway between. The maximum value of the force acting on a sphere of radius a is equal to: 10 T 2 U 3 -
F(?) = - - E 3
x
where X is the wave length. This may be rewritten in the terms of the volume of the sphere:
This relation applies to spheres whose diameter is small with respect to the wave length. The radiation pressure of the sound field having an amplitude of 50 microns and a frequency of 20 kc. is sufficient to support a sphere having the density of water. It
Figure 3.
Concentration of Suspended Particles by Action of Radiation Pressure
Calculated for uniform particles having diameters of 1 micron i n a sound field having an energy density equal to 1000 ergs per cubic cm.
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to be seen. The larger flow are disklike aggregates oriented with their planes a t right angles t o the direction of vibration. At low intensities the final stage is reached when the individual flakes combine to form large waferlike flocs suspended a t intervals of one half wave length along the axis of the tube or projecting out from the walls as thin shelves. The flocs along the walls usually occur along several parallel closely spaced planes arranged roughly symmetrical with the antinode. This is analogous to the fine striations observed in the Kundt tube and confirms our conclusions regarding the importance of harmonic antinodes. At very high intensities flocculation takes place in a few seconds but large floes are no longer formed because of the instability of the sound field. Swirling nebulous clusters of flocculated smoke particles are observed a t intervals along the axis of the cylindrical chamber and striations form and dism QEAN R ~ E C T O R appear along the walls. Tuning of the chamber is quite critical a t low intensiFigure 4. Apparatus Used for Experiments on Sonic Agglomeration of Smokes ties but becomes less and less important as the intensity is increased. The present discussion has been made on the tacit assumption that the radiation pressure acting on each strong second, third, fourth, and fifth harmonics are observed. particle is determined only by its position relative to the acoustic I n one instance a pressure wave was observed on the oscillograph field; the effect of neighboring particles on the radiation pressure in which the seventh harmonic was plainly evident. Therefore, has been disregarded. This is probably a serious omission. It the actual wave pattern existing during agglomeration is not a simple standing wave as shown in Figure 1 but a more complex seems likely that attractive and repulsive forces will arise between neighboring particles as a result of radiation pressure somewhat vibration made up of the fundamental and many harmonics analogous to the hydrodynamic forces already discussed. There superimposed on each other. Instead of a single antinodal region there is a series of antinodal planes becoming progressively more closely spaced as the fundamental antinodal plane is approached. It now seems likely that the fine structure of the striations ob30 served in the Kundt-tube experiment is a result of concentration of the lycopodium powder a t these harmonic antinodes. Sonic 28 agglomeration and the Kundt-tube striations are different mani26 festations of the same forces; both of these may be explained on 24 the basis of radiation pressure. It is evident that the change of concentration shown in Figure 3 32 represents a process that will be occurring for each harmonic. Furthermore, s h c e the exponential factor B is inversely progE 20 portional to the square of the wave length, concentration at the ' harmonic antinodes may be more effective than a t the fundamental antinodes. Even though the relative intensity of har9 10 monies decreases with increasing order, their effectiveness and the 14 number of antinodes increase. For this reason it is probable that 12 the rapidity of sonic agglomeration is due in a large part t o the nonlinear distortion of the sound field. It should also be pointed 10 out that radiation pressure is actually greater than shown here 0 when the nonlinear response of the medium is taken into account (6). 0 The behavior of suspended particles under the influence of radiation pressure as described above is quite consistent with 4 observations that are made during flocculation experiments. e When flocculation of a dense ammonium chloride smoke takes place a t relatively low intensity (particularly if the flocculating '0 4 0 12 I0 20 24 Z0 32 3S M 44 48 52 60 tube is only several inches in diameter), several seconds before the TIME. SECONDS smoke begins to flocculate the smoke has a banded appearance Figure 5. Rate of Flocculation of Ammonium Chloride owing to migration of the particles from the nodal to the antinodal Smoke at Various Sound Intensities regions. Shortly afterward the smoke begins to break down, taking on a granular appearance as the floes become large enough Smoke concentration, 2 mg. per liter
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E = energy density, ergs/cu. em. = intensity, watts/sq. em. p = densityofgas f = frequency, cycles/sec. 5 = amplitude,cm.
I
Figure 6.
FloccuIation of A m m o n i u m Chloride Smoke in Four Successive Stages
need for an analysis of the radiation of two neighboring sphere6 similar to that made by King ( 7 ) for a single sphere.
IS
EXPERIMENTAL TESTS ON SONIC AGGLOMERATION The apparatus used for an experimental study of sonic agglomeration is illustrated in Figure 4. The essential elements are a sound generator mounted a t the top of a resonant cylindrical enclosure. The smoke is introduced through an annular ring of holes a t the top of the cylindrical chamber and the flocculated smoke and gas pass through corresponding exit ports near the bottom. The sound is generated by a cylindrical bar electromagnetically excited into longitudinal vibration (9). The cylindrical enclosure is tuned to resonance by an adjustable reflector a t the bottom. The degree of flocculation was measured by the change in light transmission of the smoke before and after flocculation [see pages 4 to 9 of (9)J. The rapidity of flocculation of ammonium chloride smoke is shown in Figure 5. Similar studies were made for other smokes such as zinc oxide, tobacco smoke, carbon smoke, water fog, oil fog, and dust suspensions. The properties of the smoke which determine its response to flocculation are the size and density of the particles and the concentration of the particles (number per unit volume), The increase in particle size is shown by the microphotographs in Figure 6 . The original ammonium chloride smoke consisted of particles 0.3 to 0.5 micron in diameter. The flocculated particles are of the order of 1M) microns, or larger, in di%meteror large enough to be readily separated by settling, filtration, or centrifugal separation. Many dust particles are temporarily flocculated while in the sound field but are dispersed immediately after leaving. Flocculation can be made permanent by introducing a spray of fine droplets of Prater or oil which is agglomerated with the dust particles and causes them to adhere to each other. The rapidity of flocculation is determined by the acoustic energy density of the sound or the number of ergs of acoustic energy per cubic em. The energy of the sound field may also be expressed in terms of intensity or watts of acoustic energy per square cm. The energy density and intensity are related t o the frequency and amplitude of vibration as follows:
E = 272pj2t2
z
=
2?r2pcfZp
x
10-5
Flocculation begins to be effective a t an energy density of about 90 ergs per cubic em., but rapid agglomeration requires energies of greater than 100 ergs per cubic cm. Energy densities of several thousand ergs per cubic cm. have been attained in the flocculating chamber. The corresponding acoustic intensity is of the order of several watts per square em. The amplitude required for 100 and 1000 ergs per cubic em. a t a frequency of 10 kc. is about 80 and 250 microns, respectively. The energy density required to support a water droplet against the force o€ gravity is about 400 ergs per cubic em. at 10 kc. The essential elements required for sonic agglomeration of aerosols are a resonant enclosure and a soudd generator capable of attaining sound intensities of the order of 1 watt per square cm. When the enclosure is large with respect to the wave length its dimensions are not especially critical for there will be many modes of vibration and SO within certain limits it will be resonant to continuous range of frequencies. More investigation is needed regarding the design of inlet and outlet ports that will transmit a minimum of high frequency sound energy but will allow passage of a unidirectional flow of gases. Other factors to be studied are the shapes of the enclosures to give the optimum standing wave pattern and other features that will minimize dissipation and radiation of acoustic energy. The electromagnetic sound generator used in these experiments was used primarily for its advantages in experimental control and measurement. Generators operating on compressed air or gases offer a simpler and more practicable sound source for industrial application. High frequency sirens as described by Allen anti Rudnick (I) and by Danser and Neumann (4) seem t o be the most practicable sound sources available currently. The Hartmann air jet generator (6) is another generator of the same type whose practicability has yet to be demonstrated. The forces acting to cause sonic agglomeration are complex. A complete theory must take into account the radiation pressure on the particles, hydrodynamic forces arising as a result of variation in velocity of the medium, and the vibratory motion as well as the random motion of the particles. Although the details of these forces are not yet well enough understood to give a quantitative theory, it seems fairly certain that the major effectsare the result of acoustic forces and are not purely kinetic effects. These acoustic forces, arising from radiation pressure, act to cause a concentration of the suspended particles in the regions of maximum displacement and to produce attractive and repulsive forces between the particIes.
LITERATURE CITED Allen, C. H., and Rudnick, I., J. Acoust. SOC. Am., 19, 867 (1948).
Andrade, E. N. da C . , Trans. Faraday Soc., 42,1111 (1936). Brandt, O., Hiedemann, E., and Freund, H., 2. Physik., 104 511-33 (1937).
Danser, H.W., and Neumann, E. P., ISD. ENG.CHEST., 41, 2439 (1949).
Fubini-Ghiron, Eugenio, Altn Frequelzza, 6, 640-53 (1937). Hartmann, J., and Lazarus, E’., Phil.M a g . , 29, 140-7 (1940). King, L. V., T r a n s . R o y . Soc. ( L o n d o n ) , 147A,233-6 (1934). Koenig, W., Ann. phys., 42, 353, 549 (1891). St. Clair, H. W., U . 8. Bur. Mines, Rept. Invest. 3400,pp. 51-61; conference on metallurgical research, lMetallurgioa1 Div., U. 6 . Bur. Mines, Salt Lake City, Utah ( M a y 1940); Rea. Sei. Instruments, 12, 250-6 (1940). 8t. Clair, H. W., Spendlove, M.J., and Potter, E. V., U . S. B w . Mines, Rept. Invest. 4218. Smoluchowski, M. v., 2. physik. Chem., 92, 129-68 (1918). RECEIVEDMarch 21, 1949.
