Impaction of Dust and Smoke Particles ON SURFACE AND BODY COLLECTORS W. E. RANZ AND J. B. WONG Engineering Experiment Station, University of Illinois, Urbana, I l l .
’
A n investigation of the mechanisms of collection of dust and smoke particles was undertaken from the standpoint of a fundamental study of the impaction of aerosol particles on elementary collectors. The systems analyzed were rectangular and round aerosol jets impinging on flat plates (jet impactors and impingement separators) and cylindrical and spherical collectors placed in aerosol streams (fibrous filters and wet scrubbers). Theories of mechanisms were reviewed and extended, and an approximation method, involving dimensionless parameters,
is proposed for determining the efficiency of impaction even in the most complicated situations. Experimental data were obtained for the inertial mechanism operating in the systems under study. Kates of collection of glycerol and sulfuric acid aerosol particles of nearly uniform size were measured by impaction on wires and spheres in streams moving at various velocities and by impingement on flat plates from jets of different sizes and velocities. Experimental results and theory were compared and applied to the analysis of practical problems.
MPACTION of small particles on simple collectors, such as flat plates, cylinders, and spheres, is the means by u hich dust and smoke are removed in many types of air-cleaning equipment. Impingement separators are composed of aerosol jets directed against flat plates, air filters are mats of cylindrical fibers, and wet scrubbers are filled with high-velocity water drops. A fundamental analysis of such equipment requires an analysis of the impaction of small particles in elements of the flow system. The authors have chosen as elementary processes, impaction on flat plates from rectangular and round aerosol jets, and impaction on cylindrical apd spherical collectors from aerosol streams. For particles of normal density in the micron and submicron ranges of size, inertia, interception, electrostatic attraction, and settling a1e the primary mechanisms by which collection takes place on a surface in an aerosol stream. I n the case of inertia, a particle carried along by an air stream on approaching an obstruction tends to follow the stream but may strike the obstruction because of its inertia. In the caw of interception, the trajectory of the center of a relatively large particle, while not intersecting the collecting surface, may pass close enough for the surface of the particle to touch the collector. In the case of electrostatic attraction, the particle may be encouraged to impact upon the collecting surface by an actual or induced electrostatic force between the particle and collector. I n the case of settling, particles in a slowly moving air stream may settle out on the collecting surface under the influence of gravity. When the particle size is less than 0.1 micron, Brownian diffusion becomes significant. When a temperature gradient exists, radiometer forces are present. Thus, a fundamental analysis of the impaction process must include also an analysis of the various mechanisms of impaction and collection.
velocity jets so that the size distribution of micron and submicron sizes could be studied, but his instrument was not calibrated Kith great accuracy. Laskin ( 7 )made an extensive study of the use of May’s impactor for assessing heavy aerosol particles of micron and submicron sizes. In general, the limitation of the impinger for collecting aerosol particles in the submicron range of size has not been determined, and an adequate theoretical analysis of the size separation has not been developed. Previous works on the impaction of aerosol particles on body collectors, such as cylinders anh-spheres, by Albrecht ( I ) , Landah1 and Herrmann (4),Langmuir and Blodgett (6),and Sell ( I I ) , were primarily of a theoretical nature and considered inertia as the pnly mechanism of collection. Because of the complicated nature of the problem, the results of these authors were not in good agreement, particularly with regard to the question of whether a minimum particle size exists below which impaction cannot occur. For aerosol particles of normal density in the micron and submicron ranges of size, and collectors in the micron range of size, it has been recognized (10) that interception, settling, and random molecular motion are also important mechanisms of collection, but no detailed evaluation of the magnitude of each effect has been presented. Although the existence of electrostatic forces is well known in aerosol technology, no attempt has been made to relate this phenomenon to the problem of impaction. In general, experimental approaches to a solution of the problem of impaction (4,1 1 ) have failed because of the lack of adequate experimental methods and the complexities of the physical problem, which do not allow a complete separation of the effect of individual mechanisms.
PREVIOUS WORK
SUMMARY OF PRESENT WORK
Impingement of aerosol jets on flat plates has been used for many years as a means of sampling aerosols and determining particle size. Older models of laboratory impactors consisted of single stages and were primarily sampling devices. May (8) was the first to report quantitative experimental information on the performance of impactors and made a dimensional analysis of the variables involved in their operation. He introduced a cascade system in which an aerosol of the size range from 1 to 50 microns was separated into fractions of successively smaller particle size. With such a separation, cumulative plots of the particle size distributions were drawn using calibrated “characteristic diameters” for each stage. Sonkin ( I S ) extended the cascade system to high-
The present x-ork develops a mathematical statement of the problem of impaction, a t the same time realistic and rigorous, and carries out limiting solutions and order of magnitude calculations which establish the nature and importance of the various mechanisms of impaction. A method, involving dimensionless parameters, is proposed for determining the order of magnitude of the efficiency of impaction even in the most complicated situations. Experimental results are reported on the inertial impaction of aerosol particles from rectangular and round aerosol jets on flat plates. Experimental results on inertial impaction on cylindrical and spherical collectors placed in aerosol streams are reported also. In each case, the experimental and theoretical results are
lune 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
1371
Air P o l l u t i o b applied to the analysis of example problems which heretofore either could not be solved or presented such formidable difficulties that a practical solution was not possible.
where C is an empirical correction factor for particles whose diameters are of the order of magnitude of the mean free path of an air molecule. Any particle moving with an aerosol stream will follow the fluid for some distance. At first u = u ,but as an obstacle is appreached, v changes markedly to allow the stream to spread out or to pass, and the particle will follow a trajectory given by Equation l . Whether the particle trajectory will reach the surface of the collector depends on the nearness of the starting position to the axis of flow through the center of the collector, the nature of the streamlines along which and through which the particle passes, the configuration of the flow system, and the size and shape of the collector. -
I3IPACTION AND COLLECTIQN MECHANISMS
A basic approach t o the problem of small particle collection is the evaluation of forces t h a t affect the motion of a particle and cause it to move from an aerosol stream onto a collecting surface. Dimensionless parameters, which are essentially a comparison of the various forces tending t o cause impaction with the fluid resistance force opposing particle motion or a comparison of two dimensions of the physical system, characterize the mechanisms of collection and are defined as follows: Inertia. \Tr = Cp,voD~/l8pD, \Ir is the ratio of the force necessary t o stop a particle initially . trave1ing;at a velocity uo in the distance D,/2, t o the fluid resistance at a relative particle velocity of uo. It is also the ratio of the stopping distance-i.e., the distance a particle will penetrate into still air when given a n initial velocity of vo-to the diameter of the collector or width of aerosol jet. Interception. R = D,/D, R is the ratio of the particle diameter t o the diameter of the collector or width of aerosol jet. This oarameter enters into the boundary conditions of the problem aGd does not appear in the equation of motion. Settling. G = Cp,gLD~/18pvo = (gLD,/u:)* G is the ratio of the force of gravity to the fluid resistance a t a relative particle velocity of uo. It is also the ratio of the free settling velocity of the particle to the stream velocity. Electrical Attraction by Charges. K E = Cq,qa,/3~peoD,v, K E is the ratio of the electrical force a t the surface of the collector due to charges, t o the fluid resistance a t a relative particle velocity of uo. Electrical Attraction by Induction. K I = 2C(el - e2)q&D,'/ 18~€0DcU, K I IS the ratio of the electrostatic force on a dielectric particle a t the surface of a charged collector. to the fluid resistance a t a relative particle velocity of vo. Parameters characterizing the thermal force on an aerosol particle in a temperature gradient and the random thermal motion of Brownian diffusion have also been defined. However, because thermal gradients do not exist in normal practice and Brownian movement is not significant as a means of collecting aerosol particles greater than 0.1 micron in size, these mechanisms are not treated in this paper. MATHEMATICAL STATEMENT O F MECHANICS O F IMPACTION
Consider a fluid moving in a positive 2-direction spreading against a flat plate or moving around a cylindrical or spherical collector placed in the stream. Consider also a particle, carried along with this stream, whose motion will not be identical with the fluid because it is subjected to several forces which tend to impact it on the surface of the collector. Figure 1 is a graphical representation of the situation. Application of law of motion t o movement of particle gives
The first term represents the fluid resistance opposing the relative movement of the particle through the fluid, the second term represents the force of gravity, and the third term represents the electrical force. All these forces cause a change in the motion of the particle given, according t o Newton's second law, as d ( m 7 ) /dt. If the particle in question is spherical or can be assigned the diameter of an equivalent sphere, has a small diameter, and moves slox-ly so that viscous forces predominate, the mobility, 2, is a function only of the particle diameter and the physical properties of the air.
Z = (1/3npD,)C 1372
(2)
-
L
+
1
AEROSOL JET
BODY COLLECTOR
_---Streomline
-Particle Trojcstory Figure 1.
t+=
!
t
-f
Impaction of Aerosol Particles
The efficiency of impaction, '7, is defined theoretically as the ratio of the cross-sectional area of the original aerosol stream from which particles of a given size are removed because their trajectories intersect the collector surface, to the total cross-sectional area of the original stream in the case of jets or to the projected area of the collector in the direction of flow in the case of cylindrical and spherical collectors. All particles that strike the collector are assumed to adhere t o its surface, and no particle is assumed t o touch the surface unless its trajectory is tangent to or intersects the surface. As the trajectory is the path of the center of the particle, it is possible that a large particle will come in contact with the collector when its trajectory passes the collector surface a t a distance less than (D,/2) away. This factor concerns the interception effect and is discussed below. For immediate consideration, it is assumed that the particle has a finite size only in determining the resistance to its motion relative to the fluid, and a finite mass only in determining the effect of this resistance on its motion. EFFICIENCY OF IMPACTION BY INERTIA FOR SIMPLIFIED FLOW MODELS b f I N I X U Y PlRTICLE
SIZE BELOWn-HICH
IMPACTION C A K N O T
OCCUR. To obtain qualitative information about impaction by inertia on an obstacle in an aerosol stream, simplified flow models can be defined where the force of gravity and electrostatic attraction are neglected and where the flow field and boundary conditions are approximated. If the simplifications and approximations are carried far enough, analytical solutions for the efficiency of impaction are possible. If these simplifications and approxima-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 6
Air Pollution TABLE I. IMPACTION BY INERTIA FOR SIMPLIFIEDFLOW MODELS 2*-
Equations of Motion (cf. Equation 1)
d% dP
+ dz - - a, df
=
Flow Field Approximations
Model Impaction from rectangular aerosol jet of infinite length and width D, on flat plate of infinite extent
dg
d2g 2 * -d+ f 2-
0
df - a v = o
Boundary Conditions f = -1 -1 < g = go < 1
ii, = 1 ii, = 0 when I = 0
Impaction from round aerosol jet of diameter D,on flat plate of infinite extent
2 =
-1
E.
= go
= 1 uy = 0 when I = 0
Impaction from aerosol stream of infinite extent on ribbon of infinite length and width D, (two-dimensional model of cylinder) Impaction from aerosol stream of infinite extent on disk of diameter D, (two-dimensional model of sphere)
a, a,
BY
=
=
-32 - 1 < f < O 2/,.)for region( - 1 < g < 1
= -22)for 5 region(
-1/z
enceor-nonexistence of a critical q , The calculations of Langmuir and Blodgett ( 6 ) indicate that the collection efficiencies of spheres are slightly higher than those of rj-linders for lonvalues of I, but Sell ( 1 1 ) states that spheres have mucsh lower efficiencies a t all values of q. Langmuir and Blodgett (6)give qc = 1/16 for cylinders and I, = 1/*4 for spheres; Albrecht ( 1 ) gives I,= 0.09 for cylinders; other investigators give qc = 0. To emphasize the effect of particle diameter, Figures 5 and 6 have heen plotted as 7 us. .\/.I., and it can be sren that the curves are comparable in form t o those for the models of Figures 2 and 3.
0.8
z 0.6 U
0
G2 0 4 0
k2 0.2 01 0
Figure 2. 1.01
0.2
0.4
0.6
I
I
0.8
1.0
m m (CpPYO/l8pDc)1/2 Dp
12
Theoretical Impaction Efficiencies of Aerosol Jets I
Disk
I
I
i;
A b O "
I
I
I
I
I
I
2.0
1
r -
0
0.2
0.4
0.6
0.8
1.0
1.2
fl= CC~~V,/I~VD~PD~ g Figure 3.
2 I-
&
A particle will touch the collector uhenever its center approaches n-ithin a distance D , / 2 of the surface: and for the given conditions, the efficiency of interception can be defined by the ijoof streamlines n hich pass the collector a t a position 5 = 1 R a t j: = 0.
+
+ E) - 1/41+ R) = (1 + R)2 - 1/(1 + R )
70 = (1
for a cylinder
(5)
770
for a sphere
(6)
Equations 5 and 6 are shown graphically in Figure 4. These efficiencies represent the minimum value of the impaction efficiency for inertia and interception in an ideal flow. At large values of R, v-here the particles have much larger diameters than the collector, the efficiency of interception approaches a value of (1 R ) for cylinders and (1 for spheres, which are the same limits as those for I = m . If the postulated physical situation corresponds somewhat t o the actual physical situation, then the above results point out interesting facts. For example, a 20micron spray droplet in a wet scrubber has a minimum impaction efficiency of about IS'% for 1-micron particles, and 3y0 tor 0.2micron particles.
+
1374
+
1.5
E
Theoretical Impaction Efficiencies of Disk and Ribbon
0
1.0
Gz w
:0: 0.s W
P 0
0
0.2
0.4
R ' Figure 4 .
0.6
0.8
1.0
DdDc
Interception Effect for
Potential Flow
The assumption that the reduced velocity is a function of the reduced position coordinates alone is an oversimplihcation. Actually, the flow will be a function of the Reynolds number of the collector, A 7 ~ = e D c p v 0 / p , as well as the reduced position coordinates, particularly near the collector surface where the viscous forces affecting fluid motion are of the same order of magnitude as the inertial forces. r n d e r these circumstances 11 is not only a function of and R but also of
[email protected] dependency on .4-lie
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 6
Air Pollution 1.0 1
I
1
I
I
I
L
1
5
EP P
w2
_---Longmuir ond
1 4 *k *
t w
s
/I
I
b & L
ts
BlodgItt
Y
,d ,//
// ./‘
-Lanqnuir
i
and Blodgrti
0.2
Landohl ond Hrrrmann 0
0
-/
0.5
I.5
1.0
2.o
2.5
5.0
(CppbppOc,’/2Dp
Figure 6. Theoretical Impaction Efficiencies of Spherical Collectors
tends to become negligible at high N R ~where , the assumption of potential flow is a fair approximation of the actual velocity field near the forward face of a collector, but may be appreciable for the low NR*encountered with fine filter fibers. It is difficult t o predict the effect of boundary layer flow on the trajectories of aerosol particles. Probably the interception effect is decreased, as the development of a boundary layer tends t o widen the streamlines halfway around the obstacle, where the potential flow streamlines would draw close together near the surface. The picture of flow near the forward face is similar to that of potential flow, and the trajectories in this region will be essentially those predicted for ideal flow. Once inside the boundary layer, however, the trajectories are affected by two opposing actions: The tangential velocities which sweep the particle around the collector are smaller and the particle is allowed a longer time to reach the surface; but simultaneously, the negative radial velocity has decreased, tending to keep the particle away from the surface. The situation in the wake is a confusion of eddies, which can conceivably impact particles on the rear of the collector in the same manner that debris collects behind bridge piers in flooded rivers. SETTLING EFFECT
If gravity forces are considered to be important and electrostatic forces negligible, Equation 1 becomes
As an approximation, the apparent efficiency of impaction caused by settling is given by 7 = the number of particles per unit volume of gas times the terminal velocity of a particle times the cross-sectional area of the collector projected in a vertical direction, divided by the number of particles per unit volume of gas times the gas velocity times the cross-sertional area of the collector projected in the direction of flow
= G
for cylindrical and spherical collectors
and the settling parameter, G, but also several parameters for the effect of electrostatic forces. The number of calculations required would be of the order of the product of the various parameters and the number of points needed t o establish one efficiency curve. Such tedious calculations are ill advised in view of the lack of knowledge of the actual physical situation, particularly the lack of knowledge about the flow field. The relative magnitude of the effect of the various parameters, however, is instructive, and qualitative information on the effect of electrostatic forces is of practical value. The important electrostatic forces involved in the collection of particles on cylinders and spheres are t h e forces between a charged and/or dielectric particle and a charged collector. The electric fields around a charged cylindrical and spherical collector are given by ( 3 )
E, = q,,/ieo, Ee = 0, for a cylinder
E, = qoo/P2eo,Eo
=
0, for a sphere
(9) (10)
The force on an aerosol particle with a charge qp is therefore
F , = qpq,,/7e,, Fs = 0, for a cylinder
(11)
F , = q,qao/i2e,, Fa = 0, for a sphere
(12)
The inductive force on a dielectric particle in a cylindrically or spherically symmetrical electric field is given by ( 3 )
F, -
(€1
- ez)EoVE,(bE,/ar), FO = 0
(13)
I n rectangular coordinates, the equations of motion for a charged dielectric particle become, when expanded to include the electrical forces: For a cylindrical collector:
(8)
Hence, the efficency of impaction by settling is of the order of unity when G = (g~DJz1?)?1, is OP the order of unity and of more importance than the efficiency of impaction by inertia when (gLD&) is greater than 9.
For a spherical collector:
ELECTROSTATIC FORCES
The electrical properties of small particles affect their motion seriously. For physical situations involving electrostatic forces, as well as inertial and gravitational forces, the equation of motion becomes even more complex. Numerical solutions now involve not only the inertial parameter, P,the interception parameter, R, June 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
1375
Air Pollution Positive values of K E indicate a decreased efficiency; negative values of K E indicate increased efficiency. K I is always positive. In elaborate numerical solutions, high values of the interception parameter, R, are taken into account in the boundary conditions when the point' of impaction and the limiting trajectories are determined. Equations 14 and 15 with appropriate boundary conditions cannot be solved analytically, but qualitative solutions are possible for simplified models, which indicate t h a t the efficiency of impaction caused by electrostatic forces is of the order of unity when the characterizing parameter is of the order of unity.
tic dimension of the flow channel or collector, and comparing this distance with the characteristic dimension of the channel or collector. If such a ratio of forces or distances is of the order of unity, then the efficiency of impaction will be of the order of unity, and the mechanism will have merit for particle collection.
INERTIAL I-MPACTION FROM RECTANGULAR AND ROUND AEROSOL JETS Experimental efficiency curves for impaction by inertia from rectangular and round aerosol jets were established by experiment. The experimental procedure consisted of the generation of a condensation aerosol of nearly uniform particle size, the measurement of particle size by an optical method, and the determination of the efficiency of impaction by gravimetric analysis. The experimental conditions and the ranges of variables were such that mechanisms of impaction other than inertia mere absent or negligible. The accuracy and reliability of the results are deMonometers pendent largely on the uniformity of the particle size and the accuracy of the particle size measurement. Filter
P
EXPERIBIENTAL EQUlPMEhT
,
"
-
a
!Air Supply t
I
Figure 7.
,
Experimental Equipment for Impaction
GENERALIZATIONS CONCERNING MECHANISMS OF COLLECTION
Whenever one parameter characterizing a mechanism oi collection is much greater than all other parameters, collection can be attributed entirely to the mechanism which that parameter characterizes. The efficiency of impaction 1%-illbe negligible for any given mechanism when the parameter characterizing that mechanism is less than 10-2 and will be of the order of unity when that parameter is of the order of unity. Although the forces of the various mechanisms are additive, the resulting individual efficiencies are not directly additive. Each mechanism will contribute to a total efficiency, however; and no combination of favorable mechanisms will cause an efficiency lower than t h a t expected for any one of the favorable mechanisms. The efficiency of collection for a given mechanism Till be proportional to the size of the particle and the size of the collector, and to the stream velocity, in approximately the same manner t h a t the parameter characterizing t h a t mechanism is proportional t o D,, D,,and v,, by definition. ,4ny mechanism of moving a particle from an aerosol stream onto a collecting surface can be analyzed and evaluated in two VI aye: (1) by calculating all the possible forces brought to bear on the particle by the mechanism, and comparing the resultant force with the fluid resistance at a relative particle velocity of vo, and ( 2 ) by determining the distance the particle will travel in still air under the influence of the resultant force during the time it would take the aerosol stream to move a distance equal t o a characteris-
1376
Figure 7 is a schematic diagram of the experimental equipment used to establish impaction efficiency curves for rectangular arid round aerosol jets, Vacuum Pump The central feature of the Efficiencies of Jets equipment is a condensation aero$61generator similar t o that designed for aerosol research by the Department of Chemistry of Columbia University (12).Air for the generator was filtered and dried. It was then passed through a pressure regulator and an Army Chemical Corps aerosol filter canister. Two low-capacity flowmetfirs delivered air to a salt nuclei generator and t o the humidifier of the aerosol generator in a range of from 550 t o 4300 cc. per minute at 10 pounds per squaro inch gage and 70" F. The current through the salt nuclei generator was regulated by a voltage regulator and a Variac. T h r aerosol generator was inclosed by insulating walls of Marinite--4 furnished by Johns-Manville, and the temperatures in the humidifying and reheating sections were regulated by bimetal thernioregulators, relays, and 750-watt heaters. Glycerol was used as the aerosol material. The generator provided particles of nearly uniform diameter in a range from 0.3 to 1.4 microns at a generation rate of the order of 1 to 5 mg. of aerosol material per minute. The rate of generation and particle size were fixed by controlling the operating conditions. The glycerol aerosol, which formed by condensation on the salt nuclei while passing through the cooling chimney, could be disposed of through a line to a water aspirator when the generator was coming to equilibrium or could be drawn into the impactor line together with additional air when the vacuum system was operated. The additional air was room air drawn into the impactor line through an asbestos-bearing paper filter furnished by Arthur D. Little, Inc. Two types of impactors were used, in which both rectangular and round jets could be mounted. One type had a 0.5-inch approach line and another type, smaller and more compact, had a 0.375-inch approach line. The rectangular jets had cylindrical, convex inside walls; the round jets had a 60" cone as an approach shape. The outside walls of the jets were streamlined at an angle of 30" for the first type of impactor and 45" for the second type to allow entrainment and t o prevent the aerosol stream from spreading before it reached the plate. Rectangular jets were from 10 to 50 times longer than vide, so that the length came into consideration only in the calculation of the free open area of the jet. The jets were directed against a collector plate a t a distance of
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 6
Air Pollution from one to three jet widths or diameters away. The collectors were flat-bottomed glass cups which could be removed from the impactor and weighed for impacted aerosol material. Aerosol particles which escaped impaction were drawn into a filter train consisting of three separate filters, each containing about 1 inch of tightly packed, No. 800 Pyrex brand wool filtering fiber. These filters could be removed and weighed. As all or nearly all of the weight increase appeared in the first two sections, a complete removal of the particles was assumed. The aerosol particles and additional air were drawn through the impactor and filter train by a vacuum pump, capable of delivering 1 cubic foot per minute of free air a t a vacuum of 20 inches of mercury. The rate of flow was determined by previous calibration of the jets and was controlled by needle valves in combination with a bleed line.
accuracy of the particle size measurement. The extent of application of Figure 8 beyond the range of variables used to establish the curve may be considerable. May (8) obtained a curve of similar shape, less sharply defined, for atomized sprays in a range of particle size of from 1 to 50 microns with a &for 17 = 0.5 equal to 0.47. Laskin (7) obtained comparable results using a particle density of pp = 10.9 gram mass per cc. but did not give an interpretation of his work in the form of Figure 8.
EXPERIMENTAL PROCEDURE
The aerosol generator was operated approximately 4 hours before impaction data were taken. In this period of time, the operating conditions, were adjusted for a certain general particle size, and equilibrium and homogeneity of particle size were obtained. The diameter of the aerosol particles leaving the generator was measured optically ( l a ) with Owl No. G-2, calibrated by the Department of Chemistry of Columbia University and loaned t o the University of Illinois by the Army Chemical Corps. I n several instances the particle size of aerosols of approximately 1micron diameter was checked independently by falling velocity measurements. It was estimated that the sizes of the particles did not deviate more than 10% from the average diameter read by the Owl and that this reading was proably more reliable and consistent than falling velocity measurements for particles in the 1-micron and 0.1-micron ranges of size. As soon as the article size was determined, the vacuum pump was started and t f e needle valves were adjusted for a given volumetric velocity through the jet as indicated by manometers. The aerosol jet was allowed to impinge on the collector cup for approximately 20 minutes, after which the cup and filters were removed and reweighed. Since 30 to 100 mg. of aerosol material was apportioned between the cup and filters, the efficiency of impaction was readily deteqmined by this method. DISCUSSION OF EXPERIMENTAL RESULTS
Figure 8 shows in graphical form the results of the experimental measurements. The ranges of variables represented are: particle sizes, 0.34 t o 1.38 microns; jet velocities, 1050 t o 18,100 cm. per second; rectangular jet widths, 0.020 to 0.071 cm.; and round jet diameters, 0.10 t o 0.19 em. Because of the experimental difficulties involved, a curve for a given jet was established, in general, at a single particle diameter by varying the jet velocity, but sufficient data were taken t o show a cross plot of the same curve at a single jet velocity with varying particle diameter. These curves for impaction by inertia show a characteristic shape, almost steplike in form, demonstrating the ability of a jet impactor to classify the particle size distribution of an aerosol into two size ranges, the dividing point being a t a diameter represented by .\/$ = 0.57 for rectangular jets and dq = 0.38 for round jets. Furthermore, there is indicated a minimum particle size below which impaction cannot occur and a maximum particle size above which all particles are removed. For a given value of the parameter, \k, which takes into account the operating conditions, round jets show a higher efficiency than rectangular jets, but such a comparison is not the only criterion in choosing an optimum impactor design for a given application. As the ratio of particle diameter t o jet diameter or width was never greater than R = 0.007, impaction by interception could be considered negligible. As aerosol particles from the generator were found t o be uncharged, impaction by an electrostatic mechanism was improbable. Figure 8, therefore, should represent impaction by the inertial mechanism alone. These results establish the general shape and relative position of the inertial impaction c1irvea for rectangular and round aerosol jets. The exact position of the curves is dependent largely on the uniformity of the particle size used in the experiments and the June 1952
Figure 8. Experimental Impaction Efficiencies of Aerosol Jets
All the important characteristics of Figure 8 were anticipated by the t,heoretical curves shown in Figure 2. Because these curves represent a n ideal situation with maximum efficiencies-Le., the velocity is uniform and the aerosol stream changes direction in the minimum volume of the flow field-experimental efficiencies lower than theoretical efficiencies were obtained for the upper sections of the curves, As the actual flow fields had larger negative gradients of the %-component of velocity a t the stagnation point, minimum values of fi for finite impaction efficiencies were lower for the experimental curves than for the theoretical curves. Consequently, the experimental curves cross over the theoretical curves, have a lower slope, and show higher d@for total impaction.
, I
APPLICATION OF EXPERIMENTAL RESULTS
To show the application of Figure 8 t o practical problems, the following examples are given.
PERFORMANCE OF A N IMPINGEMENT SEPARATOR. A gas-cleaning device consists of a series of erforated plates placed one after the other in such a way t h a t tge perforations are staggered. The gas is passed throu h each perforated plate, and the particles are impacted on the folfowing plate. The perforations are 0.125 inch in diameter, and there are 400 holes per square foot of plate surface. The gas is passed through the perforated plate at a rate of 50 cubic feet per minute, measured a t 70" F. and 1 atm., per square foot of plate. Estimate what size of particles of a specific gravity of unity is 90% removed by passing through one stage of such a system when it is operating at a temperature of 300' F. and 1 atm. Assuming d/\k(for q = 0.9) = 0.50 = (Cp,vo/18pD,)1/2D,. C = 1, D, for an q of 0.9 is 5.6 microns. Also from Figure 8, the article size 10%removed would be (0.28/0.50)5.6 = 3.1 microns. f n five stages, 4 1 7 of the 3.1-micron size would have been removed. Particles with sizes below (0.2/0.5)5.6 = 2.2 microns would pass through such a device. DETERMINATION OF SIZE DISTRIBUTION OF
AN
AEROSOL.
Ammonium chloride aerosol is passed through a slit jet of 0.020cm. width against a flat-bottomed cup at a velocity of 8000 em. per second. The aerosol material collected on the cup and in the filter is washed off, and the proportion of ammonium chloride in each is determined colorimetrically using Nessler's reagent as
INDUSTRIAL AND ENGINEERING CHEMISTRY
1377
-4ir Pollution the indicator; 46% of the aerosol was collected in the filter. Estimate the particle diameter at, a. cumulative mas? distribution of 46% if the density of the part,icles is assumed to be that of pure nonporous aerosol material. As the curve of Figure 8 is nearly a step curve, we can assume 7 = 0 for < 0.57 and 7 = 1.00 for 4 G > 0.57, xhere the effective diameter a t which the impactor has cut the size distribution sharply into tv.o distinct ranges of size is by 4.1. for II = o,5. Thus, the part,icle diameter at n.hich the classification occurs can be estimated from 4 s = 0.57 and is 0.42 micron as a first approximat,ion nit.h C = 1. Recalculation with C = 1.38 for a diameter of 0.42 micron gives an estimated D, of 0.36 micron for a cumulative mass distribution of 46%.
4s
INERTIAL IMPdCTIOY ON CYLINDRICAL AND SPHERICAL COLLECTORS EXPERIMENTAL EQUIPh'IENT
Figure 9 is a schemat'ic diagram of the experimental equipment used t o establish efficiency curves for impaction by inertia on cylindrical and spherical collectors. The aerosol generator the same as that previoush- described and shown in Figure 7. 111 this setup, hon-ever, the air s u p p l ~(90 pounds per square illch,
into an 8-mm. glass wash tube about 4 feet in length. To Caditate introduction and removal of wash water, a side arm was attached near the top of the glass tube, and a stopcock was COIInected to t,he lower end. A filter train similar to that described previously for experiments with flat plates was placed in the line d o w ~ t r e a mfrom the nozzle. A platinum sphere 900 microns in diameter, formed by melting the end of a 5-mil plat'inum wire, was employed as the spherical collector. Formed in this manner, the sphere was attached to the 6-mil m-ire and could be held in place by inserting the wire into the end of a hypodermic needle. llounted on the end of t.he needle, tile sphere could then be positioned at the centerof a 5is2-iilch T-enturi-shaped nozzle. 4 s in the case of the cylindrical collector, aerosol particles t'hat escaped impaction were collect~edin a filter train which followed t,he nozzle. The aerosol stream could he directed through the equipment by five different paths: (1) discarded through the aspirator, (2) discwded into the vacuum system filter, (3) sent, through the jet impactor in order to collect, enough acid to analyze for acid ooncentration, ( 4 ) Sent through I&,-] x o . G-2 so that the. parti(;lc size could be measured, and (5) during test runs, direct,ed by a vick-opening, tu-o-Jvay valve through the nozzle past the cylindrical or spherical collector into the filter train. The amount of aerosol impacted on t,he c:ollector determilie(i hj- 17-ashing the wire or sphere \vith a measured amount of conductance 1%-ater and determining the conrentration of the wash n-ater with a conductance cell, the measuring circuit being balanced with the aid of a caihoderay oscilloscope. EXPERIMENTAL PROCEDURE:
.kfter equilibrium had been reached by theaerosol generator and the desired particle size indicated h y the 0 ~ ~the 1 , aerosol stream was directed by the two\yay valve t,hrough the nozzle and the filter train. The needle valve regulating the vacuum t,o the system was adjusted to give a desired flow rate as meas b y the flowmeters. In the of the c>-lindrical collector, soon as the valve was opened the nozzle, t'he drum on n-hich the 1vil.e was wound \vas turned slo.i\-l>-, allon.ing the wirc to move down ward t hro u y h the throat secxtion and preventing toomuch aerosol from collecting on ail>.one section of the wire. JVhen the w i g h t attached to the wire had nearly rcachecl the h t , t o n i of the 8-mm. glas Figure 9. Experimental Equipment for Impaction on Body Collectors the t,n-o-\vayvalve wav re shutting off the test secti directing the aerosol stream to paw t,hrough the Owl, where the particle size was determined again. saturated \Tith water vapor) \vas llot dried, slid additional air The total time during which the wire was exposed to the aerosol added to the relatively dellse aerosol rising from t,he generat,or tream was measured by a stop watch. The total amount of aerowas reduced in pressure and metered from the same supply. 01 passing the nozzle vias obtained by weighing the filter train beConcentrated sulfuric acid was used as the aerosol material. fore and after the test run. After loxering the a e t length of \Tire into the washing tube, the acid impacted on the wire was n-ashed The range of particle size and particle number concentration was off with conductance water, and the quantity of acid was deternearly the Same as that obtained glJ,cerol. ~h~ acid conmined by a conductance measurement. After a run, the aerosol centration in the aerosol particles was nearly constant under the stream was directed to pass through the jet impaotor, and enoug~l ' sulfuric acid, prevailing conditions with a mean of 50.5 weight % acid was collected in the cup of the impactor to determine tho concentration of the sulfuric acid in the aerosol particles. in equilibrium nTith the moisture content of the expantied supply The experimental procedure for meawring the impaction efair, Although the moisture content of the air n-as ficiencies of spherical collectors was identical with that for cylintively lorn-, there was a great excess Of moisture in t,he air Supplied drical collectors, except that the spherical collector b17as taken out to the generator over t h a t needed to form the fog. As a result, the of the sphere holder and washed in a test tube, whereas tho cylindrical collector was x-ashed inside an 8-mm. glass tub. aerosol particles did not change in size \%-henadditional air of practically the same humidity was added, and the aerosol velocity DISCUSSION OF EXPERIMENTAL RESULTS through t,he test section could be varied without changing the particle size. Figures 10 and 11 show- in graphical form the results of the ezperimental measurements. The ranges of variables represented A 3-mil platinum wire was used as the cylindrical collector. The wire xas wound on a drum which could be rotated bj- a knob are: particle sizes, 0.36 to 1.30 microns; relative velocities of attached to it. Below the drum, a Venturi-shaped nozzle having stream, 1200 t o 9700 cnl, per sec,ondl dialneter ol ca,ylina throat diameter of 0.125 inch and fabricated of polystyrene was illstalled with its center line in a horizontal ~h~ \%-ire drical collector, 77 microns: and diameter of spherical collec~tor, 900 microns. passed vertically dornn-ard across the midsection of the throat 1378
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 6
A
i
r Pollution
APPLICATION OF EXPERIMENTAL RESULTS These curves for impaction by inertia show a characteristic Sshape, indicating a tendency to separate the particle size distribuTo show the application of Figures 10 and 11to practical probtion of an aerosol into two ranges; but this ability of classification lems, the following examples are given: is much smaller than that shown by aerosol jets impinging on PENETRATION OF FIBROUS FILTER.A padof spun glass 0.5 inch flat plates, As expected, a minimum particle size is indicated, bethick weighs 0.045 pound per square foot of surface and is comlow which impaction by inertia does not occur. A t high values posed of fibers 9 microns in diameter. For a face velocity of 120 of the inertial parameter the curves appear to be, and should be, feet per minute estimate the initial percentage penetration of 3-, asymptotic to a value of TI = 1. No values of q greater than 0.80 1-, and 0.3-micron particles of unit density. were obtained for the sphere because experimental conditions for the large inertial parameter necessary for such a high efficiency also caused re-entrainment of aerosol material already collected on the sphere. As the ratio of particle diameter to collector diameter was never greater than R = 0.017, impaction by interception 8 could be considered negligible. Impaction by an electrostatic mechanism was also improbable. Figures 10 and 11, 2 0.6A therefore, should represent impaction by the inertial mechA anisni alone. k A A These results confirm experimentally the general shape t, 0.4I and relative position of the inertial impaction curves for cyA lindrical and spherical collectors, originally shown by the A theoretical curves of Figures 3, 5 , and 6. The positions of 02the curves are dependent largely on the uniformity of parA P A ticle size used in the experiments and the accuracy of the particle size measurements. Because the experimental 0 variables were difficult to control, it is perhaps more accu0 0.5 I .o I .s 2.0 2.5 3.0 rate t o consider these curves as experimental confirmation fi (Cp#o/16pDcf/24 of theoretical calculations (1, 4, 6, 11), which are based on some form of ideel flow for the region in front of a cylindriFigure 11. Experimental Impaction Efficiencies of Spherical cal or spherical collector. Collectors
E est' 9
-A Here 0.045 pound of glass (specific gravity 2.2) per square foot of pad surface represents a 1.46 X 107 cm. length of 9-micron fiber. If this fiber is distributed in a simple, nonstatistical pad model, so that all the fibers are in one direction perpendicular to the direction of flow and the rows and layers of fibers are equally spaced, then the fibers, as well as the rows and layers, will be spaced 90 microns apart. Thus, in passing through 0.5 inch of such a pad, the aerosol stream would encounter 141 layers of fibers. Since about 10% of the open area in any cross section is blocked by fibers, vo can be estimated a t 120 X 2.54 X 12/0.90 X 60 = 67.7 em. per second. Assuming fi = 1.80 X lo-* poise, the following table represents the values of the important impaction parameters:
I.o
2 0.8
P f
0.B
b w
g
0.4
0.2
0
I.o
0
fl' Figure
10.
1.1
2.0
2.5
3.0
Efficiencies
of
ccpp,vo/leyy"eg
Experimental Impaction Cylindrical Collectors
All the important characteristics of Figures 10 and 11 were anticipated by the theoretical curves shown in Figures 5 and 6. The curve of Figure 10 for cylindrical collectors follows closely the theoretical curve of Langmuir and Blodgett (Figure 5 ) for low efficiencies but falls below the theoretical curve for values of efficiency in the middle range. Likewise, the curve of Figure 11 for spherical collectors follows closely the theoretical curve of Langmuir and Blodgett (Figure 6) for low efficiencies, but a t high efficiencies it falls above the theoretical curve. The relative spacing of the two experimental curves is more nearly that which would be expected on the basis of Figure 3, a result that speaks in favor of the experimental curve for spheres a t high efficiencies. for finite impaction efficiencies can The minimum values of 4% be taken as the theoretical values of 41/16 for cylinders and 4 1 / 7 4 for spheres, but this information is of significance only in establishing the shape of the efficiency curves for various values of the interception parameter, R, since R is appreciable in most applications of cylindric*aland spherical collectors. June 1952
DB Microns 3 1
R = Dp/Dc 0.333
0.3
0.0333
0.1111
Interception Efficiency, n o
V = CppDgvo/18fiDc
0.58
2.20 0,268 0.032
0.21 0 066
dG 1.48 0.52 0 18
The impaction efficiencies with which individual fibers operate when both inertia and interception are important can be estiin a curve on a plot of 77 us. & starting a t mated by sketching 7 = ?lo at d/Jr= 0, ending asymptotically a t a value of qmax = (1 R ) at dq = a,and paralleling the curve for R = 0 in the intermediate region. For the 0.3-micron particle, impaction will be due entirely t o interception. For the 1-micron particle, inertia will account for about one half of the impaction; and f o r t h e 3-micron partic.le, three quarters of the impaction. For dq > 0.25, q can be estimated by adding R to the v for R = 0 obtained from Figure 10.
+
Dp,
Microns 3 1 0.3
11,
Estimated Total
1.07 0.32
0.07
I n passing the first layer of fibers, the per cent of penetration is l O O ( 1 0 . 1 ~ ) . If complete mixing of the aerosol occurs before the stream passes the second layer, the per cent of penetration for . the present model, the second layer will be lOO(1 - 0 . 1 ~ 1 ) ~For the aerosol stream is assumed to impact upon and mix beyond 141 layers, The per cent of penetration for the 0.5-inch pad is given, therefore, by l O O ( 1 - 0.1~)'". For the various sizes of aerosol particles:
-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1379
A
i
r Pollution0'3
Dp, Microns
3
Penetration 1.2
1
x
10-
1.0 37
0.3
The sensitiveness of these calculations to the assumptions indicates that the estimated penetrations may be gravely in error compared to actual penetration measurements under such conditions; but the calculations dramatically point out the effect of the various variables, particularly particle size, fiber diameter, and packing density.
information concerning the theoretical development and compilations of the experimental data are available as Technical Reports which can be obtained from the Technical Information Service, United States Atomic Energy Commission, Oak Ridge, Tenn. NOMEA-CLATURE
C
+
i*2
1
(2L/Dp)[1.23 ( 2 L / D m )< 134
+ 0.41exp(-0.44Dp/L)J
for 0.1
nuclei. The lower cold plate is most easily maintained by t h e use of dry ice in contact with a brass plate 0.375 inch thick, t o which is soldered a copper block 4 inches in diameter which serves as a cold sink. The top of the cold sink c linder is positioned 4 inches below the top of a well insulated ;ox. The cold plate of the cloud chamber rests on top of t h e cold sink and is constructed as shown in Figure 1, so that reactions in t h e lower region of the chamber are easily seen in a beam of parallel light. Resting on top of this is a glass cylinder or square box of late glass sealed with a silicone rubber gasket or with ice. %his forms the test chamber. Resting on top of this is a flat plate of brass sealed with a rubber gasket and warmed with a soldering iron heater. I n contact with the undersurface of the warm plate, a small pad of felt soaked with distilled water serves as a source of June 1952
OPEN BASE CHAMBER
A very convenient type of chamber utilizes the upper 6 inches of a cold box as the cold zone of the cloud chamber. The assembly is illustrated in Figure 2. A plate glass box cemented with glyptal rests on a silicone rubber gasket which, in turn, is positioned on a brass plate. A brass box 6 inches high is soldered on this brass plate. I t s outside dimensions are slightly smaller than the inside dimensions of the glass chamber. This produces a temperature zone slightly colder than t h e surroundin air and also serves as a trap for any drops of water which may j i d e down the glass walls The t o p plate is warmed with a soldering iron heater, with water vapor supplied from a small pad saturated with water and placed on t h e undersurface of t h e warm plate. fieveral holes in the top plate, fitted with rubber stoppers, permit ready access t o t h e interior of the chamber with various types of sample tubes and nuclei generators. Flat glass surfaces are far better than a glass cylinder for viewing reactions t h a t occur in the chamber. The open base chamber, although convenient in many respects, must be used with caution, because contaminated air may easily be chimneyed into the upper warm zone. The greatest source of trouble in this respect is water drops formed from the accumula-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1381
