ENGINEERING, DESIGN, AND EQUIPMENT
Collection of Aerosol Particles in Presence of Electrostatic Fields HERBERT F. KRAEMERl AND H. F. JOHNSTONE University of Illinois, Urbana, 111.
A
LTHOCGH numerous investigations have been made on the Cottrell precipitator and, to a lesser extent, on the resin-wool charged filter, comparatively little information has been published on the fundamental principles b y which electrostatic forces promote the deposition of aerosols on collecting surfaces. The deposition of charged aerosols on the inside walls of tubes ( S I ) and on plane surfaces (4,7 , 15, 2 2 ) has been studied. It has been shown empirically that aerosols of electrically charged particles are removed more completely than uncharged aerosols b y filter paper (8). The collection of fog droplets by charged sand particles or water droplets spread from an airplane has been suggested ( 2 4 ) . This idea has been investigated b y Cochet (S) who also considered the capture of uncharged freely falling fog particles by electrified high tension lines (18). Ranz and Wong have presented dimensionless groups of force ratios which characterize some of the electrostic forces influencing the deposition of aerosol particles (21). This article presents a general theoretical solution and experimental verification for the deposition of aerosol particles from a moving stream on spherical surfaces and an introductory study of the deposition on cylinder?. The various types of electrostatic forces, including coulombic forces, space charge effects, and forces of induced charges, that act on aerosol particles are discussed. The differential equations that describe the path of the particles toward a spherical collector were solved numerically b y the ILLIAC electronic digital computer. Experimental measurements of aerosol deposition were found to agree fairly well with the theory. As a result of the investigation, two new types of dust collection equipment are proposed. Theory of motion of aerosol particles around a collector
The motion of aerosol particles under the influence of electrostatic forces was investigated first from a theoretical viewpoint. The determination of the efficiency with which particles are deposited from a moving aerosol on the surface of collectors is of particular interest. The collection or target efficiency, 17, is defined as the ratio of the cross-sectional area of the unobstructed stream from which all the particles are collected to the projected area of the collector normal t o the direction of flow. If the particles are not affected by stochastic diffusional or turbulent processes, the cross-sectional area of the stream from which deposition occurs can be determined uniquely and exactly from the trajectories of the particles. A summation of the forces acting on the particle can be integrated to obtain the trajectories and the collection efficiency of the collector. The forces of gravity and of inertia were negligible under the conditions of the experiments and in the theoretical treatment were assumed to be absent. The electrostatic forces were equated to the force of fluid resistance. The resulting differential equations of force, although of first order, were nonlinear and were solved numerically with the ILLIAC. I n a few limiting cases, 1
Present address, The Ethyl Corp., Baton Rouge, La.
2426
approximations were made in the differential equations and analytical solutions were obtained. Equation of Motion. Consider a fldid flowing uniformly in a positive 2-direction around a spherical or cylindrical collector placed in the stream as shown in Figure 1. The velocity of the stream relative to the collector is vz = 210, uY = D, = 0, a t x = m and ij at any other point. An aerosol particle in the stream traveling with velocity ti is assumed to be influenced by an electrostatic force i@ and by the fluid resistance - - 3 ~ p L D ~ ( i i O)/C in accordance with Stokes' law; other conceivable forces such as inertial, gravitational, magnetic, or thermal forces are neglected. A force balance on the aerosol particle is
-
-
or in polar coordinates
de r - = vs dt
+-3 CFs WDP
The differential equations describe the motion of an aerosol particle starting at z = m , y = yo, and traveling toward the collector. The trajectories generated b y Equation 2 cannot cross each other, because trajectories from first-order, first-degree differential equations have slopes that are single-valued everywhere. Thus, it is possible to select from a family of trajectories a limiting trajectory with initial boundary value, y o * at z = - m , which divides the trajectories into two categories ; particles having trajectories closer to the x-axis than the limiting trajectory deposit on the collector, while particles u i t h trajectories outside of the limiting trajectory pass the collector. For a collector of diameter D,, the efficiency of collection is defined as
-
7 = (2y0
for a spherical collector
7 = (2y0*/D,) for
a cylindrical collector
(3)
The force balance does not provide an adequate description of aerosol motion and aerosol deposition when a random motion caused b y turbulence or diffusion affects the particles. If the amplitude of the random motion is small compared with the dimensions of the collector and if the collection efficiency is greater than one, the equations calculated from a force balance are reasonably valid. I n the more general case of high turbulence or diffusion, a solution of the collection problem would require the use of the generalized continuity equation as well as a force balance. If the diffusional and turbulent effects are negligible, the simultaneous differential equations (Equation 2 ) can be integrated and the distance yo* of the limiting trajectory determined from the appropriate integrated solution. I n order to perform the integration, expressions for the fluid velocity, ii, and the electrostatic force, F, must be found.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 12
ENGINEERING, DESIGN, AND EQUIPMENT Fluid Streamlines Around Obstacles. The fluid streamlines a n d the velocity fi at points near an obstacle have been solved analytically for several conditions of flow (68). When the obstacle is rigid or extremely viscous and no circulation occurs, potential and viscous flow near a sphere and potential flow across a cylinder transverse t o the direction of flow may be assumed, as given b y the following equations. The dimensionless distance is F = 2r/D,. The angle e is measured from the positive z-axis. dr/dt = vo
rdeldt
=
(%) 1 a -
2F3 -vo (--2T)
A VALUABLE STUDY WHICH
. . . may
be used in predicting performance of new types of dust removal equipment
. . . proposes
two new types of equipment for pilot plant study
cos 6
+1
sin
potential flow around spheres
e
(4)
0
is located on the center line of a duct of radius R I , the velocity field for viscous flow around the sphere and through the duct is approximately parabolic and, in spherical coordinates, is
-2
+1
'
around cylinders
(6)
Equation 5 for viscous flow provides a reasonably accurate estimate of the fluid velocities when the Reynolds number based on obstacle diameter is less than 8 ( 2 ) . For values of the Reynolds number above 8, the boundary layer separates from the surface of the obstacle, and a wake appears behind the collector. For high Reynolds numbers, Equations 4 and 6 should be valid on the upstream side of the obstacle, but they do not give correct velocities in the wake on the downstream side. At a distance from the obstacle, the velocity, 0, in terms of radial and angular components is approximately
where
00
cos
e
0z = -3 =
g
)
= -vo sin 9
ii= a, or in rectangular coordinates 21,
for the region
-l 0 > 2.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 12
ENGINEERING, DESIGN, AND EQUIPMENT
Summary of Approximate Collection Efficiency Equations
Table I. Collector Shape Sphere
Electrostatic Force Coulombic
Sphere in duct
Coulombic
Sphere
Image
Flow Equation,
No. 7
Collector Charged Yes
Aerosol Charged Y es
2nd term, Equation 26
8
Yes
Yes
1st term, Equation 27 (1)
7
Yes
No
Electrostatic Equation 2nd term, Equation 26
7
Yes
Yes
(1)
7
Yes
NO
Coulombic
2nd term, Eqbation 26
9
Yes
Y es
Plane
Image
1st term, Equation 26
9
Yes
NO
Dipole cylinders
Coulombic
(87)
7
Yes
Yes
Cylinder
Coulombic
Cylinder
Image
Plane
a
+
Table II. Comparison of Collection Efficiencies Calculated by Computer with Efficiency Obtained by Addition of Partial Efficiencies for Each Collection Parameter for 63 = 0
0.1
0.1 0.6 0.03
Partial
7
KI 0.1 0.1 0.1 0.6 5.0
0.400
0,400 2.40 0,120
Partial
Effi-
Effi-
0.120
ciency,
ciency,
v
0.305 0.305 0.305 1.11 3.44
KM
Sum of Partial Efficiecies,
By
Computer,
7
7
?i
0
0
0.407
0 0,001
0 0.200
0.425 0.705 0 905 3.51 3.56
0 0
0 0
~
~
- i12[
1
~ K + -1 RI
E0.ra
.
(F K I ) " ~ -~ K E
1
+ KI KC 8
+
KE 0.03
i i z
la T h e expression f o r the collection efficiency is valid for values cf the collection parameter, K E , less than i2.
About 200 steps or intervals were used in calculating a trajectory. Successive trajectories were calculated until one was found that just touched a sphere with relative diameter (1 a), A binary chopping method was used in selecting the initial boundary conditions of the successive trajectories. Convergence was asvunied when two limiting trajectories, one touching the sphere (1 a)and the other passing, had respective collection efficiencies diff'ering by less than 0.003%. Vsing this trial-and-error method, the computer found a limiting trajectory and calculated a collection efficiency in about 8 minutes. Truncation and round-
Partial Efficiency,
Collection Efficiency - 4KE
0.652 0.716 3.03 3.52
tions that produced a relatively uniform charge by the device shown in Figure 7 ( 1 2 ) . The corona was produced at about 4000 volts direct current. The corona current was measured by a Cenco electronic electrometer. Most of the data were taken with the central wire a t positive polarity. The aerosol was diverted to the collection cell for a timed period and permitted to deposit on the collecting sphere or t o flow out to the exhaust hood. Three inch sizes of metal collecting spheres were used--'/.,, 3/8, and in diameter. The sphere was mounted on the apex of a ceramic semicondurting cone which served as an electrostatic shield around the wire connection to the sphere, thereby preserving the electrostatic field of an isolated sphere in space. Surrounding the sphere and the collection cell a t a distance of about 8 inches was a grounded copper mire screen. At the end of a timed period of flow of aerosol past the collecting sphere, the cell was SM ept clear of aerosol by a metered flow of air. Then the sphere was removed from the cell and washed with ethyl alcohol. The alcohol solution was analyzed for dioctyl phthalate by ultraviolet absorption, a t 225 millimicrons 1% ave length. The mam concentration of aerosol was measured by sampling with a small glass and platinum electrostatic precipitator and determining the amount of the deposit by ultraviolet absorption
off errors in the Runge-Kutta process are estimated to be less than 0.0006~0of the collection efficiency. A total of 177 collection efficiencies for various values of the collection parameters were calculated with the computer (IS). The collection efficiencies when only one electrostatic collection parameter is significant are plotted in Figures 3, 4, and 5 . A few collection efficiencies involving more than one collection parameter are shown in Table 11. Effect of electrostatic charges on deposition efficiency verified experimentally
T h e flow diagram of the apparatus used to study the effect of electrostatic charges on deposition efficiency is shown in Figure 6. A LaMer-Sinclair generator was used t o produce the dioctyl phthalate aerosol (26). Particle size measurements were made with the optical owl (86) and with a cascade impactor (20). The aerosol was charged electrically in a corona operated under condi-
December 1955
Figure 6.
-
L -TIC BRE. Ct PITATO R
Experimental equipment
INDUSTRIAL AND ENGINEERING CHEMISTRY
2431.
ENGINEERING, DESIGN, AND EQUIPMENT The electrostatic charge on the aerosol was measured in a “chargespectrometer” (II). A sample of the aerosol, surrounded by a simultaneously moving air stream, was conducted between two charged plates. The deffection of the aerosol stream was observed by a cathetometer, and was used in calculating the average particle charge and approximate variation in charge. Similar methods of measuring aerosol charge have been reported since the completion of this work ( 7 , 11).
efficiency was proportional t o the charge on the particles and only half of the naturally charged particles had a polarity opposite that of the collector, an average charge of 0.15 electron was used in calculating the parameters KE and KO. Appropriate averages of the charges and diameters were used in calculating the parameters. Three groups of experimental data are shown in Figure 9. I n two of the groups, the collection parameters are combined, because the computer solution showed that the same equation was valid for each of the mechanisms described by the combined parameters. When the aerosol was charged by a corona and the collector was electrified, the collection mechanisms represented by the parameters KE and KG were predominant compared with other mechanisms, and the data were plotted using ( K O- K E ) . Naturally charged particles near a charged collector are influenced by both the parameters K I and K E ; the data for this condition were plotted using ( K I - KE). When the aerosol was charged by a corona but the collector was grounded, the only collection parameter of importance is KO and this was used in plotting the data. I n all cases in which experimental data could be obtained, the applicable theoretical curve was a straight line that was solved for - K E , KQ and the lower values of Kr. Experimental measurements of the collection caused by the mechanisms corresponding to K M , Ks, and (R could not be obtained. With all possible operating conditions of the equipment, one of the collection parameters ( - KE, KQ,or K I ) was much larger than the other parameters.
-
-
BRASS C Y L I N D E R 0.435 IN. l.D.
Figure 7.
Corona device for charging aerosols
Validity of Aerosol Charge Measurements. The average charge obtained by the charge-spectrometer agreed with measurements on single particles in a Millikan cell and with an approximate theory of charging in a corona. The theoretical charge was assumed to be the sum of the charge produced by ion interception as described by Pauthenier (19)and the charge produced by ion diffusion, as described by Arendt and Kallman and modified by White (50). The theoretical charge is
Q~ = T 1 0 7 e 0 ~ , 2 ~(1,
+2c + 2)1 ( l * % Z ) E
+
where the radial field E,.in the corona is equal to
Solutions of equations for aerosol collection compare favorably with computer solutions
The approximate solutions of the theoretical equations for aerosol collection shown in Figure 2 compare favorably with the computer solutions shown in Figures 3 and 4 for large values of the collection parameters. For low collection efficiencies and small values of the parameters, the separation of the flow lines by the collector greatly reduces the collection below that predicted by the approximate equations, exckpt for the parameter KE. In the latter case the approximate and the computer
cn Z
-
i d
2
m
Figure 8 shows the theoretical charge and the charge measured with the charge-spectrometer to be in agreement. Calculation of Collection Efficiency. Since low flow rates were used in the experiments, a parabolic velocity profile prevailed in the collection cell. The appropriate equation for calculation of the collection efficiency is not 4R1*W,/DC2TV but
100-
J
a 9 c
50
-
I
0
,a
w U
The effect of the nonuniform velocity profile in increasing deposition near the center line and decreasing deposition near the duct wall must be considered. Experimental Results. Measurements were made on the deposition of aerosol particles for both charged and uncharged collecting spheres over a wide range of the experinlental variables as follows: collector voltage, 0 to 6400 volts direct current; aerosol diameter, 0.54 to 1.18 microns; average aerosol charge, 0.15 t o 137 electrons per particle; aerosol concentration, 3.3 to 197 micrograms per liter; and aerosol velocities, 1.56 to 6.89 cm. per second. Approximately 30% of the aerosol particles produced by the LaMer-Sinclair generator had unit charges. Since the collection 2432
sI
I
I-
20P 20
I
/ 1
1
I
50
I
I
100
J 200
MEASURED CHARGE, ELECTRONS Figure 8. Comparison of charge-specfrometer measurements and theoretical charge
solutions are identical. It is reasonable to suppose that the approximate solution for K Efor the cylindrical geometry should also agree with a solution by the computer. A t low collection efficiencies the curves for the parameters KE and K I converge into one Iine. Except for the parameter KE, the flow lines for viscous flow appear to give lower collection efficiencies than those for potential
I N D U S T R I A L AND- E N G I N E E R I N G C H E M I S T R Y
Vol. 47, No. 12
ENGINEERING, DESIGN, AND EQUIPMENT flow. The interception parameter, a, increases the collection. The interception effect calculated by the computer LEGEND agrees asymptotically for zero values of 0 - C O L L E C T O R CHARGED, the electrostatic parameters with the AEROSOL CHARGED BY CORONA, PARAMETER,(KG- KE) approximate equation given by Ranz A-COLLECTOR CHARGED, and Wong for interception ( $ 1 ) . AEROSOL W I T H NATURPLLY OCCURRING CHARGE, When several collection mechanisms PARAMETER,(K[ -KE) act simultaneously, the total collection -COLLECTOR GROUNDED, can be found by addition of the partial AEROSOL CHARGED BY CORONA, PARAMETER,(K~) collection efficiencies calculated €or each of the collection parameters individuallv. 0 Since the validity of this procedure is questionable, it was studied by use of the exact solutions with the computer, as shown in Table 11. The electrostatic collection efficiencies calculated by the addition method may be as much as 30% high if the several collection mechanisms are about equal in effect. If one collection mechanism is predoininant the error is less. A Cochet has presented an equation for the collection of uncharged fog particles A by a falling charged water droplet (9). A A The equation is identical with the approximate value in Table I if the velocity, 00, in parameter K I is taken / 4 as the free falling velocity of the droplet calculated from Stokes' law. The experimental data confirm the theory for collection by the combined mechanisms represented by the paramFigure 9. Collection of dioctyl phthalate aerosol particles on spherical collector eters ( K a - K E ) , ( K I - K E ) , and KG. Experimental studies could not be made of each mechanism independently because (a)a completely unchamber. The spray nozzles are insulated from the chamber and charged aerosol could not be obtained, ( b ) the collector diameters are charged to 5000 volts negative with respect to the grounded were so large that the image force K M and the interception effect metal chamber. The spray nozzles are connected t o the water GI became negligible, and ( c ) the collector could not be supported supply by rubber hoses to insulate the nozzles from the water by a perfect insulator, hence the parameter KQovershadowed the supply. The charge on the spray can be estimated from the parameter Ks. voltage and the capacity of an isolated sphere in space (f0). In Figure 9 the data for low values of the collection parameters For 50-micron water droplets settling at 0.25 foot per second, the are above the theoretical curve. This discrepancy may have been electrostatic parameter K E is 830, and the collection efficiency of caused by analytical errors in measuring the low collection effieach spray droplet is 3320 times its projected cross-sectional area. ciencies or b y errors in measuring the naturally occurring charge Even with low water rates, the over-all collection of the spray on the aerosol. chamber should be complete. &4Pease-Anthony cyclone scrubber with the central spray manifold insulated and electrified would provide de-entrainment of the water droplets and collecTwo new types of dust tion of the fine aerosol. The calculation of the over-all collection ,collection equipment proposed efficiency of a scrubber from the individual droplet efficiencies is Many types of dust collection equipment are in existence. discussed by Ranz and Wong (21). The electrified scrubber Some of these would have improved efficiencies if electrostatic could treat gases with high dust loadings without using the high forces were utilized in promoting particle collection. Two exvoltages needed with the Cottrell precipitator. Problems of amples of interest are an electrified wet scrubber and an electridust re-entrainment and of dust resistivity frequently encounfied filter mat. For maximum collection, the aerosol particles tered with the Cottrell precipitator would be absent. The and the collecting surfaces should both be highly charged. The electrified scrubber would require a lower water rate and lower equations show that collection by the electrostatic mechanism is pressure drop through the equipment than a regular scrubber enhanced with increased times of retention in the dust collection operating a t the same collection efficiency and would have a equipment and with low relative velocities between the aerosol higher efficiency for the removal of submicron particles than the and the collecting surfaces. The optimum design of equipment nonelectrified scrubber. utilizing electrostatic forces, therefore, requires lower velocities Filter mats electrified by carding resin wool or synthetic fibers than comparable equipment in which the inertial collection is have been studied (23,ZQ). The high efficiency of these filters is predominant. destroyed by high humidity, x-rays, and atomic radiation. A The removal of 0.05-micron aerosol particles by an electrified filter mat can be electrified permanently if a low energy source of wet scrubber will be considered as an example of the use of electropotential is used. It is easily shown that the simple attachment static forces. The aerosol can be charged positive with about of one terminal of a battery t o a mat of conducting wire fibers will four electron units per particle by passage through a corona prohave only a small effect on the collection efficiency. This suggests duced on the standard parallel-wire charger used with two-stage that a mat be made from two fine twisted wires insulated from precipitators. The charged aerosol is sent to an electrified spray each other and tangled randomly into a mat. A battery is at-
1
I
/
'. -
December 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
2433
ENGINEERING, DESIGN, AND EQUIPMENT tached across the two wires, which form a continuous cylindrical dipole throughout the mat. As an example, consider the collection of 0.05-micron aerosol particles charged with four electron unit charges per particle. Aerosol velocity through the filter is taken as 100 cm. per second, and the wires are No. 36 enamelcoated copper wire (0.0126 em. diameter). If a potential of 100 volts is used, the dipole moment of the two wires separated a distance 0.0204 cm. (9) is approximately (2.04 r e o ) and the parameter KCis 5.17. The collection on each section of the wire dipole is 5.17 times the projected area of the wire section. The inertial parameter $ under similar conditions is 6 X 10-6. The collection of the mat is increased several orders of magnitude by the electrification of the filter mat and the aerosol. Acknowledgment
This work was supported by a fellowship sponsored by the Ethyl Corp. and b y funds provided by the U. S. Atomic Energy Commission under Contracts AT( 30-3)-28 and AT( 11-1)-276. Appreciation is expressed t o A. 0. Hanson of the Physics Department, University of Illinois, for his suggestions and comments on the theoretical section.
= constant
c = Cunningham factor, (1 + 1.6
D = diameter, cm. D, = diameter of collector, cm.
X
$
= -CDpapffo, inertial deposition parameter
18@0
-
Superscripts = dimensionless distance or velocity ratios * = trajectory just touching the coliector
+1)8cD,2v12, +
-
m
Literature cited
AID,)
D , = diameter of particle, cm. E, = radial electrostatic field in corona charger, volts/cm. F = force on particle, dyne K = mobility of air ions, approximately 1.75 sq. cm./(sec.) (volt) -2Q2mc , parameter for coulombic force of cylindrical KO = 3~~pD~D~~~oeo dioole 2c02v1parameter for coulombic force for a spherical 3rpDpDe210’ collector a t constant voltage; also equal to CQaQ.o/ ~ T L L D for, a~collector ~ ~ ~ a t constant charge -, parameter for induced electrification for KG = cQ2iAvpiia 37rpD,~oeoD, a spherical collector at constant voltage parameter for image force for a spherK I = (‘ le 2\3uvnDP , . ” ” ‘ical collector at constant voltage; also equal to 2 ) 3 p D , ~for~ ~a ~collector a t ( e - l)2CD,zQac2/(e constant charge CQ2‘ 2, parameter for image force, aerosol only KM = 37rzpDp~o~oDc charged R s = CQzZDcNp,parameter for space charge effect, spherical 1~ T E O U D ~ V O coliecior L = length of electrode in corona charger, em. N o = concentration of collecting spheres, number/cc. N , = concentration of aerosol particles, particles/cc. charge on collector, coulombs &I Qz = charge on aerosol Darticle. coulombs Qac = charge on collect& per unit area, coulombs/sq. em.; for an isolated sphere, Qac = 2eoV1/D0 Q. = charge on cylinder per unit length, coulombs/cm. R = generalized coordinate, or radius of corona charger, or radius of a spherical aerosol cloud, cm. R1 = radius of collection cell, cm. 63 = D,/Dc, interception parameter, dimensionless T = temperature, ’ K. VI = voltage of collecting sphere, volts W , = rate of aerosol deposition on collector, micrograms per min. W = rate of aerosol flow past collector, micrograms per min. E = average molecular velocity of air ions, approx. 5 X l o 4 em. /sec. e = charge of one electron, 1.6 x 10-18 coulombs i = current in corona charger per unit length of electrode, ampere per em. IC = Boltzmann’s constant, 1.37 X ergs/’ K. m = dipole moment of a collector
2434
;I,
Subscript 0 = conditions at x =
Nomenclature
A
pij = coefficient of potential P = dimensionless distance, 2 r / D , rii = radial distance between sphere i and sphere j t = time fi = velocity of aerosol particle, cm./sec. B = velocity of air stream, cm./sec. vo = relative velocity between air stream and collector v = average velocity through corona charger x = distance in direction of flow, em. 1~ = distance normal to direction of flow, cm. f j o = 2y/D,, boundary value a t x = - 0) €0 = permittivity of free space, 8.85 X coulomb2P dyne-cm.2 = dielectric constant of aerosol particle = effective dielectric constant of entire aerosol 11 = collection efficiency 0 = angular position from positive z-axis X = mean free path of gas molecules p = viscosity of fluid surrounding aerosol particles p = particle density
Bottcher, C. J., “Theory of Electric Polarisation,” pp. 102, 126, Elsevier, New York, 1952. Bull. Natl. Research Council, No. 84, p. 10 (1932). Cochet, R., Ann. geophys., 8 , 33 (1952). Daniel, J., and Brackett, F., J . A p p l . Phys., 22, 542 (1951). Debye, P., “Polar Molecules,” Dover Pub., New York, 1945. Gill, S., Proc. Cambridge Phil. Sac., 47, 96 (1951). Gillespie, T., and Langstroth, G., Can. J . Chem., 30, 1056 (1952). Goyer, G. G., Gruen, R., and LaMer, V. K., J . Phgs. Chew‘., 58, 137 (1954). Harnwell, G. P., “Principles of Electricity and Electromagnetism,’’ p. 40,McGraw-Hill, New York, 1938. Helwig, A. W., M.S. thesis, University of Illinois, 1952. Hinkle, B. L., Orr, C., and DallaValle, J. M., J . Colloid Sci., 9, 70 (1954). Kraemer, H. F., M.S. thesis, University of Illinois, 1952. Kraemer, H. F., Ph.D. thesis, University of Illinois, 1954 (microfilm obtainable from University Microfilms, Inc., Ann Arbor, Mich.). Langmuir, I., and Blodgett, K. B., General Electric Research Laboratory, Schenectady, N. Y., Rept. RL225, 194445. Lipscomb, W. N., Rubin, T. R . , and Sturdivant, J. H., J . A p p l . Phys., 18, 72 (1947). Livens, G. H., “Theory of Electricity,” pp. 57, 134, Universit.y Press, Cambridge, 1918. Maxwell, J. C., “A Treatise on Electricity and Magnetism,” vnl. I, p. 231, Clarendon Press, Oxford, 1904. Pauthenier, NI., and Cochet, R., Compt. rend., 231, 213 (1950). Pauthenier, M., and Moreau-Hanot, M., J. Phys. R a d i u m , 3, 590 (1932). Rsnz, TV. E , , and Wong, J. B., Arch. I n d . Hyg. and Occupational M e d . , 5, 464 (1952). Ranz, W. E , , and Wong, J. B., IND.ENG.CHEM.,44, 1371 (1952). Rohmann, H., 2. P h y s i k , 17, 253 (1923). Rossano, A. T., and Silverman, L., Heating bnd Ventilating, 51, No. 5 , 102 (1954). Sci. American, 128, 244 (1923). Sinclair, D , in “Handbook on AeroBols,” p. 97, U. S. Atomic Energy Commission, Washington, D. C., 1950. Sinclair, D., and LaRiler, V. K., Chem. Revs., 44, 245 (1949). Smythe, W. R., “Static and Dynamic Electricity,” pp. 5 , 27, 37, 114, 116, McGraw-Hill, New York, 1939. Streeter, V. L., “Fluid Dynamics,” pp, 41, 67, 141,236, McGrawHill. New York. 194s. Walton, W. H., Chemical Defense Experimental %ation, Porton, England, Rept. 2465, 1942. White, H. J., Trans. Am. I n s t . Elec. Engrs., 70, 1186 (1951). Wilson, I. B., J . Colloid Sci., 2, 271 (1947). ACCEPTED August 25, 1955. RECEIVEDfor review December 22. 1954. Division of Industrial and Engineering Chemistry, 127th Meeting, ACS, Cincinnati, Ohio, April 1955.
I N D U S T R I A L A N D E N G I N E E R I N G C H’E M I S T R Y
Vol. 47, No. 12
