A Miniature Electrostatic Precipitator for Sa mpIing Ae rosoIs Theory and Operation MYRON ROBINSON1 U. S. Army Chemical Corps, Fort Detrick, Frederick, Md. b Equations are derived describing the performance of a miniature electrostatic precipitator used for sampling aerosols, the particles of which may be considered charged exclusively by ion bombardment. Paying particular attention to the time required for the changing process, criteria are developed for judging the effectiveness with which a wet precipitator will concentrate the nongaseous constitute of an aerosol. The theory is tested experimentally.
comes important only for particles smaller than a few tenths of a micron in diameter. For present purposes attention will be confined solely to those particles of larger size for which the process of ion bombardment is by far predominant. The charge Q gained by a spherical particle undergoing charging by ion bombardment has been found by Pauthenier and Moreau-Hanot (6) t o be
A
where Q,,,
OF TECHNQUES is available for measuring the concentration of particulate matter in a gas. These techniques generally require the use of a sampling instrument which removes the particles from a known volume of gas and concentrates them in a manner which makes possible their subsequent quantitative and qualitative determination. -4pparatus employing the principles of filtration, gravitational and centrifugal settling, impingement, and thermal and electrostatic precipitation have been successfully utilized for this purpose. Electrostatic precipitation, however, is often acknowledged to be the outstanding over-all method of extracting fine suspended particles from gases. VARIETP
PARTICLE CHARGING AND MIGRATION
The physical process of electrostatic precipitation has been described by a number of recent writers and will not be considered here. It suffices to mention that under the usual conditions of electrostatic precipitation two different particle charging mechanisms have been shown to be active ( 2 , 6, 6, 10): bombardment of the particles by ions moving under the influence of the applied electric field, and attachment of ionic charges to the particles by ion diffusion in accordance with the laws of kinetic theory. This latter effect is independent of the external field and ordinarily bePresent address, Research-Cottrell, Inc., Bound Brook, N. J. 1
is given by (M.K.S. units)
Q,,
=
3K 4ae,a2Eo K+2 ~
and T,the period in which half of is acquired, by T = 4e,/.Vpk
tm to
(3)
(4)
further charging will occur in accordance with Equation 1 to give to
to
+t
+t +T
(5)
The particles, once having accepted some charge, are driven by the force field to the collecting electrode a t a migration velocity w given by the expression F - m ( d w / d t ) - 6avaw = 0
(6)
The quantity 6 ~ q a wis the viscous drag of a spherical particle as given by Stokes's law in which q is the viscosity of the gas. Although it is assumed that the particles are of uniform size, departures from this condition in practice by a factor of two or more may not invalidate the theory (4). Setting (7)
and L
=
Ut
d',
+
6 ~ a w
vm-
The standard solution to this firstorder linear equation takes the form
whence
Qmax
charge &me.,
dw
(2)
If a particle initially possesses a Qo
Equation 6 becomes
(8)
S*
L
eerTaL/vm
ut,
+ UT + L dL -
(11)
The first term on the right-hand side of Equation 11 gives the migration velocity w for a spherical particle impelled through a viscous medium by a constant force, The negative second term is the correction required t o account for the varying force that is actually applied in the problem a t hand. Equation 9 shows that as L increases, the migration velocity rises asymptotically to a maximum. This transient behavior is attributable to two distinct effects: the inertial reaction of the particle, and the increasing coulomb force acting on a growing accumulation of charge on the particle. The mathematical complexities arising in the use of the exact solution to Equation 9 may be avoided by assuming that the inertial time lag that a particle experiences in attaining what is effectively its limiting migration velocity is small compared to the time lag imposed by the particle-charging mechanism. From physical considerations, it appears that if the viseo-inertial time constant m / 6 m ~ ais sufficiently small relative to the charging time constant T, the effects of inertial retardation may be neglected. Thus, setting the inVOL. 33, NO. 1, JANUARY 1961
* 109
ertial reaction m(dw/dt) = um(dw/dL) equal to zero, we have from Equation 9 w = wo
vto ut.
+L
+ UT + L
w. = EpQmax/6rr?a
(13)
Kote that for the 3.25micron diameter, air-suspended, solid polystyrene particles later employed experimentally, the visco-inertial time constant equals about 2.5 X 10-5 second. This is two or three orders of magnitude less than the values of T that are normally encountered in electrostatic precipitation. The preceding relations may be simplified further by assuming that the charging time and inertial lag are both insignificant, regardless of relative magnitude. An approximation subject to such conditions introduces error only for a negligible distance beyond L = 0.
The purpose of industrial precipitator construction is to achieve maximum efficiency of gas cleaning within the design limitations imposed by technical and economic considerations; the aim of a sampler, on the other hand, is to provide in concentrated form a maximum quantity of the suspended liquid or solid constituent of the aerosol. It will be shown that these two desiderata do not necessarily coincide. Precipitation studies dealing with industrial precipitators commonly consider that all the limiting charge of a particle is acquired within a negligibly small time relative to the total time spent in the cylinder, for it may be assumed without sizable error that particles enter the active region of the precipitator already fully charged. This is the approach that has been taken by Deutsch (S),White ( I l ) , Rose and Wood (Y), and others who have treated the problem. A portable sampler, however, of about one tenth the cylinder length of commercial installations, but maintaining roughly similar air flow velocities, can be expected to invalidate the above assumptions because charging will not have progressed appreciably before the particles will have traversed a relatively large length of cylinder. For this reason it is imperative that in the present application charging time be duly considered. Aerosol Concentration. Consider t h a t an element of volume of a cylindrical precipitator is a right cylindrical disk, the plane faces of which lie at the distances L and L dL from the input end of the precipitator. I n a time interval dt a quantity of aerosol dQl enters the disk a t L, dQ2 leaves a t L d L , and dQs
+
ANALYTICAL CHEMISTRY
- dQ3 = 0
(14)
Assuming that because of the effects of turbulence and, somewhat questionably, the electric wind, the volume concentration C, of particulate matter in the gas is uniform throughout a given cross-sectional area of the cylinder, we may write dQ1 = A v C ~ ( Ldt) dQ2 = AvC,(L d L ) dt
+
(15) (16)
Further, consider the precipitation from the elemental disk in time dt to occur only, but completely, from that volume of the disk lying within a radial distance dr of the collecting wall where dr = wdt
(17)
The infinitesimal annular volume cleared of particles in time dt is d V = 2mdrdL
THEORY OF SAMPLER OPERATION
+
- dQz
dQi
where w ois given by
110
is precipitated on the cylindrical wall of the disk. That is, for equilibrium conditions,
(18)
centrations C, and C,,,, as
E
=
V = ddL
(19)
dV/V = 2dr/T
dQs = (2dr/r)AC,dL
(29)
E
= 1
AvC,(L)dt
- e-2woL/rv
E
(31)
= &,/&e
Precipitate Concentration. The total quantity of contaminant precipitated on the n-alls of a colIecting electrode of length L is, from Equations 29 and 31, Qp
=
Qt[1
uto
-
+ vT
e-2tnoL/ru]
(32)
The surface concentration C, of this precipitated material may be written
- AvC,(L + dL)dt -
C, = ( I / 2 n r ) ( d Q p / d L )
(2dr/r)ACdL = 0 (22)
(30)
which, in accord with expectation, is the special case of Equation 29 when T = 0. The efficiency may also be written in terms of the total quantity of particulate matter entering, Q t , and the quantity precipitated, &,, in a given time period :
(21)
Comparing Equations 14, 15, 16, and 21 we have
(28)
Deutsch (3) and, by another method, White (11) have derived an efficiency equation applicable when the particles enter the precipitator fully charged. These authors obtain
(20)
for which the corresponding quantity of precipitate is
1 - Cout/C.
Setting C. = Gout Equations 26 and 28 yield
The total volume of the disk is given by Of the aerosol contained within this volume the fraction precipitated in time dt becomes
respectively,
(33)
whence
which may be written
+
AvCu(L)dt - A u [ C ~ ( L ) (dC./aL)dL]dt (2dr/r)AC,dL
=
0 (23)
Simplifying, there results
The concentration of precipitate a t the mouth of the cylinder is, then,
+ (2C,/rv)(dr/dt)dL = 0
(dC,/dL)dL
(24)
or, by Equation 17 dC,
=
- (2w/~)C,dL
(25)
Introducing the right-hand term of Equation 12 and integrating, we have
(26)
When T
=
0 Equation 26 reduces to
c,
C,e-2woL/rv
(27)
which, except for the short distance beyond the intake, is applicable to precipitators of industrial length. Efficiency. The fractional efficiency of operation, E , of a precipitator may be expressed in terms of inconling and outgoing particle con-
which, in the absence of any initial charge on the entering particles (to = 0), is zero. Particles which accumulate charge while traversing the cylinder might be expected to display a maximum concentration of precipitate a t a point yhere appropriate values of aerosol concentration and particle charge obtain. This maximum is, from Equation 34, a t
L
=
c[(Tr/2w0)1’2- t,] ( C , = maximum) (36)
Taking the derivative with respect to L of the logarithm of Equation 34 we have
4
/
7-
0
c'
I
I 3
I
2
I
AXIAL GAS
VELOCITY
I
I
5
4
v, METERS/SEC.
Figure 1. Variation of concentration ratio with aerosol velocity and cylinder length Under experimental conditions described, R is typically of the order 10' to 1v
L
+
vto
The problem, now, in designing a precipitator for sampling purposes is to render the concentraton ratio a maximum. In practice, the most readily adjustable variable is v , the gas velocity, and the value of velocity a t which the optimum concentration ratio is obtained is given by the transcendental equation
rv
which, as L increases, approaches
This relationship provides a means for conveniently determining the migration velocity w o in terms of experimentally measurable quantities. Concentration Ratio. If, in order to remove tho precipitate, the inner surface of the cylinder is continuously washed with a suitable liquid, a concentration ratio R may be defined such that
rv
- e--2woL/n~(ut,
vt.
Certain special cases merit attention:
SWi
limR = - ( T = 0 ) u+m
R
=
CJC,
(39)
The concentration ratio is clearly a measure of the success with which an instrument removes the contaminant from a large volume of gas and concentrates it in a small volume of liquid. If, during a time t, VI is the volumetric flow rate of effluent from the cylinder, then C. = EQ,/Vft = EC,irr%/V,
(40)
and
R = n+Ev/Vf (41) In general, the rate a t which liquid leaves the cylinder will be less than the input flow rate because of evaporation from the cylinder walls produced by the rapidly moving air stream. From Equation 29 R = -n7% [lVI
+ v T ) - - 2 w o T / r (L+;
+ V?")-[(~WOT/T) - Il(rZJL + rv2to+ T V ~+ T 2w,L* + 2w,LvTe) = 0 (43)
Vf
lim R = 0 ( T Ircm
> 0, to = 0)
(45) (46)
Equation 44 offers the maximum concentration ratio that may be approached in a single-stage precipitator. At T = 0, a condition which exists in practice when a fully precharging device is used in combination with the precipitating cylinder, the upper limit of R shown in Equation 45 holds. Figure 1 is a typical illustration of the dependence of concentration ratio on axial gas velocity. -4maximum concentration ratio is reached eventually for all finite lengths, but for the velocity range plotted, a maximum appears only in the case of the 0.1-meter cylinder, As v increases, the ring of peak precipitation moves further downstream and ultimately out of the cylinder altogether. If the initial charge on the particles is zero, this behavior leads to the condition described by Equation 46. Limitations. The assumed physical conditions on which the preceding
paragraphs are based are often met only approximately in practice; nevertheless, accumulated laboratory and industrial experience of the past several decades confirms, for the most part, the basic assumptions made regarding the charging and precipitation processes. More than one theory of electrostatic precipitation has indeed been advanced, but none of these theories does, or apparently can, account accurately and completely for all phases of the problem. The present theory assumes monodisperse spherical particles and is therefore subject to the same limitations as other precipitation theories that, in their practical application, also make the same assumption. White ( I l ) , Troost (Q),and Allender ( 1 ) have suggested laborious graphical and analytical procedures to deal with broad particle-size distributions. These methods are, however, impractical for general application. Engineering solutions to precipitator design problems must, in the interests of expediency, continue to rely on a single migration velocity for characterizing a polydisperse aerosol. The end results, to be sure, are approximate but, for a variety of purposes, adequate. Use of a polydisperse aerosol introduces the further question of how representative a collected sample will be of a wide distribution of particle sizes in the original suspension. In conformity with Equations 2 and 13, the migration velocity is proportional to particle diameter. Consequently, the larger particles will precipitate out first. If the axial gas velocity is high enough, or the cylinder short enough, the smaller particles will never reach the collecting wall. The extent to which this occurs may be determined by dividing the incoming particle-size distribution into narrow fractions and solving Equation 32 for each fraction. For the precipitate to be representative of the aerosol, the efficiency of collection must be close to 100%. If the cylinder is not too short this high figure is attainable. This is true even a t very high axial gas velocities, since the wet collecting wall eliminates particle re-entrainment, a serious problem in dry, high-velocity precipitation. EXPERIMENTAL
Electrodes. The experimental precipitator comprised a n aluminum cylinder of 60 cm. length and 3.65 cm. radius enclosing an axial electrode of 10-mil tungsten wire. The first few centimeters of the wire's down stream length a t the input end of the cylinder were insulated by painting with anticorona lacquer, thereby preserving a radial electric field configuration but eliminating the corona discharge along the insulated distance. By this arrangement, the region of ionization, and VOL. 33, NO. 1, JANUARY 1961
11 1
a
W
t-
0.31
W
THEORETICAL EXPERIMENTAL
5 Y a
i W
-1
LL W
+ z u W z
2- 100
0
k
8
ILL
B
tt
z
U 0
P
u W a
10
n.
t 0
0
I
1
05
1.0
1.5 20 DOWNWIND DISTANCE L , METERS
25
25
Figure 3. Dependence of precipitate concentration on downwind distance and efficiency on cylinder length in an industrial precipitator
U W E a
'0
01
0.2
03
04
05
DOWNWIND DISTANCE L , METERS
Figure 2. Concentration of precipitate on cylinder wall as a function of aerosol velocity and downstream distance Curves a r e arbitrarily positioned relative to each other along vertical axis At 100 liters/min., 0 and 0 represent duplicate tests run to check reproducibility
hence of precipitation (at least when the particles are initially uncharged), began far enough inside the collecting electrode to minimize distorting edge effects which would otherwise extend the charging as well as the Precipitation processes into a region external to the geometric volume of the cylinder. The potential of the inner electrode was maintained positive a t 17 kv.; higher voltages occasionally produced sparkover. Aerosol Production and Precipitate Air carrying 3.25Measurement.
micron diameter spherical particles of polystyrene latex was drawn through the cylinder a t rates of 100, 500, and 1000 liters per minute corresponding to the average linear velocities of 0.40, 2.0, and 4.0 meters per second. The choice of material to be precipitated was dictated by the remarkable uniformity of both size and spherical shape possessed by the polystyrene particles in question. The latex was aerosolized with an atomizer which introduced the polystyrene aerosol into a conduit independently fed with sufficient filtered air to provide the required total volumetric flow of aerosol. A partial obstruction in the conduit created the turbulence needed to accomplish mixing and achieve uniformity of the now diluted aerosol prior to its entrance into the precipitating cylinder. Microscopic examination of slides placed, facing upstream, in the mouth of the precipitator furnished no evidence of modification of particle size, as might possibly be expected, because 1 12
-
W
U
5
I
-
z
k
W
-
-
z 0
1
-
ANALYTICAL CHEMISTRY
of agglomeration arising from particle cohesion or incomplete evaporation of the liquid constituent of the original latex. Polystyrene spheres were uniformly impacted across the surface of the slides. Since no more than a few milliliters of the latex were procurable, of which the solid matter available for precipitation constituted but a small fraction, direct gravimetric determination of the precipitated deposit per unit length of cylinder was not practicable. Instead, the interior of the cylinder was completely lined with aluminum foil, and following each test the foil was removed with the precipitate adhering to the surface. The variation of surface concentration C, with distance downstream L was measured by cutting the aluminum foil into circumferential sections, washing the foil strips with water to resuspend the particles, and finally determining the concentrations of the solutions by photometrically observed scattering. The results appear in Figure 2. Unfortunately, the difficulties of achieving complete removal of the particles without agglomeration vvere not always successfully met; hence, the wide scatter of experimental points. The point L = 0 marks the beginning of the corona-i.e., the start of the uninsulated central wire-and not the mouth of the cylinder. The average values of the time constant and migration velocities relevant to the precipitation process were found to be T = 1.43 x 10-2second w o = 3.41 x lO-'meter/second tui = 5.0 X 10-2 meter/second The migration velocity wi that the particles possess on entering the cylinder is significantly greater than zero. The particle charge producing this is presumably acquired by friction during the process of aerosolization. The theory assumes this charge to be of one sign and uniformly distributed
among all particles of the aerosol. Experimentally, this is not found to be strictly true. Some precipitation occurs on the insulated portion of the central wire as well as on the enclosing cylinder. This effect, however, does not appear to be responsible for sharp departures from the theory. The data reported by Kalaschnikow (4) for the precipitation of 0.5- to 3-micron coal dust is reproduced in Figure 3. The precipitator in this instance was more nearly of industrial dimensions: 0.13 meter in radius and 3.62 meters long. The aerosol was blown through a t a linear rate of 2.60 meters per second in an electric field maintaining a current density of 1.7 X ampere per meter. The theoretical concentration and efficiency curves matching the experimental data assume the following constant values : T = 1.97 x 10-2 second w o = 3.38 x lO-lmeter/second WI=
0
In order to test the theory i t was necessary to run the sampler dry. Under normal conditions of wet operation, the effluent, with or uithout the addition of a wetting agent to facilitate uniform coating and washing of the cylinder wall, flows onto the cylinder's inner surface a t its upwind edge. The liquid is supplied through a length of hypodermic tubing from a reservoir, the flow rate being maintained a t about 5 cc. per minute by a peristaltictype pump. In order to spread the stream of effluent over its entire inner surface, the cylinder is rotated about the axis a t 30 r.p.m. by a small motor suitably geared down. Nevertheless, the cylinder often exhibits a tendency not to wet throughout. The effluent may stream along the wall of the rotating cylinder in a spiral path, leaving alternating wet and dry streaks. This flow pattern, once initiated, continues, preventing complete washing Experimental Sampler.
of the cylinder and consequent removal of the precipitate. The difficulty was remedied by extending a piece of stiff wire along the length of the cylinder, parallel t o its axis and lightly touching the line marking the instantaneous bottommost portion of the cylinder’s inner surface. The backwash of effluent thrown up along the wire as the cylinder wall brushes by beneath is sufficient t o wet the entire surface and achieve efficient washing action. To ensure effective drainage the cylinder is tilted a t a n angle of five degrees with the horizontal, and a circumferential sump, in which the effluent collects, is cut into the wall of the cylinder at its downwind end. The performance characteristics of a modified version of the electrostatic aerosol sampler described in this report are considered elsewhere ( 8 ) . ACKNOWLEDGMENT
The author expresses his appreciation t o the Research and Development Command, U. S. Army Chemical Corps, for permission t o publish this paper and t o David Steetle and Clyde Walter for their assistance in gathering the experimental data contained herein. NOMENCLATURE
a A
=
c
=
C.
=
=
radius of particle, meters cross section of cylinder, square meters magnitude of velocity of light in meters/second = 3 X 108, dimensionless volume concentration of particles in effluent, kg./cubic meter
= initial volume concentration of
C,
particles in gas, kg./cubic meter C, = surface concentration of precipitate, kg./square meter CoUt = outgoing volume concentration of particles in gas, kg./cubic meter C, = volume concentration of particles in gas, kg./cubic meter e = base of natural logarithms, dimensionless E = fractional efficiency, dimensionless E , = charging electric field intensity, volts/meter E p = precipitating electric field intensity, volts/meter F = coulomb force precipitating particles, newtons k = ionic mobility, (meters/second)/ (volts/meter) K = dielectric constant of uarticle, dimensionless L = downstream distance from mouth of cylinder, length of cylinder, meters m = mass of particle, kg. N = ion concentration, ions/cubic meter p = ionic charge, coulombs Q = charge on surface of particle, coulombs Q1 = quantity of particulate matter entering element of cylinder, kg. Qz = quantity of particulate matter leaving element of cylinder, kg. QS = quantity of particulate matter precipitated in element of cylinder, kg. Qux = maximum charge on surface of particle, coulombs &, = quantity of particulate matter precipitated, kg. Qr = total quantity of precipitate, kg. r = radius of cylinder, meters R = concentration ratio, dimensionless S = area of cylindrical wall available for precipitation, square meters t = time, seconds
to
=
T
= =
= =
= =
= = =
equivalent precharging time, seconds particle-charging time constant, seconds axial velocity of gas through cylinder, meters/second volume of cylindrical element, cubic meters volumetric flow rate of effluent from cylinder, cubic meters/ second migration velocity, meters/second migration velocity on entering cylinder, meters/second limiting migration velocity, meters/second permittivity of free space, l O 7 / 4i~c2farads/meter viscosity of gas, dekapoises ~~
LITERATURE CITED
(1) Allender, C., Matts, S., Staub 52,
738-45 (1957). (2) Arendt, P., Kallmann, H., 2. Physik 35,421-41 (1925). (3) Deutsch, W., Snn. Physik 6 8 , 335-44 (1922). (4) Kalashnikow, S., 2. tech. Physik 14, 267-70 (1933). (5) Pauthenier, A I . M., Moreau-Hanot, M., J. phys. radium 3, 590-613 (1932). (6) Rohmann, H., 2. Physik 17, 253-65 (1923). (7) Rosk, H. E., Wood, A. J., “An Intro-
duction to Electrostatic Precipitation in Theory and Practice,” Chap. 2; Constable, London, 1956. (8) Stern, S., Steetle, D., Bolduac 0. E. A., A . M . A . Arch. Ind. Health
18,30-1 (1958). (9) Troost, N., Proc. Insl. Elec. Engrs. (London) 101, 369-89 (1954). (10) White, H. J., Trans. Am. Inst. Elec. Engrs. 70,1186-91 (1951). (11) White, H. J., Ind. Eng. Chenz. 47, 932-9 (1955).
RECEIVED for review March 29, 1960. Accepted October 10, 1960.
FIuoresce nce Ana lyses
for PoIycycIic Aromatic Hydrocarbons J. H. CHAUDET and W. 1. KAYE’ Research laboratories, Tennessee Easfman Co., Division o f Eastman Kodak Co., Kingsport, Tenn.
b Fluorescence spectra of solutions of polycyclic aromatic hydrocarbons of a suitable quality are often difficult to obtain because of concentrationquenching, localization of fluorescence, a.nd self-absorption effects. If a proper solute concentration is used, it is possible to minimize these effects and still maintain a sufficient fluorescence intensity for the recording of spectra. This optimum concentration has been determined from the ultraviolet absorption at 365 rnp (the excitation wave length) of the polynuclear hydrocarbon in hexane. Present address, Beckman Instruments Co., 2500 Fullerton Rd., Fullerton, Calif.
Fluorescence spectra obtained at this concentration may b e used for the qualitative identification and quantitative analysis of aromatic hydrocarbons. The method is applicable to mixtures of aromatic hydrocarbons.
P
aromatic compounds in suitable solvents usually give characteristic fluorescence spectra which may be used for the identification of such compounds in rather complex mixtures. For such spectra to be suitable for reference, the fluorescence suppression associated with concentration quenching, localization of fluorescence, and self-absorption should be eliminated OLYCYCLIC
if possible ( 3 ) . These effects reduce the intensity of fluorescence peaks and in some cases perturb their positions. A method for determining the proper conditions for recording reproducible fluorescence spectra which are essentially free of these effects is described in this paper. Quantitative determinations may be made from such spectra. The method should be applicable to a large number of polycyclic aromatic compounds. Berenblum and Schoental (1, 2) photographically recorded fluorescence spectra of several polycyclic aromatic hydrocarbons, including anthracene, chrysene, benz [alanthracene, and several of their derivatives. A semiquantiVOL 33, NO, 1, JANUARY 1961
1 13
