EPA-600/2-76-067
March 1976
Environmental Protection Technology Series
EVALUATION OF THERMAL AGGLOMERATION
FOR FINE PARTICLE CONTROL
Industrial Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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EPA-600 2-76-067
March 1976
EVALUATION OF
THERMAL AGGLOMERATION
FOR FINE PARTICLE CONTROL
by
K.P. Ananlh and L..I. Shannon
Midwest Research Institute
425 Volker Boulevard
Kansas City. Missouri 64110
Contract No. 68-02-1324. Task 26
ROAP No. 21ADL-029
Program Element No. 1AR012
EPA Task Officer: D. C. Drehmol
Industrial Environmental Research Laboratory
Office of Energy. Minerals, and Industry
Research Triangle Park. NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington. DC 20460
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CONTENTS
Page
Summary 1
Introduction 2
Theoretical Aspects of Thermal Agglomeration 2
Experimental Studies of Thermal Agglomeration 8
Conclusions 12
References 13
iii
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SUMMARY
The agglomeration or growth of fine particles is, in principle, at-
tractive. If large particles can be produced with realistic residence
times and energy expenditures, conventional control systems could be used
with ease in controlling fine particulate pollutants. This task was un-
dertaken to evaluate the potential of thermal agglomeration in fine par-
ticle control.
Both theoretical analyses and experimental studies pinpoint an over-
riding disadvantage of thermal agglomeration with regard to industrial
gas cleaning applications — the long residence time required to achieve
significant particle growth. Residence times of the order of many min-
utes or even hours are required for significant agglomeration and par-
ticle growth to occur via thermal agglomeration. In contrast, industrial
gas cleaning applications would require residence times of 10 sec or less.
Successful utilization of the factors which promote thermal agglom-
eration is not likely to reduce residence times to anything near those
required for industrial applications. Thus, thermal agglomeration is
not a viable approach to pursue for augmenting the ability of control
systems to collect fine particulate emissions.
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INTRODUCTION
A variety of forces can cause the movement of particles toward one
another to produce collisions and subsequent agglomeration. When par-
ticles come into contact with each other and agglomerate, strictly as a
result of Brownian movement (diffusion), then the process is termed
"thermal agglomeration."
If the properties of the particle surfaces are disregarded and the
probability of sticking together after collision is assumed to be unity,
then the theory of coagulation depends on the mechanics of collision.
Based on these assumptions, two approaches have been reported for ex-
plaining thermal agglomeration.—' One is the continuum approach which
comes from Smoluchowski1s work on the behavior of dispersed systems^'
and the second is the free molecule approach (i.e., gas kinetic theory
approach). Each approach is reviewed in the next section. The discus-
sion of theory is followed by a section on experimental studies and an-
other on conclusions.
THEORETICAL ASPECTS OF THERMAL AGGLOMERATION
Based on Smoluchowski's assumption that thermal agglomeration is a
diffusion process, Zebell' shows that for a general case of particles of
different radii
N12 =
where N^2 is the nun*61 of particle 2 with radius r , diffusing
in unit time to a fixed particle 1 with radius r^ . In Eq. (1),
r,2 = ri + r2 and is tne distance between the centers of the two parti-
cles at the moment of contact; D2 is the diffusion coefficient for the
particles of kind 2 and n = n(T, r2> t) is the concentration of par-
ticles of radius r2 at time t as a function of distance "r from
particle 1 .
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/an \
To determine the concentration gradient \%= I > tne diffusion
equation is solved in spherical coordinates using appropriate boundary
conditions.—' This results in
— = — (2)
or r12
Substitution of Eq. (2) into Eq. (1) yields the number of parti-
cles of kind 2 diffusing towards and adhering to fixed particle 1
per unit time,
N12 =
Equation (3) assumes particle 1 to be stationary. In reality,
due to Brownian movement, particle 1 is also mobile and diffuses with
a coefficient D^ . Thus, the total particle flux is given by the fol-
lowing expression
1 + r2)(D1 + D2)n(r2,t) (4)
By expressing the diffusion coefficients in terms of the particle mo-
bility $(<£ = D/kT) and introducing the coagulation constant Ko , Eq.
(4) can be written as
N12 = KQ(r1>r2)n(r2,t) (5)
where K0(r1,r2) = 4tr(^j+^2)(rj_ + r2)kT
k = Boltzmann's constant, and
T = absolute temperature
For highly dispersed aerosols the coagulation constant must be corrected
for discontinuity in concentration at the surface of the absorbing par-
ticle. The correction becomes appreciable when the apparent mean free
path of the aerosol particles is comparable with the radius of the ab-
sorbing sphere; according to Fuchsft' this occurs when r <. 0.1 urn and
according to Hidy and Brock!/ the cutoff limit is when the Knudsen num-
ber is > 0.01. Physically, this means that diffusion equations can be
applied to Brownian motion only for time intervals which are large com-
pared with the relaxation time, T , of the particles or for distances
larger than the mean free path of the aerosol particles.
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For conditions where the diffusion equations are not applicable,
the laws of kinetic gas theory must be used. The kinetic gas theory
approach leads to the following equation for N^2
N12 = 4TT(ri + r2)(D1 + D2)n(r2,t) I 1 (6)
1/2
/ D-, + Do \ / nnmo n \
where G0 = 4( -± ^ ) ( _Ji_f_ . \
\ rl + r2 / \ml + ^ 8kT /
Equation (6) can be written in the simplified form
N12 = KQfn(r2,t) (7)
where KQ = coagulation coefficient and
f =
The factor, f , represents the gas kinetic correction factor.
Tables 1 and 2 present values of the coagulation constant calculated
from diffusion theory and from gas kinetic theory. As shown in Tables 1
and 2, significant differences exist in the values for small particles
and only slight differences occur as the particle size reaches 1 um.
Table 1. VALUE OF THE COAGULATION CONSTANT
K0(r1,r2)(10-10 cm3 sec'1)57
r2 (um)
TI (um)
0.001
0.01
0.1
1.0
0.001
803.4
2,232
20,299
201,054
0.01
84
234.3
2,121
0.1
12.68
36.69
1.0
6.6
a/ Calculated from diffusion theory.
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Table 2. THE COAGULATION CONSTANT
K(r1,r2) = K0f(HT10 cm3 sec'1)!/
rl (urn)
0.001
0.01
0.1
1.0
0.001
8.78
180.2
8,845
178,100
r2 (urn)
0.01
21.0
168.5
2,032
0.1
11.10
35.95
1.0
6.4<
£/ Taking into account the gas kinetic correction, f .
An important observation on the data presented in Tables 1 and 2 is
that coagulation coefficients are small. As a result, long times would
be required to achieve significant particle growth.
In addition to the rate of coagulation, another important factor is
the variation of particle size distribution with time. An equation for
the change with time of the size distribution of aerosols due to thermal
coagulation is given by Miiller.^/
m/2
dn(m
dt
*—^- = I K(m^,m-m^)n(m^,t)n(m-m^,
w
-n(m,t) / K(m,m1)n(m1,t)dm1
(8)
where n(m,t)dm is the number of aerosol particles per cubic centimeter
at the time t , whose masses lie between the values m and m + dm ,
while K(mi,m2) gives the value of the coagulation constant between
aerosol particles of the masses m^ and n^ . The physical meaning of
this integro-differential equation is that a particle of mass m can
only come into existence if two particles with masses m^ and (m-m^)
collide: it can be integrated either from m^ = 0 to m-i - m/2 or
from m-^ = 0 to n^ = m . The integral value must be halved as, otherwise,
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each possible combination is counted twice. The second integral expresses
the fact that each particle of mass m , disappears from the fraction m
to m + dm after colliding with a particle of mass mi .
Equation (8) requires a computer solution unless simplifying assump-
tions are made. Figure 1 illustrates a solution to Eq. (8) presented by
ZebelZ/ starting with a highly peaked particle size distribution.
Schumann^/ and Todes2/ have developed asymptotic solutions to Eq. (8).
Schumann suggests that Eq. (9) can be used for the case of constant K
when Kn0t » 1
n(m) = — e - m/m (9)
I2
where c = weight concentration of aerosol,
_ c(l + 0.5Kn0t) Kcfc
m = — = - = - = mean mass of particle at time t .
n n0 2
By making simpler assumptions Smoluchowski * ' obtained, instead of
the integro-differential equation, a simple differential equation which is
easily solved. If only the concentration of the total number of par-
ticles, n , is considered and the same value of K , the coagulation
constant, is used for all particles, then the fundamental equation of co-
agulation becomes
dt 2
n2 (10)
The factor 1/2 is again necessary so that each aggregate should be
counted only once. The solution of Eq. (10) is
.. torn
0 ° 2
where nQ is the initial particle number concentration at time t = 0 .
Equation (11) for the particle number concentration as a function
of time, t , is a good approximation for the size distributions occur-
ring in many aerosols.
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30,-
0
, tg = 0 min
= 0.053 min - 3.18 sec
t2 = 0.311 min - 18.66 sec
0.01
0.02
0.03
0.04
0.05 0.06
0.07
Figure 1. Calculated change in particle size
distribution with time.!/
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The preceding theoretical analyses of thermal agglomeration indi-
cate that the main variables influencing the rate of agglomeration are
particle concentration, particle size, gas composition, and gas tempera-
ture. Thermal agglomeration would be most effective (i.e., occur at the
fastest rate) in aerosol systems which have: (a) a high initial grain
loading; and (b) a high degree of polydispersity. However, it is clear
from the analyses that the rate of thermal agglomeration will be quite
slow for aerosols of interest in industrial gas cleaning because the
agglomeration coefficient is of the order of 10"? to 10~10 cm^ sec~l for
such systems. The long times which would be required to achieve sig-
nificant particle growth are a severe negative feature with regard to
utilization of thermal agglomeration in industrial systems.
Experimental studies on thermal agglomeration of aerosols generally
support the predictions of the theoretical analysis. Highlights of ex-
perimental work are presented next.
EXPERIMENTAL STUDIES OF THERMAL AGGLOMERATION
Many experiments have demonstrated a linear relationship between —
and time in agreement with Eq. (11), even when there is a large change
in n (as much as 10 to 30 times) during the time of the experiment.
Figure 2 presents some work of Derjaguin and Vlasenko demonstrating this
point.—' Derjaguin and Vlasenko used particles of initial average radii
of 0.1 to 0.3 urn and the particles increased in size two to three times
during the experiments. Note that times of the order of 100 min were re-
quired. This might be expected to produce curvature, and the fact that
it does not suggests that the effect of the increase in the average par-
ticle size is compensated by the simultaneous increase in polydispersion.
According to Fuchs,£/ the smaller the initial radius of the particles
the more important becomes the effect of the change in particle size and
a linear relationship might not be expected for very small particles.
The behavior of ammonium chloride aerosols studied by Whytlaw-Gray and
Patterson, shown by Figure 3, may be an example of this effect of size.—'
Both weight and number concentrations are given, and decreasing weight
concentrations in general correspond to decreasing particle size. The
top curve corresponds to a. particle size of about 0.08 vim. The increas-
ing curvature with decreasing size is very marked.
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•o
o
X
> 2
0
20
40
60
80
100
t, Minutes
Figure 2. The kinetics of thermal coagulation.
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20
40 60
Time in Minutes
80
100
Figure 3. The coagulation of ammonium chloride aerosols.—'
3/
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Table 3 presents some experimentally determined values of coagula-
tion coefficients for several aerosols. The theoretical value shown in
Table 3 is for monodisperse aerosols which are large relative to the mean
free path of the gas. In this case Ko = -^ Or in terms of the gas con-
stant K = z£!E, where N is the concentration of particles and T\ is
gas viscosity. ' The deviation from the theoretical value shown in Table 3
probably results largely from a combination of polydispersity and elec-
trical charging.
Table 3. COAGULATION CONSTANTS
FOR SEVERAL AEROSOLS
K x 108
Dispersed material (cnr min"^-)
Theoretical value 1.8
Stearic acid 3.1
Ammonium chloride 3.0-4.7
Cadmium oxide 4.0-5.3
Magnesium oxide 8.5-10.9
Copal resin 9.3
Carbon 14.1
Zinc oxide 18.9-19.6
Silica powder 26.0-28.0
11
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Experimental evidence also suggests that the more nearly an aerosol
approaches monodispersity the more slowly it coagulates. Also, a system
with sufficiently narrow size distribution exhibits second, third, and
higher modes in the size distribution as coagulation proceeds. The
higher modes correspond to the coalescence of two, three, and more par-
ticles of the initial modal radius. A polydispersed system does not
give rise to higher order modes.
CONCLUSIONS
Both theoretical analyses and experimental studies pinpoint an over-
riding disadvantage of thermal agglomeration with regard to industrial
gas cleaning applications—the long time required to achieve significant
particle growth. Residence times of the order of many minutes or even
hours are required for significant agglomeration and particle growth to
occur via thermal agglomeration. In contrast, industrial gas cleaning
applications would require residence times of 10 sec or less.
The main variables which can be used to enhance the rate of thermal
agglomeration are particle size and concentration, gas composition and
gas temperature. The temperature and gas composition are for the most
part not useful variables because they will be a characteristic of the
effluent stream from a specific source.
The possibility of influencing the agglomeration rate of particles
by introducing a second gas or vapor has been explored in several experi-
mental programs, and the only clear-cut results seem to be those in which
the added vapor in some ways affects the shape of the particles, or in
which a vapor is actually being transferred between the vapor phase and
the particles so that appreciable gaseous diffusion occurs. The latter
case is really diffusiophoresis and is not actually thermal agglomera-
tion.
One could alter the agglomeration rate by changing the particle size
distribution and concentration by seeding the aerosol with large particu-
lates which act as "agglomeration sites." However, this technique while
possibly being effective at an early stage in the agglomeration cycle,
would rapidly lose effectiveness because of the n^ dependence of the
agglomeration process. Continuous seeding would be required to maintain
the accelerated rate.
Successful utilization of the factors which promote thermal agglom-
eration is not likely to reduce residence times to anything near those
required for industrial applications. Thus, thermal agglomeration is
not a viable approach to pursue to augment the ability of control systems
to collect fine particulate emissions.
12
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REFERENCES
1. Hidy, G. M., and J. R. Brock, J. Colloid Sci., 20_, 477 (1965).
2. Smoluchowski, M. von, Z. Physik. Chem., J92, 129 (1917).
3. Zebel, G., in Aerosol Science, edited by C. N. Davies, Academic
Press, New York (1966).
4. Fuchs, N. A., The Mechanics of Aerosols, Pergamon Press, New York
(1964).
5. Hidy, G. M., and J. R. Brock, The Dynamics of Aerocolloidal Systems,
Vol. 1, Pergamon Press, New York (1970).
6. MUller, H., Kollordzentschrift, 27, 223 (1928).
7. Zebel, G., Rolloid Z, JL56, 102 (1958).
8. Schumann, T., Quart. J. Royal Met. Soc., 66, 195 (1940).
9. Todes, 0., Symposium on Problems of Kinetics and Catalysis, ONTI,
Moscow-Leningrad, 7, 137 (1949).
10. Smoluchowski, M. von, Phys. Z.. 1£, 557-585 (1916).
11. Smoluchowski, M. von, Z. Phys. Chem.. 9JZ, 129 (1918).
12. Derjaguin, B., and G. Vlasenko, Dokl. Akad. Nauk. SSSR, 63, 155
(1948).
13. Whytlaw-Gray, R., and H. S. Patterson, Smoke, Edward Arnold, London
(1932).
13
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TECHNICAL REPORT DATA
(Please read {nunictio>:s on tlic reverse before completing)
. REPORT NO.
EPA-600/2-76-067
3. RECIPIENT'S ACCESSION>NO.
4. TITLE AND SUBTITLE
Evaluation of Thermal Agglomeration for Fine
Particle Control
5. REPORT DATE
March 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
K. P. Ananth and L.J. Shannon
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Midwest Research Institute
425 Volker Boulevard
Kansas City, Missouri 64110
10. PROGRAM ELEMENT NO.
1AB012; ROAP 21ADL-029
11. CONTRACT/GRANT NO.
68-02-1324, Task 26
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND/PERIOD COVERED
Task Final; 9-12/74
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES Project officer for this report is D. C.Drehmel, Mail Drop 61,
Ext 2925.
16. ABSTRACT
The report gives results of an evaluation of the potential of thermal agglomeration
as a means of enhancing the collection of fine particle emissions. Available
theoretical and experimental information indicates that this method of particle
agglomeration offers no useful avenue for improving fine particle control.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Held/Group
Air Pollution
Agglomeration
Thermodynamics
Dust
Evaluation
Air Pollution Control
Stationary Sources
Thermal Agglomeration
Fine Particles
13B
20M
11G
14A
13. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
17
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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