SEPA
United States
Environmental Protection
Agency
Industrial Environmental Research EPA-600 7-78-097
Laboratory June T978
Research Triangle Part, NC 27711
Effects of Interfacial
Properties on
Collection of Fine
Particles by
Wet Scrubbers
Interagency
Energy/Environment
R&D Program Report
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EPA-600/7-78-097
June 1978
Effects of Interfacial Properties
on Collection of Fine Particles
by Wet Scrubbers
by
G.J. Woffinden, G.R. Markowski, and D.S. Ensor
Meteorology Research, Inc.
P.O. Box 637
Altadena, California 91001
Contract No. 68-02-2109
Program Element No. EHE624A
EPA Project Officer: D.L Harmon
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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ABSTRACT
Typical wet scrubber models were analyzed to determine the effects
of surface tension on particle removal efficiency. Particle capture (re-
moval) is a two-step process: (1) collision of a particle with a spray drop-
let and (Z) coalescence with the droplet. A change in surface tension of the
scrubber water can influence both steps.
When the surface tension of scrubber water is reduced, spray droplets
will normally decrease in size. The cumulative exposed droplet surface
area is therefore increased. The larger exposed collection surface can
improve collision efficiency. Too much reduction in droplet size, however,
can actually reduce collision efficiency. One effect of surface tension in
droplet-particle collisions is therefore to help optimize droplet size for
maximum particle removal.
The coalescence process after a particle collides with a scrubber
droplet has been described by the film thinning model. The model assumes
that coalescence is controlled by the thinning rate of an air or vapor layer
trapped between an impacting particle and droplet. If the film thins and rup-
tures before the particle rebounds, coalescence occurs. The thinning model
predicts that a reduction in droplet surface tension allows deeper particle
penetration into the droplet. The escaping vapor film therefore has a longer
more resistive path, resulting in longer thinning times, thus reduced
coalescence probability. The film thinning model is an instructive starting
point but it needs to be modified if disagreement with experimental results
is to be eliminated.
When the surface tension of a scrubber liquor is modified, collection
efficiency may be slightly improved or degraded depending on the spray
droplet sizes and the sizes of particles being removed.
111
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CONTENTS
Page
Abstract iii
List of Figures v
Acknowledgments vii
List of Symbols viii
Sections
1. Conclusions 1
2. Recommendations 2
3. Introduction 4
4. Scrubber Models 5
5. Application of Surface Tension Results to Scrubber Models 9
6. Experimental Evaluations of Coalescence Theory 24
References 48
Appendix - Surface Tension Effects on Particle Collection
Efficiency 51
IV
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FIGURES
Number Pa.g<
1 Scrubber droplet size for maximum collection effi-
ciency of particles 0. 5 to 20 pm diameter, based
on model (V = 80 m/sec. ) 10
2 Scrubber droplet size for maximum collection
efficiency, based on model 11
3 Effect of surface tension on outlet particle concentra-
tion for 20 pm particles, typical of flyash 13
4 Effect of surface tension on outlet particle concentra-
tion for 0. 8 pm diameter particles, typical of
laboratory aerosol 14
5 Effect of surface tension on outlet particle concentra-
tion for 0. 3 pm diameter particles, typical of
cupola emission 15
6 Models for surface deformation 18
7 Coalescence efficiency vs velocity of impact of 134p
droplets impinging on 2. 2 mm drops: a) distilled
water, a = 72 dyn cm ; b) 0. 5% acetic acid solution,
o = 70 dyn cm ; c) 5% acetic acid solution, o = 60
dyn cm l. Curve c) also resulted for distilled water
•when the drops were oppositely charged. (List and
Whelpdale, 1969)32 20
8 Inverted bubble 21
9 Film thinning model 22
10 High speed cine microscope equipment used for ex-
perimental evaluation of coalescence mechanisms 25
11 Glass rod with simulated flyash particle mounted on
traversing mechanism 26
12 Traversing mechanism for impacting particles into
water droplets 27
13 Coalescence of 1700 pm diameter glass particle with
water droplet, 585 usec delay, 6 cm/sec 30
14 Coalescence of 1000 pm diameter glass particle with
water droplet, 780 psec delay, 6 cm/sec 31
15 Coalescence of 725 pm diameter glass particle with
water droplet, 468 psec delay, 6 cm/sec 32
16 Coalescence of 275 pm diameter glass particle with
water droplet, 351 psec delay, 6 cm/sec 33
-------
Number Pagi
17 Coalescence of 100 i^m diameter glass particle with
water droplet, 156|-isec delay, 6 cm/sec 34
18 10 Um diameter glass fiber impacting distilled water
droplet. Coalescence delay time <1 frame (i.e.,
<39psec). 35
19 Coalescence of 725 Um diameter glass particle with
water droplet, 273 psec delay, 42 cm/sec 36
20 Coalescence of 725 Urn diameter glass particle with
water droplet, 234 kisec delay, 42 cm/sec 37
21 Coalescence of 725 Hm diameter glass particle with
water droplet, 273 usec delay, 42 cm/sec 38
22 Coalescence of 725 pm diameter glass particle with
water droplet, 234 psec delay, 42 cm/sec 39
23 Coalescence of 100 \±m diameter glass particle with
Freon TF, <39 usec delay, 42 cm/sec 40
24 Coalescence of 100 p.m diameter glass particle with
water/surfactant, <39 Psec delay, 42 cm/sec 41
25 Coalescence of 100 Hm diameter glass particle with
water droplet, 156 psec delay, 42 cm/sec 42
26 Comparison of theoretical predictions and experimental
measurements of coalescence delay time for water
at 6 cm/sec impact velocity 44
27 Comparison of theoretical predictions and experimental
measurements of coalescence delay time for water
at 43 cm/sec impact velocity 45
28 Comparison of theoretical predictions and experimental
measurements of coalescence delay time for Freon-
TF at 43 cm/sec impact velocity 46
29 Comparison of theoretical predictions and experimental
measurements of coalescence delay time for water
droplets containing surfactant and an impact velocity
of 42 cm/sec 47
VI
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LIST OF SYMBOLS
A -- Area of contact between a particle and a liquid droplet during
collision
B -- Correction factor in film thinning model
c - - Constant
Cn -- Cunningham correction factor
-- Drag coefficient
d -- Diameter of liquid droplets
D -- Actual particle diameter
D -- Aerodynamic diameter of a particle
f -- Constant that may include effects of surface tension, particle
growth, collection by means other than impaction, and other
unknown parameters
F -- Surface tension force
F(K, f) -- Function of inertial parameter, k, and undefined factors, f
F -- Resistive force exerted normal to the surface on a particle
during collision with a liquid droplet
k -- Inertial parameter
K, -- Constant
A
K -- Harmonic oscillator constant. "Spring" constant in harmonic
oscillator model of particle impact and bounce.
K -- Inertial parameter based on throat velocity
P -- Average penetration of a particle into a water dronlet during
collision
Q -- Volumetric flow rate of liquid phase
G
Q -- Volumetric flow rate of gas phase
R - - Particle radius
S -- Constant depending on the shape of the depression in a water
droplet made by an impacting particle
vii
-------
t -- Thinning time of air or vapor film trapped between a colliding
particle and a liquid droplet
v -- Impact velocity
V -- Critical impact velocity below which particle/droplet
coalescence will not occur
V -- Velocity of gas phase
G
V -- Critical impact velocity above which particle/droplet
coalescence will not occur
x -- Radius of particle/droplet contact area
y -- Penetration depth of particles into a liquid droplet during
collision
& A variable that includes all terms from Equation 5 that are
functions of droplet diameter
y -- Constant depending on surface tension and particle size
6 -- Thickness of vapor or air film at time of rupture
6 -- Angle defining particle contact surface area
A0 -- Mean free path of molecules in the vapor film separating a
particle and a water droplet
\i -- Viscosity of gas
G
p -- Particle specific gravity
p -- Density of liquid
a -- Liquid surface tension
a -- Liquid-gas flow rate parameter, Q p
Vlll
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ACKNOWLEDGMENTS
The University of Washington, under an MRI subcontract, performed
theoretical studies on the effects of surface tension on coalescence. This
work was performed by Dr. John Berg and Scott Emory.
Gratitude is expressed to Patrick A. O'Donovan, Aerojet-General
Corporation, for providing high speed photographic equipment used in these
studies.
IX
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SECTION 1
CONCLUSIONS
1. Particle collection in a wet scrubber requires impaction and coales-
cence with a water droplet. A change in surface tension can affect
both impaction and coalescence under some conditions.
2. Results of the theoretical study indicate that changes in surface tension
of wet scrubber liquids can either improve or degrade particle impac-
tion efficiency, depending on particle size and scrubber operating condi-
tions; however, changes are expected to be small.
3. Current models describing coalescence do not agree well with experi-
mental results so it is difficult to predict exact effects of surface
tension on coalescence.
4. Theoretical results from this study can be used to imply relative
effects of surface tension on scrubber performance, however addi-
tional experimental verification is needed.
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SECTION 2
RECOMMENDATIONS
1. There is a large discrepancy between theoretical predictions based on
the film thinning coalescence model and experimental results obtained.
This discrepancy should be resolved by additional studies of the basic
coalescence process. The discrepancy could be due to one of the
following factors: assumptions in the film thinning model may be
faulty, the film thinning mechanism may not be the controlling process,
approximations used in the film thinning model may be too crude, or
control of experimental conditions may have been inadequate.
2. Additional laboratory experiments will be required for theory modifi-
cations. These experiments should include:
• Demonstration of the effects of particle materials other than
silica, i.e., carbon and hydrocarbons.
• Extension of coalescence measurements to smaller particles
using higher optical magnifications and faster motion picture
cameras. Present studies were limited to coalescence delay
time measurements in the order of 150u sec. Small particles
as in a wet scrubber appear to coalesce in much shorter times.
A 10tan diameter particles, for example, might be expected to
coalesce in ZOusec, while a 1pm particle might coalesce in
approximately 4ysec. Instrumentation with a lUsec resolution
time, such as the Beckman and Whitley Model 189 framing
camera, should be used.
• Additional low surface tension liquids should be investigated
in order to verify that the observed "surface tension effects"
are real, and not due to some other property of the specific
liquids that were used in this study. The other liquids
should include (1) additional homogeneous compounds and
(2) water with other surfactants.
-------
• Water droplets have been observed to float for long periods
on a water surface under controlled conditions. This phe-
nomena cannot be adequately explained by the film thinning
theory of coalescence. Additional studies, both theoretical
and experimental, should be conducted to show the cause of
these effects (e.g., surface tension, electronic polarizability,
adsorbed monomolecular layers, or some other undefined
mechanism) and whether they can be applied to scrubber
models to improve collection efficiency. Results of such a
study may also explain some of the differences observed
between coalescence theory and experimental results.
Laboratory-scale scrubber experiments should be conducted to evalu-
ate theoretical scrubber performance predictions based on models
evolved under the present study. These experiments should show par-
ticle removal efficiency as a function of surface tension, droplet size,
particle size, and relative impact velocity.
-------
SECTION 3
INTRODUCTION
Wet scrubbers represent one of the primary methods for controlling
particulate emissions from large industrial operations. Improvements in
collection efficiency can reduce the size and capacity of the required con-
trol devices. Because of the high cost for a large control device, relatively
small improvements can provide significant savings in original capital invest-
ment and in operating costs.
The objective of this study was to conduct a theoretical and experi-
mental study to determine the effects of particle/liquid interfacial properties
on the collection of fine particles by scrubbers and to apply results to ana-
lytical scrubber models.
The technical approach included the following steps:
• Analysis of current wet scrubber models
• Theoretical analysis of surface tension effects on
particle collection efficiency
• Experimental testing of theoretical results
• Comparison of results with existing wet scrubber
performance models
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SECTION 4
SCRUBBER MODELS
The effect of surface tension is not explicit in most of the current wet
scrubber analytical models. Penetration (one minus the collection efficiency)
in the Calvert model for example, is given by Equation 1:
P = exp -
v p d
- ^ . F (k, f)
where P = average penetration
Q = volumetric flow rate of gas phase
Q = volumetric flow rate of liquid gas
.L<
V = velocity of gas phase
p = viscosity of gas
p = density of liquid
±-i
d = diameter of liquid drops
F(k, f) = function of inertial parameter, k, and unknown
factors, f
Surface tension, as such, is not one of the parameters listed; how-
ever surface tension influences droplet breakup and, therefore, the resul-
tant droplet diameter, d. A reduction in droplet diameter improves col-
lection efficiency by increasing the number of droplets and therefore the
total exposed water surface area. The interfacial surface properties may
also have a significant effect on the "F" factor because it is primarily a col-
lection efficiency factor that included both collision and coalescence probabili-
ties. It Is assumed that surface tension does not have a direct effect on col-
lision probability (other than that due to droplet diameter), but that it
could have an effect on coalescence after impact.
Only limited experimental studies on the effects of surfactants in scrub-
bers have been performed. One is by Bughdadi.2 He concluded that addition of
surfactant (0. 1 percent Triton CF-10) improved the collection •efficiency of
a venturi scrubber, especially at low liquid-to-gas flow ratios. He reported
that the overall collection efficiency improved from 99. 66 percent to 99. 93
-------
percent at 18^ water/28 m3 of gas (4 gal/1000 ft3). He attributed the im-
provement to easier penetration of the collected particulates into the scrub-
ber water droplets, thus providing more effective wetting. He also observed
a reduction in spray droplet sizes with surfactant additives. (It is difficult
to explain the large change in penetration by collision processes alone. )
It has been shown experimentally that spray droplet size is proportional
to the square root of the surface tension for sufficiently small liquid to
gas ratios:
d = ca*2 (2)
where d = droplet diameter
c = constant
o = liquid surface tension
The maximum surface tension of scrubber water is approximately
72 dynes/cm (pure water). Additives and normal contaminants in operat-
ing scrubbers will typically reduce the surface tension to 50-60 dynes/cm.
If a surfactant is added, the surface tension can be further reduced to 20-30
dynes/cm. Therefore, the maximum possible reduction, from 72 to 20 dynes/
cm will reduce the spray droplet diameter by only 50 percent at most. In
actual practice, a maximum reduction of 20 percent is more realistic. The
effect of droplet size reduction on scrubber efficiency is not easily deter-
mined from the scrubber model, Equation 1. The droplet size affects the
"F" factor which includes individual droplet collection efficiency and other
unknown factors. Decreasing the size of droplets will increase the number
of droplets so that droplet/particle collision efficiency •will be improved,
particularly for small particles. There is a practical limit, however, be-
cause when the droplets get small enough they may not be removed from
the gas stream by the entrainment separator. The droplets in a scrubber
are usually very large (on the order of 50 to 200 um diameter) compared to
the particles being scrubbed (the most difficult particles to remove are
typically 0. 05 to 3. Opm diameter). When there is a large difference in size
between the droplet and particle and the particle is in close proximity to
the liquid surface, the droplet surface can be considered as an infinite flat
plane.
4. 1 Effect of Drop Size on Collection
Typically wet scrubber models have been described by Calvert, et al.1
These models assume that impaction on the droplets is the only mechanism
active in controlling the collection process. This is a good assumption if
the particles are greater than 5 microns aerodynamic diameter and may be
good for particles as small as one micron aerodynamic diameter.
Aerodynamic diameter is defined as:
6
-------
= (PPCD) D
1/2
(3)
where D actual particle diameter
C Cunningham Correction Factor, a function of
D, and the mean free path
p = particle specific gravity
The scrubber models assume that the droplets are formed at a velocity
much slower than the gas stream and the particles moving with the gas
stream are collected as they impact the droplets. As the droplets are
accelerated by the gas flow, the relative velocity decreases and they become
progressively less efficient particle collectors. The collection efficiency
typically approaches zero at the scrubber outlet. The models also assume
that once a particle collides with a droplet, it invariably sticks. While
intuitively reasonable, much evidence suggests that this assumption may
need modification.
Surface tension enters into droplet size since the droplets are typical-
ly produced by atomization of the scrubber liquor introduced into the rapidly
moving gas in the scrubber throat. The droplet size has been historically
predicted by the Nukiyama and Tanasawa equation , based on empirical
work:
(4)
d = drop diameter, cm
O = liquid surface tension, dyne/cm
V = gas velocity, cm/sec
p = density of liquid, g/cm
U viscocity of liquid, poise
Q /Q_ = liquid to gas ratio, dimensionless
1^ \j
This correlation indicates that the droplet size is proportional to the
square root of the surface tension for sufficiently small QL/QQ. A number
of other correlations have appeared in the literature showing a similar de-
pendence. 1>4
*
Droplet size enters directly into scrubber performance models. Cal-
vert's model1 was selected as representative because it appears to be well
constructed and to agree reasonably well with experimental data. For an
infinite throat length and zero initial droplet velocity the model predicts
a penetration as indicated in Equation 5:
-------
P - exp
where
'DO
K
PO
K
DO
PO
drag coefficient
inertial parameter based on throat velocity
Q, P,
(5)
QG PG
The assumption of infinite throat length is good for small particles
(less than 2 microns diameter) and/or small droplets (less than 50 microns
diameter). In any case, the general dependence on droplet size is adequate-
ly indicated.
8
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SECTION 5
APPLICATION OF SURFACE TENSION
RESULTS TO SCRUBBER MODELS
The effect of changing droplet diameter on scrubber collection effi-
ciency was calculated by combining all of the droplet size dependent terms
in the scrubber model, Equation 5, into a single exponential factor, B.
Results indicate that for any given particle size to be removed, there
is an optimum collection droplet size that will provide maximum collection
efficiency. An example of the calculated results is shown graphically in
Figure 1. The optimum droplet diameter is the point at which the collection
efficiency exponent is the highest. Because the exponent is negative, a
large absolute value represents a low penetration of particles.
The results given in Figure 1 assume an impact approach velocity
of 80 m/sec. Calculations were also made for other velocities. The opti-
mum droplet diameters for velocities ranging from 5 to 80 m/sec are
plotted as functions of particle diameter in Figure 2.
It can be seen from the results in Figure 1 that a change in liquid
droplet size may improve or degrade particle collection efficiency, depend-
ing on the initial sizes of the droplets and the particles being scrubbed. For
example, 1 Um diameter particles are removed most effectively by 40 ^m
diameter droplets. If a scrubber produces lOOPm diameter droplets, its
collection efficiency for 1 l-tm particles can be improved by reducing the
droplet size to 40i-im. If the scrubber initially produces 40Um diameter
droplets either a reduction or an increase in droplet sizes will decrease
the collection efficiency of 1pm diameter particles.
Generally, the penetration for large particles will be increased and
that for small particles will be decreased when droplet sizes are reduced.
The overall penetration will likely decrease since nearly all large particles
will be collected in any case. If the scrubber is operating at near the
optimum efficiency over most of the size distribution, changing the surface
-------
10.000
1.000 100 10
DROPLET DIAMETER (pn)
Figure 1. Scrubber droplet size for maximum collection
efficiency of particles 0. 5 to 20 um diameter,
based on model (V = 80 m/sec.)
10
-------
10,000
1.000
I
as,
W
w
E-
U
0.
O
o
S
D
H
0.
O
100
10
y////
w
80 rn/sec.
40 m/sec.
20 m/sec.
10 m/sec.
5 m/sec.
0. 1
1 10
PARTICLE DIAMETER (fan)
100
Figure 2. Scrubber droplet size for maximum collection
efficiency, based on model.
11
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tension is not likely to have much influence (if the coalescence properties
remain unchanged) since the peaks in Figure 1 are fairly broad.
Table 1 shows the change in penetration for three different drop
sizes assuming a reduction of the surface tension by a factor of 2, (the
maximum likely due to addition of surfactant).
In this case the drop size was assumed proportional to the square
root of surface tension and independent of the liquid to gas ratio. The
initial drop sizes without surfactant are arbitrary. This table indicates
the maximum change in penetration that could be expected due to surface
tension variation. Actual changes in real scrubbers should be smaller.
TABLE 1. PREDICTED CHANGE IN SCRUBBER PENETRATION
DUE TO ADDITION OF SURFACTANT
throat velocity = 8000 cm/sec
particle size = 1 Pm (aerodynamic diameter)
penetration fraction
without surfactant = .02
Drop Size Drop Size
Without With B B Fractional
Surfactant Surfactant Without With Penetration
(Um) (Pm) Surfactant Surfactant w/Surfactant
205 144 2.10 2.44 .011
144 102 2.44 2.70 .013
51 36 2.93 2.89 .021
Note that penetration is reduced by nearly a factor of 2 in the first
two cases but increased slightly in the last. These calculations also indi-
cate that if demisting is not a problem, a spraying device which produces
smaller droplets than those indicated by Equation 4 could result in de-
creased penetration. Equation 4 predicts a drop size of about 125 microns.
Figures 3, 4, and 5 show changes in relative outlet concentration
versus size and surface tension for typical scrubber parameters. The
inlet size distributions are log normal with geometric mean diameters
and standard deviations which correspond to typical fly ash, lab aerosol,
and cupola aerosol respectively. The distributions are normalized so
that the peak value is 1000 and the area under the curves represents
the total relative amount escaping the scrubber. The drop sizes were
12
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INLFT AEROSOL DISTRI PUT I ON
d(j (Geometric Mean Diameter) =
a_ (Geometric Standard Deviation) =
(Liquid/Gas Flow Ratio) «
(Pas Velocity)
(Surface Tension):
3
1/700
4000 cm/sec
35 dynes/cm
0.1 l.n ln.n
AERODYNAMIC DIAMETER, microns
Figure 3. Effect of surface tension on outlet particle concentration
for 20 pm particles, typical of flyash.
j
inn.o
78-011
-------
500 i-
400 -
UJ 300 -
o
o
?oo -
100 -
r .1
INLFT AEROSOL 01 STPr PUTTON
dg (Geometric Mean Diameter)
-------
Ul
1000
900
•-• 800
?nn
60P
500
400
300
?00
ac.
100
J I I 1 I
0.0'
INLET AEROSOL DISTRIBUTION
df, (Geometric Mean Diameter) =
o (Geometric Standard Deviation) =
^i_ (Liquid/Gas Flow Ratio)
0.
V (Gas Velocity)
o, (Surface Tension):
70
---- 35 dynes/cm
0.3 ftm
2
1/700
4000 cm/sec
I ill
J I I l l I i
o.? o. TO. /in.', i.n ,>,o i.o ".n r, ,r
AERODYNAMIC DIAMETER, microns
ir. 0
Figure 5. Effect of surface tension on outlet particle concentration for
0. 3 pm diameter particles, typical of cupola emissions.
-------
calculated using Equation 4 and are 173 and 143 microns for surface ten-
sions of 70 and 35 dyne/cm, respectively. The drop size does not decrease
by the square root of two as in Table 1 because of the presence of the surface
tension in the denominator of the second term in Equation 4. The outlet
concentrations decrease about 15 percent between 0. 5 and 1. 5 microns, a
relatively small change in comparison to Table 1. The smaller change in
penetration is due mainly to the smaller change in drop size. The re-
sults in Figures 3 to 5 are also typical of larger liquid to gas ratios and
higher velocities. Note that the development of nozzles which produce
smaller droplets have the potential of considerable improvement in scrubber
performance.
Coalescence Effects
It has been observed that when two droplets or a particle and a drop-
let collide they sometimes bounce apart (Jayaratne5, Schotland8, Lobl ,
Levin8). The most widely cited theory predicting whether coalescence
will occur is the film thinning model.
The model assumes that as a particle collides with a water droplet,
a thin layer of air or vapor is trapped between the particle and the deformed
surface of the droplet. This air layer prevents immediate coalescence.
The layer thins under the compression forces produced during the collision
process; however, thinning is opposed by the layer's viscous forces. If
the layer thins sufficiently before the colliding particle rebounds, the layer
ruptures and coalescence occurs.
One serious problem is that the calculations based on this model,
give results that are inconsistent with those observed by experiment. Sec-
ondly, due to the crude assumptions made in order to carry out the calcu-
lations, it is not currently possible to determine whether the inaccurate
results are due to simplifying assumptions or because the thinning layer
phenomenon is not actually the dominating process in coalescence.
The thinning layer model calculations are presented and discussed in
detail in Appendix A. The salient feature of the way these calculations are
performed is that the impact process is reduced to that of a simple harmonic
oscillator with a "spring" constant given by Equation 7.
16
-------
where R = particle radius
c = droplet surface tension
Pp = particle density
S = a constant which depends only on the shape of
the depression assumed to be made by the
impacting particle.
For the model used by Lang9 and Emory10 S = 1. Jayaratne's more
rounded depression is more realistic and gives an S = (1.6). The two
shapes are shown in Figure 6.
Viscous forces acting in the liquid may also be considered. Emory10
indicates that they are several orders of magnitude less than the calculated
surface tension forces, however, and they may be neglected for practical
purposes. Emory10 and Arbel11 also indicate that electric double layer
forces are smaller than the surface tension forces and can be neglected.
Coalescence is assumed to occur if the layer thins to a rupture thick-
ness 6 before rebounding. 6 is assumed constant. A condition for
coalescence may be derived and the result is shown in Equation 8,
BV< S-(? (8)
= particle radius
B = an approximate correction factor used if 6 is less than the
mean free path, X0; B = 0. 71 (6/Xo)[2 - 0. 71 (6/\o)]
V = Impact velocity normal to the surface
S = constant depending on the shape of the depression
in a water droplet made by an impacting particle
Note that Equation 8 predicts that given a sufficiently small velocity,
coalescence will always occur. However, above a certain velocity, V ,
depending upon R, the particle radius, coalescence will not occur.
V is obtained by dividing Equation 8 by R2 B:
max 7 ^
' v = | s — V *2 <9>
maX 3 u R2B
G
The rupture thickness may be estimated from theoretical or experi-
mental determinations. The fact that coalescence is impeded by increasing
impact velocity seems intuitively incorrect and experiments confirm this
17
-------
Model 1
Lang 9, Emory10
Model 2
Jayaratne6
Figure 6. Models for surface deformation
18
-------
intuition: Below a certain velocity, Vc, coalescence does not occur and
above Vc it does (Schotland6, Jayaratne5, List52). In addition, the time for
a colliding drop to rebound is strongly dependent on impact velocity as
shown by Jayaratne . The film thinning model described above predicts a
rebound time independent of velocity (since the period of a simple harmonic
oscillator is independent of its initial velocity). Lastly, the rupture thick-
ness 6 is in fact an arbitrary factor. Emory10 suggests 50 A while
Jayaratne suggests 1000 A. This difference makes a factor of 400 differ-
ence in Equations 8 and 9.
The idea that a particle traps an air layer which impedes coalescence
seems accurate intuitively, so the question remaining is what is wrong with
current thinning layer models. The answer to this question is currently
unresolved; however, the problems fall into three areas (or possibly a com-
bination of the three).
1. Film thinning may not be the dominant process. Significant evidence
exists to suggest this possibility. The most compelling results were
obtained by List12. Figure 7 shows coalescence efficiency for small
droplets impacting upon a water surface. The addition of small and
moderate amounts of acetic acid increases the coalescence at low
velocities. These results suggest that surface forces are dominant
and that, at least for low velocities, film thinning may not be a con-
trolling factor. The thinning layer model depends only upon liquid
density and square root of the surface tension of the liquid and these
factors vary only a relatively small amount in Figure 7. Note that
for a 5 percent acetic solution, coalescence occurred at all impact
velocities.
If smaller water droplets fall onto a clean water surface from low
heights, they float along the surface for a considerable length of
time13, much longer than appears accountable by the film thinning
model. Small amounts of detergent can greatly increase the life of
these floating globules. Again, surface forces appear responsible.
It is impossible to achieve the same effect with mercury drops on a
clean mercury surface; however, a small amount of oil (di octyl
phalate in this case) will stabilize small surface drops of mercury
indefinitely (personal observation). Lastly, it is posrible to create
an -"inverted bubble" in water14. If water is carefully dropped into a
dish of soapy water, a drop may submerge itself surrounded by a
thin layer of air. These "inverted" bubbles are stable until they
drift upward and break against the surface. If a slightly more dense
liquid drop is used it may sink and thus last for a considerable length
of time.
19
-------
€>©•
VCLOOTT (ntl")
Figure 7. Coalescence efficiency vs velocity of impact of
134H droplets impinging on 2.2 mm drops: a) dis-
tilled water, a=7? dyn cm"1; b) 0.5% acetic acid
solution, o=70 dyn cm 1; c) 5% acetic acid
-i
solution, o= 60 dyn cm . Curve c) also resulted
for distilled water when the drops were oppositely
charged. (List and Whelpdale, 1969)te
20
-------
An inverted bubble is shown in Figure 8. Again it appears that surface
forces and surface layers are the dominant mechanism in preventing
coalescence. Unfortunately, all of the above effects have been observed
with fairly large liquid drops. There is no direct evidence to shov.
•whether these phenomena occur between the solid and liquid particles
in a scrubber; however, since solid particles are likely to have an
adsorbed water film (or other adsorbed films) it seems that surface
effects similar to these may occur. Also, it is interesting from a
practical viewpoint, that a compound such as acetic acid appears to
greatly increase coalescence.
AIR
SUBMERGED
WATER
DROPLET
AIR FILM
77-3'. 1
Figure 8. Inverted bubble
21
-------
2. The assumptions used to calculate the film thinning model predictions
may have been too crude. The Reynolds formula16 is used to calcu-
late the time, t, for the trapped air layer to thin to a rupture thick-
ness, 6.
2
t T U_ -4: -T (10)
where
& = area of contact
FJ^J = force acting on particle normal to surface
U Q = absolute viscosity of air
6 = film rupture thickness
Figure 9 illustrates the important dimensions in the film thinning
model.
Figure 9. Film thinning model
77-361/1
Equation 10 is valid when ymax <0. 5 R, which will include most cases
of interest; however, it is also assumed in order to calculate the
thinning time, t, that the ratio of F to A2 is constant. This is simply
.10
not the case, in fact, for the models of Lang9, Emory1", and
Jayaratne6, the ratio of F to A is a constant:
F = yA,
11)
22
-------
vhere y is a constant depending only on the surface tension and particle
radius. Thus the ratio A2/F must be proportional to A which changes
from 0 to Amax (and back to zero if the particle rebounds). Before the
particle forms a trapped layer, the area A, is zero and the thinning
time. Equation 10, also becomes zero since AS/F is zero. Thus, the
model actually appears to predict that the thinning layer collapses
before penetration begins. This conclusion does agree with the data
shown in Figure 4 for the 5 percent acid solution. The problem in
Equation 10 is that the change of A with respect to F during the col-
lision process has been neglected.
3. Important factors may have been ignored in calculating thinning time.
All the calculations discussed above assume that the major forces act-
ing to decelerate the particle result from surface tension. Inertial
forces and the droplet internal pressure are neglected. In actuality
it is these very forces that are responsible for stopping the particle;
the surface tension acts to transmit these forces (to the thinning layer).
The surface tension also plays a role in absorbing energy from the
incoming particles since the surface stretches. It is likely that the
coalescence described by Equation 8 is inaccurate because these
forces are neglected. Unfortunately, it is difficult to include inertial
effects since the entire process such as the forces acting on the
particle through the thinning layer, the thickness of the thinning layer,
the flow fields in the droplet, and the form of the depression (not just
its relative dimensions) change with time and velocity, and are inter-
related. The set of differential equations describing the process and
the method of solution are complicated and would require extensive
calculations for solution. It is difficult to simplify the processes so that
meaningful estimates can be made. Yet, it appears essential that this
type of calculation be performed if the film thinning model is to be
properly evaluated. The results could easily show that the thinning
layer plays a minor part in preventing coalescence.
Another phenomenon which is normally neglected is the stability of
the thinning layer. While it does appear likely that a higher surface
tension causes the layer to thin more rapidly, increased surface
tension will also make the layer more stable. Lang9 has given the
stability a preliminary treatment but a more detailed study is needed.
In particular, it seems intuitively likely that the layer will break
down once the thickness at some point approaches the local mean free
path. Also, the inertial forces involved in collision are quite large
and these too act to decrease stability.
23
-------
SECTION 6
EXPERIMENTAL EVALUATIONS OF COALESCENCE THEORY
Simple laboratory experiments were devised to measure film thin-
ning times and the effects of surface energy on the thinning times. These
experiments were planned to evaluate, at least qualitatively, the film thin-
ning theory.
The impact and coalescence process for a water droplet and a glass
sphere (representing a fly ash particle)was observed with a high speed motion
picture camera looking through a microscope. The water droplets were
approximately 1000 to 3000 um diameter and were suspended on the end of
a microliter syringe needle. The glass spheres were made by drawing a
glass rod into a fine fiber and forming a ball on the tip end. The particles
ranged from 1 0 to 3500um diameter. The suspending rods were as small as
lOum diameter. Rods 10 nm diameter without a sphere on the end were
also used to simulate 10 um diameter particles.
The experimental setup is shown in Figures 10 and 11 . The support-
ing syringe and glass rod were mounted on three-dimentional micromanipula-
tors so that they could be moved independently within the field-of-view of
the camera. The glass particle was caused to impact the water droplet by
rapidly advancing the horizontal traverse mechanism of the particle support,
Figure 12. Radioactive polonium strips were mounted near the particles
and droplets to eliminate electrostatic charges. Radiation from the polonium
ionizes the air so that surface charges bleed off. Experiments without the
polonium tended to give more variable film thinning time measurements.
The camera used was a Beckman and Whitley Dynafax, operating at a top
speed of 26, 000 frames per second, with individual frame exposure times
of 2. 5 y,sec. The camera is a continuous writing rotating drum camera with
224 frames.
The camera speed was measured to within ±5 percent. A measure-
ment uncertainty of ±1/2 frame at each end of the thinning time measure-
ments introduces an additional potential error of ±39 ^i sec. A thinning
time of 1,000 ysec, therefore, has a random experimental variation of
approximately ±10 percent while a thinning time of 100 y, sec, has a random
variation of approximately ±50 percent.
24
-------
'-n
Syringe
Droplet
Support
Xenon
Flash
Lamp
ic 1®
Support
77-084
Figure 10. High speed cine microscope equipment used for experimental evaluation of
coalescence mechanisms.
-------
77-083
Figure 11. Glass rod with simulated flyash particle mounted on
traversing mechanism.
26
-------
Figure 12. Traversing mechanism for impacting particles into water droplets.
77-114
-------
Coalescence delay times were measured as functions of particle size,
impact velocity, and droplet surface tension. Film thinning time was taken
as the coalescence delay time; i.e., the time from first contact until a liquid
meniscus was first discernable. For example, in Figure 13 first contact
occurred on frame 9 and coalescence occurred on frame 24. The delay is
therefore equivalent to 1 5 frames at 39 H sec/frame, for a total delay time
of 585 yisec. The time per frame is determined from the camera "speed; at
26, 000 frames per second the time between frames is 39 jisec. The camera
speed was held constant at 26, 000 frames/sec for most of the experiments.
A summary of experimental variables is given in Table 2.
TABLE 2. EXPERIMENTAL, VARIABLES
Particle Size Range: 10 to 3500 ^m diameter
Droplet Diameter: 2 mm, nominal
Droplet Surface Tension: 72 (Distilled Water), 30 (1%
Triton X-l 00 in Water), 17.3
(Freon TF) dynes/cm.
Impact Velocity: 5 to 1 00 cm/sec.
Typical high speed motion pictures produced during the test pro-
gram are included in Figures 13 through 25. Table 3 summarizes variables
that are illustrated. The cases shown in the figures were selected to show:
1. The decrease in coalescence time resulting from a decrease
in particle size (Figures 13 - 18 )
2. The minimal change in coalescence delay time resulting from
a change in impact velocity (compare Figures 13 - 18 at 6 cm/
sec impact velocity with Figures 19 - 25 at 42 cm/sec).
3. The effect of surface tension in reducing coalescence delay
times (Figures 23 - 25).
28
-------
TABLE 3. EXPERIMENTAL VARIABLES ILLUSTRATED EN FIGURES 13-25
IN)
Figure
No.
13
14
15
16
17
18
19
20
21
22
23
24
25
Particle
Diameter
(Hm)
1700
1000
725
275
100
10
275
275
275
275
100
100
100
Impact
Velocity
(cm/sec)
6
6
6
6
6
42
42
42
42
42
42
42
42
Droplet
Composition
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Dist. Water
Freon TF
1% X-100 in
Dist. Water
Dist. Water
Surface
Tension
(Dynes/cm)
72
72
72
72
72
72
72
72
72
72
17.3
30
72
Remarks
No. 13-17 show the effect
of changing particle size.
No. 19-25 are replicate ex-
periments to demonstrate
reproducibility.
Homogeneous low surface
tension droplets.
Surfactant, low surface
tension water droplets
Distilled water for compari-
son with Figure 24.
-------
Figure 13. Coalescence of 1700 Um diameter glass
particle with water droplet, 585 Usec
delay, 6 cm/sec.
30
-------
Figure 14.
Coalescence of 1000 pm diameter glass
particle with water droplet, 780 psec
delay, 6 cm/sec.
31
-------
c
77-120
Figure 15. Coalescence of 725 Um diameter glass particle
with water droplet, 468 t^sec delay, 6 cm/sec.
32
-------
Figure 16. Coalescence of 275 Um diameter glass
particle with water droplet, 351 Usec
delay, 6 cm/sec.
33
77-121
-------
Figure 17. Coalescence of 100 pm diameter glass
particle with water droplet, 156 psec
delay, 6 cm/sec.
34
77-122
-------
m~'
W
• i
^^^•takl^^^^iMi^l ^^B
MM
i^L^—^ J Hi ;
HB»lMIM«.^Mrf ••
I i m . L.
^Bt_—.^^fci^*"*^^^^^"^* ^^^^^B
^^^^1 ^^^^^^^^ ^^
77-350
Figure 18. 10 pm diameter glass fiber impacting distilled
water droplet. Coalescence delay time <1 frame
(i. e. , <39 Psec).
35
-------
77-351
Figure 19.
Coalescence of 725 urn diameter glass particle
with water droplet, 273 usec delay, 42 cm/sec.
36
-------
BBIr ^H ^_^___^_—
77-345
Figure 20. Coalescence of 725 Um diameter glass particle with
water droplet, 234 Msec delay, 42 cm/sec.
37
-------
77-342
Figure 21. Coalescence of 725pm diameter glass particle with
water droplet, 273 psec delay, 42 cm/sec.
38
-------
77-347
Figure 22 - Coalescence of 725 Hm diameter glass particle with
water droplet, 234 psec delay, 4Z cm/sec.
39
-------
77-348
Figure 23. Coalescence of 100 pm diameter glass particle with
Freon TF, < 39 psec delay, 42 cm/sec.
40
-------
77-081
Figure 24. Coalescence of 100 pm diameter glass particle with
water/surfactant, < 39 psec delay, 42 cm/sec.
41
-------
Figure 25. Coalescence of 100 Urn diameter glass particle with
water droplet, 156 psec delay, 42 cm/sec.
77-076
42
-------
Delay time measurements for water droplets with an impact velocity
of 6 cm/sec are plotted as a function of particle diameter in Figure 26 for
comparison with theoretical predictions from the film thinning model of
Emory .
The experimental results are consistent and reasonably reproducible;
however, they differ from the theoretical predictions by as much as 2
orders of magnitude for larger droplets. For the large particle experi-
ments, the particles were nearly the same size as the water droplets. An
error could, therefore, be introduced by the false assumption that the drop-
let was large compared to the solid particle. Some of the random experi-
mental variation could also be due to uncontrolled parameters including
ambient temperature, relative humidity, water purity, and particle cleanli-
ness. No special control of these factors was made; however, because of
the limited ranges of variations they are not expected to have large effects.
Ambient temperatures ranged from 19 to 22° C (67 - 12° F). Relative
humidity ranged from 40 to 50 percent.
Figure 27 shows the results obtained when the velocity was increased
to 43 cm/sec. The dotted lines showing the range of scatter for the 6 cm/
sec velocity data are included for comparison. It appears that delay times
are slightly shorter at the higher velocity, especially for small particles.
The high velocity results were repeated using droplets of Freon-TF
instead of water. The Freon represents a homogeneous liquid with a low
surface tension, approximately 17.3 dynes/cm, (compared to 72 dynes/cm
for pure water). A homogeneous liquid was selected in order to minimize
the effect of the polarized Helmholtz double layer that is expected to be
present at the surface of water droplets containing a surfactant. The short
range molecular dipole forces in the double layer could have an effect on
coalescence that is separate from the surface tension effect by itself.
Results of the Freon coalescence measurements are given in Figure
28. It appears that the range of random variation in the measurements
is wider than for the water droplet coalescence measurements. None of the
Freon-TF delay times were longer than for water but some were consider-
ably shorter. Therefore, if there is an effect on a delay time due to the re-
duced surface tension of Freon-TF, the effect appears to reduce the delay
time.
Results of experiments using surfactants in water are given in Figure
29. There is insufficient data available to draw conclusions at this time,
however, it appears that if there is an effect on coalescence delay time due
to addition of a surfactant, the delay is shorter.
43
-------
a
H
U
2
Q
U
U
§
<
000
100
10
10
1
1
1
1
1
i
1
1
1
1
1
1
1 l\ 1
V
\ '
j \
i
;
.
**•*
1
i
1
J
i
1
y
\
^
\ i
\ ' '
\
\
\i
1
0 \(
Ko
\
i '
\
X
>
(
\ ,
i\ 1
\'
i
O »»ter
tt
6 em/«cc
1
\
. \
i \
,0 \
K
\i \
. ,
1
1
i
1 1 '
\
\
I K.
1 X
\
0 \
\
\
1 ' i\ »•
: ; • , \
| ; ! '
^r^ —
!
" S-^?'-v^
i
;
^N
*<^
1
t '
L.
^
•>*.
i
• —
^ —
\
\
\
\
*• —
"2 io"3 10
COALESCENCE DELAY TIME, second
Figure 26. Comparison of theoretical predictions and experi-
mental measurements of coalescence delay time
for water at 6 cm/ sec impact velocity.
44
-------
10,000
Jj 1,000
o
u
a
H
w
S
Q
w
o
H
«
2
•_«
o
o
XII l\.
SJ\ I
^
rV!-
\\
\
43 cm/>cc
! i^
^v
Vv
i v
^ \
V 1 \
I I
i
.
\
SM9
\
1 • !
loLU
COALESCENCE DELAY TIME, second
Figure 27. Comparison of theoretical predictions and
experimental measurements of coalescence
delay time for water at 43 cm/ sec impact
velocity.
45
-------
10.000
• 1,000
u
H
W
5
Q
U
O
P
05
100
10 • 10"" 10"4
COALESCENCE DELAY TIME, second
Figure 28. Comparison of theoretical predictions and experi-
mental measurements of coalescence delay time
for Freon-TF at 43 cm/sec impact velocity.
46
-------
10,000
c
o
u
U
H
U
2
5
Q
W
O
M
H
ct
1.000
100
COALESCENCE DELAY TIME, second
Figure 29. Comparison of theoretical predictions and experi-
mental measurements of coalescence delay time for
water droplets containing surfactant and an impact
velocity of 42 cm/sec.
47
-------
REFERENCES
1. Calvert, S. , Yung, S., Barbarika, H. , Venturi Scrubber Performance
Model. Air Pollution Technology, Inc., Final Report to U. S. En-
vironmental Protection Agency, Research Triangle Park, North
Carolina, 1976. 196 pp.
2. Bughdadi, S. M. , Effect of Surfactants on Venturi Scrubber Particle
Collection Efficiency, M. S. Thesis. Department of Thermal and
Environmental Engineering, Southern Illinois University of Carbon-
dale, 1973.
3. Nuykiyama, S. , and Tanasawa, Y. , Trans. Soc. Mech. Eng. (Japan)
4, 86, 138 (1938); 5, 62, 68 (1939); 6, II-7 11-15 (1939); 6, 11-18
(1940).
4. Wolfe, H. E. , and Andersen, W. H. , Kinetics, Mechanism, and
Resultant Droplet Sizes of the Aerodynamic Breakup of Liquid Drops.
Aerojet-General Corporation Report No. 0395-04 (18) SP, 1964.
5. Jayaratne, O. W., and Mason, B. J., The Coalescence and Bouncing
of Water Drops at an Air/Water Interface. Proc. Roy. Soc. , A(280):
545, 1964.
6. Schotland, R. M., Experimental Measurements Relating to the
Coalescence of Water Drops with Water Surfaces. Disc. Faraday
Soc., (30): 72, I960.
7. Lobl, E. L. personal communication, 1976.
8. Levin, Z. , Neiburger, M., and Rodriguez, L. , Experimental
Evaluation of Collection and Coalescence Effects in Cloud Drops.
J. Atmos. Sci., 30(1): 944-946, 1973.
9. Lang, S. B., and Wilke, C. R., A Hydrodynamic Mechanism for
the Coalescence of Liquid Drops. University of California, Berkeley,
California, 1971. 23 pp.
48
-------
10. Emory, S. , and Berg, J. , The Effect of Liquid Surface Tension on
Solid Particle-Liquid Droplet Coalescence. University of Washington,
Task Report to U. S. Environmental Protection Agency, Contract
No. 68-02-2109. May, 1977.
11. Arbel, N. , and Levin, Z. , The Coalescence of Water Drops, I. A
Theoretical Model of Approaching Drops, and II. The Coalescence
Problem and Coalescence Efficiency. Department of Geophysics and
Planetary Sciences, Tel Aviv University, Rarnat Aviv, Israel, 1977.
I. 25 pp. II. 25 pp.
12. List, R. , and Whelpdale, D. M., A Preliminary Investigation of
Factors Affecting the Coalescence of Colliding Water Drops. J. Atmos.
Sci., (26): 305, 1969.
13. Stong, C. L. , Water Droplets That Float on Water, and Lissajous
Figures Made with a Pendulum. Scientific American, August, 1973.
pp. 104-109.
14. Stong, C. L. , Curious Bubbles in Which a Gas Encloses a Liquid
Instead of the Other Way Around. Scientific American, April, 1974.
pp. 116-121.
15. Reynolds, O. , Phil. Trans. Roy. Soc., A(177):157 1886.
49
-------
APPENDIX
SURFACE TENSION EFFECTS ON PARTICLE COLLECTION EFFICIENCY
By
Scott F. Emory and
John C. Berg
Department of Chemical Engineering
University of Washington
Seattle, WA 98195
51
-------
ABSTRACT
Modifications in existing theory concerning the collection on non-
wet table or partially non-wettable particles in wet scrubbers are presented.
In particular, the requirement for the thinning and rupture of a gas film
between particle and liquid is included. Results suggest that decreasing
the liquid surface tension may decrease the probability of particle capture.
52
-------
Introduction
The commonly used models for the wet scrubbing of particulates from
gases assume that collision of the solid particles with the surface of the
scrubbing liquid always results in the capture of the particles (loldshmid &
Calvert, 1963). Such a view seems to be supported indirectly by tie gen-
eral success of predictions based on that assumption, of overall collection
efficiency of scrubbers removing a wide variety of particulates.
Nonetheless, the formal possibility of collision efficiencies less than
100% was acknowledged by Fuchs (1964), and seemingly valid reasons Were
advanced for supposing that all collisions should not necessarily result
in attachment. In particular it was believed that non-wettable particles
might simply be reflected if they did not penetrate the liquid to suffi-
cient depth to allow total envelopment. Pemberton (1960) developed predic-
tions of collection efficiencies for totally non-vettable particles (contact
angle = 180°) based on the above envelopment criterion, and McDonald (1963)
later extended the model to cases of partial non-wettability (90°" <
contact angle < 180°). The Pemberton-McDonald model implied that for given
solid particles the capture fraction, and hence the collection efficiency,
should increase if the surface tension of the collecting liquid is reduced.
The use of surface active agents might thus be advantageous in improving
collection efficiency, and indeed some reported results suggest that this
is the case (Hesketh, 1974; Rabel, 1965). Such increases in overall col-
lection efficiency might also be explained, however, by a greater degree
of atomization of the collecting liquid. Other results (Taubman &
Nikitina, 1956,1957; Drees, 1966; Goldshmid & Calvert, 1963) suggest, more-
over, that just the opposite occurs, i.e., collection efficiency falls when
53
-------
Che liquid surface tension is reduced. Still other reports (Weber, 1968, 1969]
claim no effect at all. In an attempt to resolve some of the above apparent
contradictions, and in particular to assess the findings of adverse effects
of surfactant, the present work re-examines the assumptions and development
of the Pemberton-McDonald theory.
Improved Model
Two significant shortcomings of the Pemberton-McDonald theory are that:
1) No allowance for the thinning of the vapor film between the
solid particle and liquid surface is made i.e., the film is assumed
to rupture immediately upon "impact", and
2) Rebounding particles, i.e, particles without sufficient kinetic
energy to produce total envelopment are thought to escape even
though coalescence has been assumed.
A more plausible sequence leading to particle capture is as follows.
Initially at least, a particle deforms the liquid surface inward while nested
in a thinning but unruptured vapor film. Short of complete envelopment, the
particle is caught if coalescence, i.e., vapor film rupture, occurs before
the particle comes to rest and rebounds. After coalescence, wettable
particles would reside in the droplet interior and non-wettable particles,
rather than escaping, would be retained in the liquid surface by surface
tension forces acting as dictated by small receding contact angles. This
new view is strongly supported by the work of Weber (1968, 1969) who observed
experimentally that reduction In particle wettability did affect the loca-
tion of the captured particle but did not prevent capture itself, which
occurred every time actual contact was observed between liquid and particle.
Thus an appropriate criterion for capture, in contrast to that of complete
54
-------
envelopment, is that the vapor film thinning proceed fast enough for
coalescence to occur during the particle penetration/rebound cycle. All
particles except those corresponding to the limit of total non-wetting
should be equally capable of capture regardless of their specific wettability,
provided only that the particle/liquid interaction time is greater than the
time required for the vapor film thinning. Predicted trends in capture
efficiency with fluid properties and system parameters should thus reflect
the trends predicted for the ratio of interaction time to film thinning
time, R. Large values of this ratio assure capture while values much less
than unity indicate no capture. Present knowledge of the details of the
film thinning process in particular is not adequate to permit quantitative
evaluation of the above ratio, but qualitative predictions of its trends
with such parameters as liquid surface tension, particle size and particle
velocity (relative to the liquid) should be possible if other factors are
assumed to remain unchanged.
The objective of the computations which follow is the prediction of
such qualitative trends, and while the models used for calculating both the
particle/liquid interaction time and the film thinning time are highly
simplified, we believe them to reflect the important features of both
processes.
An. approximate solution for the pa-ticle/liquid interaction time can
be obtained.by considering the vapor and liquid phases separately and
assuming the liquid surface at any instant to have the easily-described
shape shown in Figure 1. The particle is thus modelled as a smooth sphere
nested in a vapor filB of uniform thickness. The liquid surface is initially
flat, a good assumption since the collecting droplets are usually more than
a thousand times larger than the particles. We assume further that the
total force resisting deformation of the liquid surface is the sum of a
55
-------
surface tension and a viscous contribution so that the equation of motion
for the particle becomes:
with initial conditions (t - 0) : Z - -R and dZ/dt = V . Inertial effects
in the liquid are thus neglected. Neither Brownian motion nor slip between
the particle surface and the gas are considered so that the present treatment
is restricted to particle sizes larger than approximately 0.5 urn.
Referring to Figure 1, we write for the surface tension force
resisting particle entry:
F - 2iroR sin20 (20)
o
The viscous resistance to deformation will be a form drag only, ignoring
the viscosity of the thinning film in the computation of particle/liquid
interaction time. We assume provisionally that the drag experienced by the
vapor-enveloped penetrating particle can be approximated as the appropriate
portion of the drag on a completely submerged bubble moving with the same
velocity through an infinite medium in pseudo-steady creeping flow. For
this case, the pressure profile is (Levich, 1962):
p, • -v — j cos 8, (3)
from which
F^ - | iruRV [(|)3 + 1] , (4)
It is found that for all reasonable values of the system parameters, F is
at least three orders of magnitude less than ?Q. It thus appears to
contribute negligibly to the total force resisting particle entry, and
refinements in the computation of its value are unwarrented.
56
-------
The rate of thinning of a spherical film of vapor (air) has been
given by Lang (1962) in the form:
_
dt 4 »
24»R%alrP<9)
where P(0) - cos(ir-G) - 1 - 4 In [cos(^)]- The compressive force, F,
in Equation (5) is equal at any instant to the total force resisting penetra-
tion, viz., FO + F ~ F An estimate of the time for thinning to rupture
can be obtained by assuming that the rupture thickness, H, is very much
smaller than the initial thickness and that the compressive force is constant
with time and equal to the average penetration resistive force. We can then
write for the thinning time •
t - - P(6) - . (6)
F
o
In order to obtain numerical estimates of t, we assume further that rupture
occurs at a film thickness of 5oX [Ewers and Sutherland (1952) predict that
molecular fluctuations will guarantee rupture at this film thickness . ] and
that the angle 6 used in the calculation corresponds to the point of maximum
penetration depth.
Results and Discussion
Solutions of Equation (1) were obtained using the Runge-Kutta method, and
results for several values of particle size, velocity, and liquid surface
tension are shown in Table 1 and Figures 2 & 3. Table 1 shows the maximum
predicted extent of liquid surface indentation prior to either capture or
rebound, and it is seen that such deformation is typically very shallow.
Such a picture is at variance with the deep penetration capture models of
57
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Pemberton and McDonald for non-vetted particles but In agreement with
numerous published photographs of the particle/liquid interaction (e.g.,
Woffinden, et al., 1977). Trends in capture probability with surface tension a
particle size are most clearly seen in Figure 2 & 3. Decreasing surface
tension is seen to have a small negative effect on particle capture. As
surface tension is lowered, the penetration depth increases, enlarging the
area of the thinning film. The resulting increase in thinning time is
greater than that in the interaction time, providing a possible explanation
for an observed negative effect on collection efficiency of adding surfac-
tant to the liquid.
The computations also predict that small particles are more readily
collected than larger ones, but this result reflects the fact that the
particles have been taken as smooth spheres. For most particulates, this
assumption is not valid. Particles will usually be rough, and asperities
on the particle surface will produce local thin spots in the vapor film
leading to film collapse at much shorter times than predicted on the basis
of a uniform film. The minimum size of asperities on a particle surface
would probably be a more characteristic size parameter than the particle
diameter.
Finally, increased impact velocity is also seen to decrease the capture
probability. This is explained, as is the surface tension effect, by the
increase in-penetration depth leading to longer film thinning time.
Acknowledgement
This work was supported by funds from the Environmental Protection
Agency administered as a subcontract of Meteorology Research, Inc.,
Altadena, California. The authors are indebted to Dr. L.E. Sparks of EPA and
to Mr. G.J. Woffinden and Dr. D.S. Ensor of MRI for helpful discussions.
58
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Nomenclature
D B particle diameter, urn
F - compression force on vapor film, dynes
F - viscous force resisting particle penetration, dynes
FQ - liquid surface force resisting particle penetration, dynes
F « F averaged over the particle/droplet interaction time
H » vapor film rupture thickness, cm
M = particle mass, g
P(0) « dimensionless function of 0, defined in text
R « particle radius, cm
R « ratio of interaction time to film thinning time
V = relative velocity between particle and collecting drop, cm/sec
V = "impact" velocity (V at time zero), cm/sec
o
Z « particle penetration, cm (cf. Figure 1)
0 = angular measure of particle penetration
h = vapor film thickness, cm
p = pressure, dynes/cm
r B radial coordinate
t = time, sec
z « axial coordinate
6 = angular coordinate
V - liquid viscosity, poise
o » liquid surface tension, dynes/cm
59
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Literature Cited
Drees, W., Staub-Reinhalt. Luft. ^6, 31 (1966).
Ewers, W.E., Sutherland, K.L., Aust. J. Sci. Res.. Series A. 5^ 697 (1952).
Fuchs, N.A., The Mechanics of Aerosols, pp. 338-352, MacMillan, New York, 1964,
Goldshmid, Y., Calvert, S., A.I.Ch.E. J.. £, 352 (1963).
Hesketh, H.E., J. Air Poll. Control Assoc.. 24. 939 (1974).
Lang, S.B., A Hydrodynamic Mechanism for the Coalescence of Liquid Drops,
Univ. of California Lawrence Radiation Lab. Report No. UCRL-10097,
Berkeley, 1962.
Levich, V.G., Physiochemical Hydrodynamics, p. 395, Prentice-Hall,
Englewood Cliffs, 1962.
McDonald, J.E., J. Geophysical Res.. £8, 4993 (1963).
Pemberton, C.S., Int. J. Air Poll.. _3, 168 (1960).
Rabel, G., Neuhaus, H., Vettebrodt, K., Staub-Reinhalt. Luft. 25, 4 (1965).
Taubman, A., Nikitina, S., Akad. Nauk SSSR. 110. 816 (1956).
Taubman, A., Nikitina, S., Akad. Nauk SSSR. 116. 113 (1957).
Weber, E., Staub-Reinhalt. Luft. 28, 37 (1968).
Weber, E., Staub-Reinhalt. Luft. J9, 12 (1969).
Woffinden, G., Ensor, D., Markowski, G., Sparks, L., "Interfacial Surface
Effects on Particle Colection," Second Fine Particle Scrubber Symposium,
New Orleans, May, 1977.
60
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Captions to Figures
Figure 1. Coordinate system for particle penetration.
Figure 2. Ratio of interaction time to film thinning time, R, as a
function of liquid surface tension with particle diameter as
parameter (for an "impact" velocity of 7.6 cm/sec).
Figure 2. Ratio of interaction time to film thinning time, R, as a
function of "impact" velocity with particle diameter as
parameter (for a liquid surface tension of 72.A dynes/cm).
61
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TABLE 1
"Impact"
Velocity
(cm/sec)
7.6
it
it
it
tt
tt
35
64
Liquid
Surface Tension
(dynes /cm)
72.4
60
50
40
30
20
72.4
it
Penetration Depth/Particle Radius
8.2 x 10~3
9.0 x 10~3
9.8 x 10"3
1.1 x 10"2
1.3 x 10~2
1.6 x 10~2
3.8 x 10"2
6.9 x 10"2
Dimensionless penetration depths (penetration depth/particle radius) for
a 0.5 urn particle. (Impact velocities of 7.6 and 64 cm/sec are the
terminal falling velocities in air of 50 and 200 um water drops, respectively.)
-------
vapor
liquid
Fluid advances toward
particle with velocity, V.
FIGURE 1
63
-------
100.0
LJ
j| 10.0
0
=! 1.0
O
1 0.1
LU
0.01
D=0.5
D=1.0jjm
20 30 40 50 60 7O
LIQUID SURFACE TENSION (dynes/cm)
FIGURE 2
64
-------
100.0
LJ
o 10.0
UJ
1.O
o:
u
0.1
0.01^—l
10
= O.5jum
20 30 40 50
IMPACT VELOCITY (cm/sec)
60
FIGURE 3
65
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TECHNICAL REPORT DATA
(Please read Inunctions on the reverse before completing)
NO.
EPA- 600/7-78-097
2.
3. RECIPIENT'S ACCESSION NO.
J TITLE AND SUBTITLE
Effects of Interfacial Properties on Collection of
Fine Particles by Wet Scrubbers
5. REPORT DATE
June 1978
6. PERFORMING ORGANIZATION CODE
7 AUTHORIS)
G. J.Woffinden, G.R. Markowski, andD.S.Ensor
8. PERFORMING ORGANIZATION REPORT NO
MU 77 FR-1503
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Meteorology Research, Inc.
P.O. Box 637
Altadena, California 91001
10. PROGRAM ELEMENT NO.
E HE 62 4 A
11. CONTRACT'GRANT NO.
68-02-2109
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
Final; 6/75-12/77
PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/13
is. SUPPLEMENTARY NOTES JERL-RTP project officer is D.L.
541-2925.
Harmon, Mail Drop 61, 919/
16. ABSTRACT
The report gives results of an analysis of typical wet scrubber models to
determine the effects of surface tension on particle removal efficiency. Particle
capture (removal) is a two-step process: collision of a particle with a spray droplet,
and coalescence with the droplet. A change in surface tension of the scrubber water
can influence both steps. The coalescence process (after a particle collides with a
scrubber droplet) has been described by a film-thinning model that assumes that
coalescence is controlled by the thinning rate of an air or vapor layer trapped be-
tween an impacting particle and droplet. If the film thins and ruptures before the
particle rebounds, coalescence occurs. The thinning model predicts that a reduction
in droplet surface tension allows deeper particle penetration into the droplet. The
escaping vapor film therefore has a longer more resistive path, resulting in longer
thinning times, thus reduced coalescence probability. When the surface tension of a
scrubber liquid is modified, collection efficiency may be slightly improved or de-
graded depending on the spray droplet sizes and the sizes of particles being removed.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Dust
Scrubbers
Gas Scrubbing
Mathematical Models
Interfacial Tension
Efficiency
Coalescing
Air Pollution Control
Stationary Sources
Particulate
Removal Efficiency
13B
11G
07 A, 131
13H
12A
07D
14B
IS. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (TM* Report/
Unclassified
21. NO. OF PAGES
71
20. SECURITY CLASS (This page I
Unclassified
22. PRICE
EPA Form 2220-1 (»-73)
66
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