EFFECTS OF SURFACE PROPERTIES OF COLLECTORS
ON THE REMOVAL OF CHARGED AND UNCHARGED
PARTICLES FROM AEROSOL SUSPENSIONS
K. H. Leong, Research Associate,
Department of Civil Engineering and
Institute for Environmental Studies
J. J. Stukel, Professor,
Department of Civil Engineering and
Mechanical Engineering
P. K. Hopke, Associate Professor
Institute for Environmental Studies
Advanced Environmental Control Technology Research Center
&EPA
-------
The Office of Research and Development (ORD) of the U.S.
Environmental Protection Agency (EPA) has the responsibility
to produce scientific data and technical information on which
to base sound national policy in the development of effective
pollution control strategies and the promulgation of appropri-
ate environmental standards. As part of its program to meet
this responsibility, ORD established its Center Program in 1979
for the purpose of supporting long-term environmental research
in engineering and science. One of the first Centers estab-
lished was the Advanced Environmental Control Technology
Research Center (AECTRC), which is administratively located
under the Engineering Experiment Station of the College of
Engineering, University of Illinois at Urbana-Champaign. This
publication is an output of AECTRC.
Funding of AECTRC is provided under ORD/EPA Cooperative Agree-
ment CR806819. Mr. William A. Cawley, Deputy Director, EPA
Industrial Environmental Research Laboratory, Cincinnati, Ohio
45268, serves as Project Officer. The Director of AECTRC is
Professor R. S. Engelbrecht, Department of Civil Engineering,
University of Illinois at U-C, 208 North Romine Street, Urbana,
Illinois 61801.
Publication No. 81-2
September 1981
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EFFECTS OF SURFACE PROPERTIES OF COLLECTORS
ON THE REMOVAL OF CHARGED AND UNCHARGED
PARTICLES FROM AEROSOL SUSPENSIONS
by
K. H. Leong
Department of Civil Engineering and
Institute for Environmental Studies
J. J. Stukel
Department of Civil Engineering and
Mechanical Engineering
P. K. Hopke
Institute for Environmental Studies
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
US EPA COOP AGREE CR 806 819
September 1981
ADVANCED ENVIRONMENTAL CONTROL TECHNOLOGY RESEARCH CENTER
3230 NEWMARK CIVIL ENGINEERING LABORATORY
208 NORTH ROMINE STREET
URBANA, ILLINOIS 61801
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ABSTRACT
The literature on the adhesion of particles impacting on solid and
liquid collectors was reviewed. Different forces or mechanisms affecting
collision and adhesion of particles with collectors were described. Good
qualitative agreement existed between experiment and theory in the case
of solid collectors, although the presence of and variation in surface
asperities prevented good quantitative agreement. For liquid collectors,
disagreements both theoretical and experimental abounded in the literature
on the ability of such collectors to collect non or partially wettable
particles. The use of charge on drops in particulate control devices
has been shown to greatly enhance the collection of fine particles.
However, data indicate that too high a charge may lead to a decrease
in efficiencies due to Rayleigh instability of the drops and charge
exchange between particles and drops. A program of experimental and
modelling studies is proposed to resolve these difficulties in order to
be able to optimize control of particulate emissions for fine particles.
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CONTENTS
Abstract ii
Abstract
List of Figures and Tables
List of Symbols
IV
vi
1. Introduction 1
2. Summary and Recommendations 3
3. Adhesive Forces 5
Adhesion of Particles to Surfaces 5
Van der Waals Force 5
Electrical Double Layer Force 6
Capillary Force 8
Electrostatic Force 8
Gravitational Force 10
Other Forces ' 10
Relative Importance of Forces 10
Surface Effects 12
Adhesion of Particles Impacting on a Solid Surface 12
Adhesion of Particles Impacting on a Liquid Surface 18
Deficiencies in Theories on Adhesion of Particles 18
The Role of Surfactants in the Collection of
Nonwettable and Partially Wettable Particles 21
4. Collection Efficiency 26
Methods of Computation 26
Trajectory Method 28
Convective Diffusion Method 28
Collision Mechanisms 28
Diffusion 28
Electrostatics 29
Thermophoresis 31
Diffusiophoresis 31
Gravity Effect 32
Inertia Effect 32
Interception Effect 33
Sonic Agglomeration 33
Comparison of Forces or Mechanisms 33
Comparison Between Theory and Experiment 35
Particle Collection by Charged Drops 42
Limits in Charged Particle Collection 42
5. Proposed Studies 44
Experimental Studies 44
Adhesion Efficiency 44
Particle Wettability 46
Modelling Studies 49
Adhesion of Particles Impacting on a Drop 49
Collision Efficiency 52
Limiting Factors in Particle Collection by Charged Drops. . 52
Results and/or Benefits Expected 52
References 54
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LIST OF FIGURES AND TABLES
Figure 1. Experimental variation of the force between two curved mica
surfaces as a function of separation.
Figure 2. Adhesion of glass spheres to glass slides as a function of
relative humidity.
Figure 3. Variation in contact area between particle and surface for
different degrees of roughness.
Figure 4. Relative pull-off force for smooth rubber spheres in
contact with a flat Perspex surface as a function of the
roughness of the Perspexj effects of modulus of the rubber.
Figure 5. Computed maximum impaction energy and fraction of
uranine particles bounced for brass substrate.
Figure 6. Experimental and calculated values of the force on a
particle, nondimensionalized by the surface tension force,
as a function of the separation from the drop surface
nondimensionalized by the diameter of the particle.
Figure 7. Collection efficiencies for hydrophilic (ferrous sulfate)
and hydrophobic (paraffin wax) particles as a function
of the inertial impaction parameter (Stokes number).
Figure 8. Effectiveness of dust removal, r\, as a function of
pressure drop, Ap, in a venturi scrubber.
Figure 9. Effectiveness of dust removal by charged fog expressed as
dust concentration remaining after passage of fog.
Figure 10. Definition of collision efficiency.
Figure 11. Theoretical collision efficiencies for a 100 ym radius
water drop falling at terminal velocity in air.
Figure 12. Ratio of collection efficiency taking into account previous
particles collected on the collector surface compared to
the efficiency computed when the collector surface has no
adhered particles.
Figure 13. Collection efficiencies of metal spheres by Brownian
diffusion, interception and inertial impaction.
Figure 14. Collection efficiency of charged particles on a charged
sphere.
Page
7
9
13
14
17
19
22
23
24
27
34
36
37f
39
IV
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Page
Figure 15. Collection efficiencies of charged particles by charged
and uncharged spheres. 40
Figure 16. Collection efficiencies of manganese hypophosphite
particles by a 66 ym radius drop. 41
Figure 17. Experimental design for determining adhesion efficiency
of particles to drops. 45
Figure 18. Aerosol generating system. 47
Figure 19. Aerosol conditioning system. 47
Figure 20. Aerosol chamber design 48
Figure 21. Experimental design for determining contact angle of sphere. 50
t
Figure 22. Experimental design for determining wettability of powder. 51
Table 1. Adhesive Forces in Millidynes for Different Particle Sizes 11
Table 2. Comparison Between Theoretical and Experimental Adhesive
Forces Using the Centrifugal Method 15
Table 3. Definitions of the Dimensionless Parameters and the
Variation in the Radial and Angular Components 30
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LIST OF SYMBOLS
A drop radius
AH Hamaker constant
a particle radius
B particle mobility
C slip correction factor
DB Brownian diffusivity
D eddy diffusivity
Df fluid eddy diffusivity
D particle diffusivity
d diffusion .coefficient of vapor in gas
d particle diameter
E electric field
E collection efficiency
E surface energy
e adhesion efficiency
F capillary force
F electrostatic force
F Coulombic force
C\*
F ., electrical double layer force
F , electrical force
F . external force
ext
F gravitational force
F. image force
F ,w Van der Waals force
f dimension!ess radial component
F 9 dimensionless angular component
g gravitational acceleration
h flattening of sphere
J particle flux
Kr Coulombic electrostatic parameter
VI
-------
KD diffusiophoretic factor
K dimensionless electrostatic parameter
KS Stokes parameter
KT thermophoretic factor
k Boltzmann constant
k, diffusion slip coefficient
k sum of bulk mechanical properties of particle and surface
L characteristic length
In natural logarithm
m molecular mass of gas
g
m particle mass
m molecular mass of vapor
n particle number concentration
n. number of molecules per unit volume for body i
Q charge on sphere or drop
q particle charge
R radius of sphere or tube
r radial coordinate
S initial contact area of particle
T temperature
t time
U contact potential difference
U free stream velocity
ti fluid velocity
V velocity of drop
V,2 interaction energy between two molecules
v critical velocity for particle bounce
VD diffusiophoretic velocity
Vp particle velocity induced by external forces
v minimum normal velocity for particle penetration into drop
v^ settling speed
v<. velocity due to Stefan flow
VT thermophoretic velocity
^ particle velocity
y critical separation resulting in a grazing trajectory
vii
-------
z distance between nearest surfaces of two bodies
z minimum separation between surfaces
$12 London interaction constant
t collision efficiency
e permittivity of air
a
e.(i^) dielectric constant of material i along the imaginary axis
e. collision efficiency due to impaction
e. collision efficiency due to particle size
e weighted mean of static dielectric constant of adhering bodies
TT pi
cj> electron affinity
a charge density
a. surface tension
p fluid density
p particle density
p vapor density
r, dynamic viscosity
9 contact angle
'no) Lipshitz interaction constant
T relaxation time of particle
Y Euler's constant (= 0.5772---)
YT ratio of the thermal conductivities of the fluid to the particle
v kinematic viscosity of the fluid
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SECTION 1
INTRODUCTION
The amount of suspended particles in the atmosphere has very significant
impacts on the environment (NRC, 1980). Variability in the atmospheric
aerosol affects the earth's climate through modifications of the earth-
atmosphere radiation budget and the availability of condensation and ice
nuclei necessary for cloud formation. Adverse biological and material
impacts (e.g., sulphuric acid, smog) are caused by the physical and chemical
characteristics of the aerosol. Anthropogenic activities (e.g., coal-fired
boilers, automobiles) have led to the release of significant amounts of
particles into the atmosphere. Increases in the fine (1 ym radius) particle
content of the air poses possible serious health hazards because particles in
this size range can penetrate into the deepest reaches of the lungs. In addi-
tion, visibility is significantly degraded by the presence of minute amounts
of fine particles (Friedlander, 1977).
Both natural and anthropogenic sources contribute to the particulate
loading of the atmosphere. The former sources are estimated to contribute
approximately 2 x 1012 kg/year (Butcher and Char!son, 1972). This total
includes wind-blown and volcanic dusts, emissions from natural vegetation
such as pollen, spores, pine scents, and sea spray. The latter emissions
are primarily from industrial and automobile emissions, and dust from anthro-
pogenic activities such as mining and construction is estimated to be about
3 x 1011 kg/year. Although the relative contribution of anthropogenic
sources to total mass loading is small, the effects are significant and
largely detrimental. These effects may be localized as in air pollution
(e.g., smog) and decreased visibility (haze) or widespread as in acid rain.
The establishment of the National Ambient Air Quality Standards based on
the total suspended particulate mass in 1971 has led to a significant reduc-
tion in the total mass of suspended particles. Several particulate control
devices have been primarily responsible for this reduction in anthropogenic
emissions. They include fabric filters, electrostatic precipitators, and
scrubbers. These devices are very efficient in removing particles larger
than 1 ym radius, which make up the major bulk (mass) of the emissions. How-
ever, all these devices have a minimum in collection efficiencies in the par-
ticle size range of 0.1 to 1 ym (NRC, 1980). Hence, even though large reduc-
tions in the total mass of the emissions have been achieved, the control of
fine respirable particles (0.1 to 1 ym radius) has been deficient.
Recent studies have suggested, however, that the collection of fine par-
ticles can be greatly enhanced by utilizing electrostatic forces in particulate
1
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control devices (Drehmel, 1977). For example, charging the particles in a
spray scrubber increased the efficiency of collection for 0.3 ym particles
from 35 to 87% (Pilat, 1975). While there is considerable promise for the
use of electrostatic forces for the collection of fine particles, there are a
number of serious problem areas. For example, the literature suggests that
adhesion forces between the particles being collected and collector surfaces
are extremely important for wet collectors. Contradictory evidence exists,
however, concerning the nature of this interaction and the role of surfactants
in enhancing or inhibiting the collection of fine particles by wetted sur-
faces. Also, no adequate model exists to explain the observed behavior of a
charged or uncharged particle coming into contact with a charged or uncharged
droplet.
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SECTION 2
SUMMARY AND RECOMMENDATIONS
Optimization of participate control devices requires a clear understand-
ing of the basic collection process involved. The placement of charge on
collection surfaces in particulate control devices shows great promise for
the efficient control of fine particulates. However, the processes affecting
the adhesion of particles after collision with the collecting surface are not
well understood. The particle adhesion problem can be treated as a surface
energy problem. The difficulty is in determining quantitatively the contri-
bution of the various adhesive forces. For the case of a solid collecting
surface, the major difficulty is in the modelling of surface asperities and
deformation of the particles, although good qualitative agreement between
theory and experiment has been achieved. Even though further refinements in
the theory .are foreseeable, the variation of microscopic asperities with dif-
ferent collectors is a major barrier to the particle theory that could give
good quantitative results.
Particulate collection by liquid collectors is a substantially different
problem. Instead of deformation of the particle, the surface is deformed. In
addition, the liquid surface has no asperities. For wettable particles, the
primary factors in the adhesion of particles to the liquid surface are cap-
illary forces. For nonwettable particles, other forces can affect particle
capture. However, the literature on this area abounds with contradictions in
both theory and experiment. The addition of surfactants to the collecting
liquid would increase the wettability of the impacting particles and hence
would be expected to increase particle adhesion or collection; however, exper-
imental data have not been definitive. In addition, the use of charge to
increase collection efficiencies in control devices (e.g., charged droplet
scrubbers) has not been as effective as theorized. Formation of a coating of
nonwettable particles on the drop surface, Rayleigh instability of highly
charged drops, and charge transfer between particles and drop may be contrib-
uting factors.
Since the reduction of fine particulate emissions is an important goal,
these contradictions in the literature on the collection of particles by
liquid collectors should be resolved. To resolve these contradictions and to
gain a clearer understanding of the basic collection process, which is needed
for the optimization of particulate control devices, the following studies
are recommended:
1. Adhesion and Collection Efficiency: Experiments should be conducted to
determine the collection efficiency of charged drops (50 to 200 urn radius)
falling at terminal velocity for charged and uncharged fine particles
-------
(0.1 to 1 ym radius). The charge on both drops and particles should be
varied to study effects of different amounts of charge in relation to
Coulomb and image forces. Volatile (water) and nonvolatile (e.g., Dow
Corning 200) drops should be used to differentiate phoretic and surface
property effects. Hydrophilic and hydrophobic particles should be used
to discriminate the effects of wettability on particle adhesion. Effects
of particle shape and roughness should also be included. The adhesion
efficiency can then be derived from the ratio of the experimental collec-
tion efficiency to the theoretical collision efficiency.
2. Wettability: A separate experiment should be conducted to determine the
relative wettability of the particles used in the experiment and the
effects of size and roughness on wettability. In addition, the net
adhesion force acting on a sphere near a drop surface should be measured
to help in clarifying the model developed for particle adhesion.
3. Collision and Adhesion Efficiency: For comparison with the data obtained
from the above experiments, the collision efficiency of drops for par-
ticles should be modelled, taking into account electrostatic Coulomb and
image forces, inertia! impaction, phoretic forces, and Brownian diffu-
sion. Convective diffusion and trajectory computations should be used
to obtain the collision efficiencies with analytical and numerical flow
fields. A comprehensive modelling of the dynamics of the impaction pro-
cess3 including the dynamics after coalescence has occurred, should be
conducted to determine the important factors affecting adhesion.
4. Charged Particle Collection by Charged Drops: The factors optimizing
particle collection should be determined by a study of the effects of
charged drop instability and charge transfer between particle and drop
on collection.
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SECTION 3
ADHESIVE FORCES
ADHESION OF PARTICLES TO SURFACES
The problem of adhesion has been studied by numerous investigators both
experimentally and theoretically. Several review papers in this field are
available in the literature (Corn, 1966; Krupp, 1967; Zimon, 1969; Visser,
1972; Deryagin et al. , 1978). The adhesion of particles to a solid or liquid
surface or the "cohesion" of a particle to agother is subject to several kinds
of forces. These forces include the Van der Waals, electrical double layer,
capillary, electrostatic, and gravitational forces. These forces are deter-
mined to a large extent by the properties of the adhering surfaces and the
surrounding medium. A brief review of the nature and magnitude of these
forces will be helpful in determining their relative contributions to the
adhesion of particles. The review will concentrate on the problem of
interest: particle adhesion to flat or spherical surfaces in air.
Van der Waals Force
Electrical field interactions between or among molecules result in
attractive Van der Waals forces. These forces are usually differentiated
into orientation, induction, and dispersion forces, which are due to dipole-
dipole, dipole-induced dipole, and induced dipole-induced dipole interactions,
respectively (Krupp, 1967). For two interacting molecules, the energy of
interaction is
V12 = ~612/r6 (1)
where 3]2 1S the London interaction constant (London, 1937). For the case of
macroscopic bodies, two theoretical methods have been developed for estimating
the Van der Waals forces. The microscopic approach entails the estimation of
the Hamaker constant for all the interacting molecules in the adhering bodies.
The Hamaker constant is given by
2
AH12 = * nln2^12 ^
where n-j and n2 are the number of molecules per unit volume for the two inter-
acting bodies. The macroscopic approach of Lifshitz (1956) treats the Van der
Waals forces as the result of the interaction of the fluctuating electromag-
netic field in the adhering bodies. The Lifshitz interaction constant is
-------
(15)
for two bodies (1 and 2) separated by a medium (3), where ej(i?) is the
dielectric constant of material j along the imaginary frequency axis i
(Lifshitz, 1956). In vacuum e3(i£) = 1 and the Lifshitz interaction constant
is related to the Hamaker constant by
AH =
(4)
The latter approach is considered to be more accurate since fewer assumptions
are used. A comparison shows the Hamaker constants are larger than the
Lifshitz constants by about 10-25% (Nir, 1976). Values of the Hamaker con-
stants range from 0.03 180 x 10"13 erg (Visser, 1972; Nir, 1976), with
6 180 x 10~13 erg for ionic crystals, 14 46 x 10~13 erg for metals,
1 100 x 10~13 erg for hydrocarbons, and 5 - 45 x 10~13 erg for polymers
(Visser, 1972).
For two spheres of radii R-j and
Waals force is given by
A
separated by a distance z, the Van der
r 3 r M
FvdW ~ 37 C~ T2
w +wp+w w +wp+w+p
2
W+WP+W -
-2 - K -
w +wp+w+p
/_.»
(5)
where w z/(2R-|), p = Rg/R] , RI < R? (Nir, 1976). For the case of a sphere
of radius R] and a semi-infinite slab, the force is obtained from the above
equation by taking the limit R-|/R2 •*• 0, obtaining
FvdW = -AHR!/(6z) for z « 1
(6)
In general , the Van der Waals force between two surfaces is proportional to
z-(m) where m is the power law dependence (Israelachvill i and Tabor, 1973).
The above equations are valid for z < 200A. For larger separations, a retar-
dation effect occurs due to the finite time required for the interaction of
the electromagnetic fields (Krupp, 1967). The retarded force decreases as
(z)-(m+l). This is illustrated in Figure 1 where the force between two mica
surfaces was measured for different separations. The power law dependence of
the force changes from m to m+1 at about z = 200A.
Electrical Double Layer Force
These forces are due to the contact potential difference between the
adhering bodies (Krupp, 1967). The contact potential difference is the dif-
ference between the electron affinities of the two contacting bodies, i.e.,
U =
-
(7)
-------
10
10
10
8
o:
LJ
i-
LU
o:
UJ
O
(T
O
10'
LJ
O
(T
=>
CO
10'
10'
I
NONRETARDED
FORCES
RETARDED
FORCES
1
_L
10 20
_L
50 100 200 500
SEPARATION (A)
1000
Figure 1. Experimental variation of the force between two curved mica
surfaces as a function of separation. The force parameter is
such that the slope has a gradient (m+2) where m is the power
law dependence of the force (Israelachvilli and Tabor, 1973).
-------
For metals, a, the surface charge density is related to the contact potential
by
a = e U/z (8)
a
where ea is the, permittivity of air. For the case of a conducting particle
near a grounded conducting half-space, the attractive force assuming a con-
stant potential difference U is
Fedl ~ ^a1^/2 for z
Capillary Force
Different substances have varying degrees of affinity for water molecules.
Hygroscopic particles have a tendency to absorb water vapor even at relatively
low humidities and form a solution on the surface. These particles will be
completely wettable with 6=0° (see Equation 10). Non-hygroscopic particles
can be hydrophilic and have varying degrees of wettability but do not neces-
sarily strongly absorb water. Hydrophobic particles are nonwettable and have
little or no affinity for water.
In conditions of high humidity, condensation causes a liquid film to be
formed between a hygroscopic particle and the surface. For cases where the
adhesion between the particle and surface is small, the presence of the
capillary film may dramatically increase the particle adhesion to the surface,
especially for hydrophilic surfaces. The adhesive force is given by
F = 4TTO.R cos 9 (10)
w U
where at is the surface tension of the liquid and 9 is the contact angle
(Zimon, 1969). The presence of the capillary force is shown in Figure 2,
where the force of adhesion increased with humidity.
Electrostatic Force
The effect of charges placed on an insulating half-space has been deter-
mined by Krupp (1967) to be negligible compared to charges induced by contact
potential differences. For the case of a conducting half-space, an opposite
charge will be induced on the surface, resulting in the attractive image
forces given by
Fel = Q2/(16TTea(Y + ln(2R/z))2Rz/2) (11)
where y is Euler's constant (Krupp, 1967). For nonconducting bodies the
force will be smaller and can be approximated by
8
-------
110
i 1 1 1 1 r
90
O 70
LJ
X
Q
<50
o
O
30
10
10
I I I I
I I
J I
30 50 70 90
RELATIVE HUMIDITY (%)
110
Figure 2. Adhesion of glass spheres to glass slides as a function of
relative humidity (Bowden and Tabor, 1954).
-------
Q2
__
el 16TTE RS (Y+ln(2R/z)/2)(y+ln(2R/(z+S))/2)
a
where 6 is the sum of the boundary charge density layers of the sphere and
half-space (Krupp, 1967). Values range from 0 to 1 ym (Krupp, 1967). For
conductors 6 is zero and Equation (12) reduces to (11). After contact, the
maintenance of this electric force will depend on the resistance of the par-
ticle and the contact resistance. For total resistance less than 103 ohms,
particles will fail to hold their charge (Zimon, 1969).
Gravitational Force
Particles are subjected to the earth's gravitation, resulting in the
force given by
Fg = -mg = -4TTR3 ppg/3 (13)
where pp is the particle density. Gravitational attraction between two
adhering bodies is. much smaller than this force and hence can be ignored.
Other Forces
The forces described above may be termed long-range forces, compared to
the short-range nature of such forces as chemical bonding, sintering, diffu-
sive mixing, or alloy formation (Krupp, 1967). Chemical bonding between
adherents is a rare occurrence (Krupp, 1967), since the interacting surfaces
are usually chemically saturated, e.g., oxide layers. Sintering, diffusive
mixing, and alloy formation usually require elevated temperatures. Not much
theory or data are available on these forces, and since they are believed to
be of no great significance in most adhesion problems (Krupp, 1967), they
will not be included in the discussions below.
Relative Importance of Forces
The magnitudes of the Van der Waals, electrical double layer, capillary,
electrostatic, and gravitational forces for different particle sizes are
shown in Table 1. The values of the Lipshitz constant and contact potential
used are in the higher range of values. The particle charge Q corresponds to
values obtained by diffusion charging (Liu and Pui, 1977) for particles
smaller than 1 ym radius. For larger particles, a saturation charge associ-
ated with a field strength of 20 kv/cm is used. A nominal value of 65 dynes/
cm for the surface tension of water is used. From Table 1, it is evident
that electrostatic forces are significant for particles larger than 10 ym and
gravitational forces become significant only for particles larger than about
1 mm. For wettable or partially wettable particles, capillary forces, if
present, are dominant. Otherwise, Van der Waals and electrical double layer
forces are dominant.
10
-------
TABLE 1. ADHESIVE FORCES IN MILLIDYNES FOR DIFFERENT PARTICLE SIZES
Particle
Radius
(urn)
10,000
1,000
100
10
1
0.1
0.01
Van der Waals
wR
8-rrz2
160,000
16,000
1,600
160
16
1.6
0.16
Electrical
Double Layer
z
43,000
4,300
430
43
4.3
0.43
0.043
Capillary
4ira.R cos 6
580,000
58,000
5,800
580
58
5.8
0.58
Electrostatic
Q2
16™- [Y+0.51n(2R/z);pRz
a
450,000
4,500
45
0.45
7.1 x 10~3
3.9 x 10-"
3.0 x ID'1*
Gravi
8,200
8
8.2
8.2
8.2
tational
,000
,200
8.2
0.0082
x 10-6
x ID'9
x 10-12
Values of variables used are: z = 4 x 10"1* um, liw = 4eV, U = 0.5eV, a. = 65 dynes/cm, 6 = 45°,
p = 2g/cm3, g = 980cm/s2, ea = 8.84 x 10~12, Q = 1.6 x 10~19C x (particle radius/0.01 um)
for diffusion charging (R £ lum), Q = 1.6 x 10~l9 x 500 x (particle radius/lym) for
field charging (R > lym),y = 0.5772.
-------
Surface Effects
The discussion above has been for idealized smooth solid bodies. In
reality, surfaces possess a certain degree of microscopic or macroscopic
roughness. The surface roughness will affect the area of contact and, hence,
increase or decrease the adhesion. For example, in Figures 3b and 3c, the
surface roughness decreases the area of contact of the particle with the sur-
face and decreases the adhesion, whereas the adhesion in Figures 3d and 3e is
increased (Zimon, 1969; Tabor, 1977). In addition to roughness, the adhesion
is affected by contact deformation between adhering bodies, which increases
the area of contact (Tabor, 1977). Figure 4 shows these effects of surface
roughness and degree of contact deformation on the adhesion of rubber spheres.
The relative detaching force is measured as a function of the center line
average of the asperities which is a measure of the roughness of the surface.
For a given rubber sphere the force decreases for increasing roughness
(decreasing contact area). With a lower value of the modulus the rubber was
softer and deformation was greater. Hence, with the increase in contact area,
a greater detaching force was needed.
For the case of the adhesion of solid particles to a liquid surface, sur-
face tension and wettability of the particle (Morishima and Kariya, 1978) will
be primary factors, while surface roughness of the particle will be secondary.
Alternatively, the effects of all the surface forces can be treated together
and the adhesion considered as the result of surface energy (Deryagin et al. ,
1978), resulting in the force needed to detach particles from the surface as
F = 4irREs where Es is the surface energy.
The measurement of particle adhesion to a flat surface has been achieved
by the use of the centrifuge method, where the force of adhesion is determined
from the surface. Due to surface asperities (roughness), not all particles
will be detached at a given force. However, reasonable agreement between
experiment and theory has been obtained for the force required to remove 50%
of the particles on the surface (Krupp, 1967), which is shown in Table 2. The
data in Table 2 also show the decrease in adhesion when the roughness of the
particle increases. A substantial amount of these data on different particles
and surfaces has been obtained using this method (Krupp, 1967). Other methods
employed gravitation, vibration, electrostatics, or a microbalance (Visser,
1972). However, this type of experiment generally does not give much insight
into the more practical problem of determining whether particles will stick
to a surface after impact.
ADHESION OF PARTICLES IMPACTING ON A SOLID SURFACE
Recently, there has been substantial research on particle bounce as
applied to impactors. Dahneke (1971, 1972, 1973) modelled particle bounce as
a function of the elastic deformation of the particle on impact using Hertzian
theory on the deformation. Flattening of a spherical particle was found to
contribute an additional term to the Van der Waals forces and the adhesive
force was given by
F = AHR (1 + AH2kyR/(54 zQ7))/6 zQ2) (14)
12
-------
(a)
(b)
(c)
(e)
Figure 3. Variation in contact area between particle and surface for
different degrees of roughness.
13
-------
0
0.5 1.0
CENTRE LINE AVERAGE
Figure 4. Relative pull-off force for smooth rubber spheres in contact with
a flat Perspex surface as a function of the roughness of the
Perspex; effects of modulus of the rubber: curve 1, 2.4 x 106
N nT; curve 2, 6.8 x 105 N m~2; curve 3, 2.2 x 10-5
(Fuller and Tabor, 1975).
m
'2
14
-------
TABLE 2. COMPARISON BETWEEN THEORETICAL AND EXPERIMENTAL ADHESIVE FORCES
USING THE CENTRIFUGAL METHOD (Krupp, 1967)
COMPARISON BETWEEN THEORY AND KXPERIMBNT
1 'a rt icle- Pa rl icle
siibstfdte vndi its /i
(/mi)
•c (reduced) - 2
•"e (reduced)
•"c (reduced) - 2
•"c (oxidised)
'"e (oxidised)- 2
Fc (oxidised)
Au-r|iiartz 3
(rou^'h)
(smooth) 3
An -plastic 3
films
Order of magnitude of
radii of curratiirc of
asperities (/tin)
Particle
0.7
0.7
0.1
0.1
0.1
0.1
Substrate
0.1
0.1
0.1
0.1
0.1
0.1
Effective
radi us J\
(/'»>)
0.7
0.1
0.05
0.1
3
0.1
Intimated values
Hardness
Particle
10"
10"
1 0"
10"
10"
10"
,
(dyn/cin-)
Subs/rale
10"
10"
10"
10"
10"
10-
hw
ff V 1
( e ' )
8
8
8
H
5
5
25
Adhesive i'urcc (ind\n)
calculated median
22 20
3 4
1.5 2
? 11
96 1 00
80 100-250
Litef
-------
where k is the sum of the bulk mechanical properties of the particle and the
surfaced Values of ky range from 0.436 x 10~12 cm2/dyne for steel to
27.5 x 10~12 cm2/dyne for polystyrene (Dahneke, 1972). It was concluded that
elastic deformation of particles increases the minimum velocity for particle
bounce. Dahneke's results were later confirmed by Esmen et al. (1978). The
fraction of particles that bounced was found to increase with increasing
impaction energy, as shown in Figure 5 for uranine particles impacting on a
brass plate. Cheng and Yeh (1979) obtained an empirical relation for the
critical velocity for particle bounce where
vc < B x 10-6/(dp(pp/pJ0'5) (15)
where B is an empirical constant having a value between 2.5 and 9.2, dp is the
particle diameter, pp is the particle density, and p* is unity density. Hence
for a given impacting velocity, larger particles are more susceptible to
bounce.
However, close examination of Dahneke's theory, which ignores electrical
double layer forces'by Derjaguin et al. (1975), has revealed several major
inconsistencies. The more rigorous theory put forward by Derjaguin et al.
shows that the force needed to detach a particle is independent of the defor-
mation, if electrical double layer forces are not considered. The correct
expression for the Van der Waals force was found to be
F = AHR/(6zQ2) + (4R°-5/(3ky))hK5 (16)
where h is the distance between the penetration of an imaginary undeformed
sphere, at the same position as the deformed sphere, into the surface and the
closest approach of the deformed sphere to the surface. Hence, the dependence
of the force of adhesion on the elastic deformation of the particle is unclear.
The dependence of the detaching force on the square of the radius of the par-
ticle is actually a result of electrical double layer forces, which depend on
the area of contact. According to Deryagin et al. (1978), the electrical
double layer force between a sphere and a flat plane is
Fedl < 2m?2s (17)
where S is the initial contact area. An examination of this electrical
double layer force and the molecular component of the adhesive force shows
that the two are comparable. However, the total energy expended to detach
particles is an order of magnitude higher for the electrical double layer
force, assuming no neutralization, since this force does not decrease as
rapidly with separation as the molecular component of the force. The assump-
tion of no neutralization will hold for dielectric or nonconducting particles.
Hence, the factors of significance in determining adhesion or particle bounce
on solid surfaces are the electrical double layer and molecular forces, the
16
-------
10 " -
Brass substrate
O.I 02 0.3 0 4
( Fraction bounced) "
0 5
Figure 5. Computed maximum impaction energy and fraction of uranine particles
bounced for brass substrate (Esmen vt at., 1978).
17
-------
elasticity or degree of deformation of the particle or surface, the surface
textures or characteristics of the contacting bodies, and the velocity of
impact.
ADHESION OF PARTICLES IMPACTING ON A LIQUID SURFACE
The process of particle impact on a liquid surface differs considerably
from the case for a solid surface. Wettability is the dominant factor, since
nonwettable particles may not adhere. Depending on the energy of impact, the
liquid surface is deformed considerably. Theory and well-defined experiments
on the problem are lacking and contradictions abound in the available litera-
ture (Stulov et al., 1978).
The only available measurements on the adhesive force of a liquid drop
with different surface curvatures on spheres with varying degrees of immer-
sion into the liquid surface are those of Morishima and Kariya (1978). The
force on the particle varied with drop to particle size ratio and contact
angle as shown in Figure 6. A larger force was needed to pull the particle
from the drop surface for more wettable particles (smaller contact angle).
However, this static measurement of the force will not reveal the intricacies
of the dynamic process of a particle impacting on the liquid surface.
Deficiencies in Theories on Adhesion of Impacting Particles
Pemberton (1960) treated the problem of the capture of a completely non-
wettable particle (6 180°) impacting on a drop in terms of the ability of a
particle to completely penetrate into the fluid. Only surface tension forces
were considered, and the particle was assumed to bounce off if complete pene-
tration was not achieved. Different angles of incidence of the particle on
the fluid surface were taken into account, and it was found that for complete
penetration a particle required a normal velocity to the fluid surface of
v 0 5
v = (8a.,/(p d )) (18)
where a^- is the surface tension of the fluid. McDonald (1963) extended
Pemberton's theory to particles with contact angles (6) less than 180° result-
ing in
vpn = (8otcosU-e)/(ppdp))°'5 (19)
His computations showed that particles with contact angles less than 90°
would penetrate into the fluid. For a completely nonwettable particle (6 =
180°) Equation (19) reduces to (18). Equation (19) shows that a particle
with a contact angle less than 180° needs less kinetic energy to penetrate a
fluid surface than a completely nonwettable particle. For contact angles
less than 90°, vpn is negative. This means that a wettable (9 < 90°) particle
need not expend energy to penetrate the drop. Hence, adhesion problems exist
only for nonwettable particles with contact angles larger than 90°.
18
-------
i.O
b
o
1=
CVJ
0.5
CONTACT ANGLE
A (/j.m)
o.o
33.7 123.7
88
31
143
6629
6006
4362
0
-1.0
-0.5
0
S/D
0.5
1.0
Figure 6. Experimental and calculated values of the force on a particle,
nondimensionalized by the surface tension force, as a function
of the separation from the drop surface nondimensionalized by
the diameter of the particle (Morishima and Kariya, 1978).
19
-------
The Pemberton-McDonald theory is a rather crude model for predicting
particle adherence to a drop and has several deficiencies. Effects not con-
sidered by the Pemberton-McDonald theory include the following:
1. For partially wettable particles, some degree of adhesion may
occur and the particle may adhere to the surface even if no
penetration occurs.
.2. The dynamics of the impaction process, such as the viscous
interaction of the particle before coalescence with the liquid
surface, and the interactions after coalescence, such as
processes promoting escape of particles from the surface
(reentrainment), are not accounted for.
Allen (1975) modelled the particle surface interactions in terms of the
energy of the impacting particle. A captured particle would lose all its
energy while a rebounding particle would not. The computations were carried
out for particles larger than 10 urn radius. Taking into account viscous
interactions, Allen concluded that all particles that did not penetrate into
the drop rebounded and that Van der Waals and electrostatic forces were
negligible. Emory and Berg (1978) attempted to improve the theory by using
the film thinning theory, which has been widely used in predicting drop-drop
coalescence (Arbel and Levin, 1977). The particle was assumed to coalesce
when the air film separating particle from drop surface thinned to a minimum
thickness. Once coalescence occurred, the particle was assumed to be col-
lected by the drop. To determine coalescence, the film thinning time was
compared to the particle drop surface interaction time. Results obtained
were contrary to the predictions of the Pemberton-McDonald theory. A
decrease in surface tension of the liquid by the addition of surfactants led
to an increase in the film thinning time. This increase implied a decrease
in adhesion efficiency. An increase in the impact velocity led to the same
conclusion. The film thinning model depends on the definition of the minimum
separation between particle and drop surface when coalescence will occur.
This definition has been rather arbitrary, and Emory and Berg (1978) used a
value of 5 nm while Jayaratne and Mason (1964) used 100 nm. Another defi-
ciency of this model is that the assumption of particle capture once coales-
cence has occurred may not be valid since a particle impacting at an oblique
angle may coalesce but have enough energy to "tear off" after coalescence.
In addition, particles impacting on particles already adhering on the surface
may bounce off or cause the adhering particles to escape.
For particles less than 1 ym radius, the net adhesion force that has been
neglected in the theories for large particles given above, has to be con-
sidered. For hydrophilic or wettable particles, the capillary force is the
dominant adhesion force (Table 1). For hydrophobic (partially wettable or
nonwettable) particles, the capillary force will be small or even negligible.
The dominant force will then be the Van der Waals force. Due to the par-
ticles' hydrophobic (nonwettable) nature, the Van der Waals force will tend
to be low. Hence, there is a substantial difference of about an order of
magnitude in the net adhesion force between the case of a hydrophilic particle
and a hydrophobic particle. Particle wettability may then also be a factor
in particle adhesion for submicron particles.
20
-------
The Role of Surfactants in the Collection of
Nonwettable and Partially Wettable Particles
The literature on the collection of particles that are not completely
wettable abounds with conflicting conclusions and interpretations. The
Pemberton-McDonald theory predicted low adhering efficiencies. Experimental
works by McCully et at. (1956), Oakes (1960), Goldshmid and Calvert (1963),
and Allen (1975) confirmed this tendency. The decrease in collection effi-
ciency of hydrophobic particles is shown in Figure 7. For hydrophilic fer-
rous sulphate (completely wettable) particles, there is relatively good
agreement between the experimental data and the theory, whereas the experi-
mental collection efficiency of hydrophobic paraffin wax particles (contact
angle 102°) is only about half the predicted collision efficiency values.
Agreement with theory was also obtained with particles of methylene blue and
water and lower efficiencies were obtained for hydrophobic particles of oil,
OOP and talc. However, Weber (1968) observed in his work with glass spheres
(10 urn radius) that all spheres with different wettabilities stick on impact
on a drop. This inconsistency was explained by Stulov et al. (1978), who
noted that nonwettable particles adhered to the drop surface on impact and
consequently formed a layer on the surface, causing bounce-off of particles
impacting later. Stulov's work is not definitive since only particles
larger than 5 ym diameter were used. Weber's and Stulov's work indicated
that the Pemberton-McDonald theory is invalid. Allen (1975), however, con-
cluded that the layer of particles formed on the drop surface was actually
the consequence of particles first penetrating the drop surface and then
being brought to the surface, due to the nonwettable nature of the particle
and the internal circulation of the fluid inside the drop.
In attempts to increase collection efficiencies, surfactants were used
to decrease the surface tension of the drop. Goldshmid and Calvert (1963)
and Rosinski et al. (1963) observed that collection increased with increases
in wettability. In addition, the results of Goldshmid and Calvert (1963) and
Montagna (1974) indicated that collection decreased for particles with con-
tact angles less than 90°, contrary to McDonald's (1963) findings. In scrubber
studies, Rabel et al. (1965), Bughdadi (1973), Hesketh (1974), and Fainerman
and Levitasov (1976) obtained positive results. This is illustrated in
Figure 8, where the effectiveness of smelter dust removal was measured as a
function of pressure drop in the Venturi scrubber used (Fainerman and
Levitasov). Significant increases in dust removal were obtained using a sur-
factant that wetted the smelter dust. A decrease in efficiency was obtained
using 0.08% heptyl alcohol, which did not wet the dust. In addition,
Woffinden et al. (1978) looked at the coalescence delay time of a glass rod
with a water drop and the results indicated that surfactants decrease the
delay time, promoting adhesion efficiency. However, scrubber studies by
Taubman and Nikitina (1956) and spray collection by Hoenig (1977) found
insignificant or negative effects on the collection efficiencies. The effect
of using a glycerine water mixture (Figure 9) was found to have a negative
effect on dust removal by charged sprays (Hoenig). However, the ability of
the mixture to wet the dust was not measured. The observed increases in col-
lection efficiencies by the addition of surfactants may be plausibly explained
by the increase in wettability of the particles leading to immersion of the
particles into the drop and eliminating the formation of a particle layer on
21
-------
ro
no
^1.0
UJ
O
U_
LU
0.8
O
h-
o
UJ
o
o
0.6
g 0.4
h-
o
o:
• ferrous sulfate a =6.2, 5.4
850/im< A
-------
100
80
60
40
20
1.0 2.2 3.4 4.6 5.8 7.0
AP
Figure 8. Effectiveness of dust removal, n» as a function of pressure drop,
Ap, in a venturi scrubber. 1) 0.08 heptyl alcohol solution,
2) water, 3) and 4) 0.15% and 0.3% oxyethylenated dibutylphenol.
23
-------
DUST
mg /
DENSITY
II
10
8
CRUSHER DUST
STEEP ROCK IRON MINE
ATIKOKAN , ONTARIO CANADA
AIRFLOW 100 SCFH
FOG WATER FLOW 30 ml / min
'DUST WITH UNCHARGED FOG
'INITIAL DUST LEVEL
.DUST WITH (-) CHARGED FOG
AND GLYCERINE 50% v/v
DUST WITH (-) CHARGED FOG
DUST WITH (+) CHARGED FOG
"AND GLYCERINE so % v/v
DUST WITH (4-) CHARGED FOG
2 3
PARTICLE
45678
DIAMETER { MICROMETERS )
Figure 9. Effectiveness of dust removal by charged fog expressed as dust
concentration remaining after passage of fog (Hoenig, 1977).
24
-------
the drop's surface (Stulov et at., 1978). The observations of negative or
insignificant surfactant effects may be the result of the surfactants affect-
ing the size distribution of the drops (Woffinden et at. , 1978). However, an
understanding of the basic relevant processes based on definitive data col-
lected from well controlled experiments is definitely lacking, especially for
fine particles.
25
-------
SECTION 4
COLLECTION EFFICIENCY
The previous sections reviewed the problems in the adhesion of particles
impacting on surfaces. For a thorough comprehension of the process of par-
ticles capture by surfaces, the forces or mechanisms that influence the
motion of the particles to the surface need to be considered. These forces
and mechanisms affect the collision efficiency of the collector for particles,
e.g., collecting plates or charged drops in a particulate control device.
The collision efficiency of a collector for aerosol particles is defined
as the ratio of the number of particles that collide with the collector to
the number of particles passing through the collecting system or swept out
geometrically by the collector (drops). For the case of drops, the collision
efficiency is
e =
ds/U(A+arVn)
(20)
where J is the particle flux, A and V are the radius and velocity of the
collector drop, a is the radius of the particle, and n is the particle con-
centration. For computational convenience, an effective collision area yc is
usually defined as shown in Figure 10, where the separation yc results in a
grazing trajectory. The collision efficiency is then
(yc/(A+a))'
(21)
The collection or capture efficiency, the product of the collision and the
coalescence or adhesion efficiency, e, is
(22)
METHODS OF COMPUTATION
There are two methods used to compute the collision efficiencies of
drops.
26
-------
COLLECTOR
DROP
= RADIUS OF GEOMETRIC
CROSS SECTION
yc = RADIUS OF COLLISION
CROSS SECTION
Figure 10. Definition of collision efficiency.
27
-------
Trajectory Method
This method is used for particles with significant inertia, with radii
usually larger than about 0.5 ym radius. The trajectory of a particle
towards the drop is computed ignoring the small contribution of the particle
to the total fluid field. The force balance equation for a particle of
radius a in the flow field of the drop is given by
(23)
where C is the slip correction factor. Starting the particle at an adequate
distance away, the trajectory of the particle is integrated numerically,
using the external forces on the particle and the flow field of the drop.
The collision efficiency is then computed from the critical displacement, yc,
of the particle, which gives a grazing trajectory.
Convective Diffusion Method
With this method, particles must be small enough so that their inertia
can be neglected. The efficiency is computed from the particle flux, which
consists of a diffusional component, a drift component induced by external
forces, and an advection component
-*• .». _». +
J = -D vn + nv + nu (24)
where vp = BFgXt Wltn B = C/(6-rma) being the mobility of the particle. The
collision efficiency is evaluated using Equation (1) and the continuity
equation for the particle concentration
|£ = - $ • J = 0 (25)
These two methods can be similarly applied to collectors other than spheres
such as parallel plate precipitators. The first method is suitable for lami-
nar flow, and the second for turbulent flow where an eddy particle diffusivity
can be used. A brief review of the basic mechanisms affecting collection
efficiencies will be helpful in determining the dominant forces in a particu-
lar system.
COLLISION MECHANISMS
Diffusion
The first term on the right hand side of Equation (24) results from
particle diffusion where
28
-------
Dp = DB + De (26)
Brownian diffusion, Dg, and eddy diffusion, De (from turbulent motion), of
the particle contributes to the total diffusion coefficient. The Brownian
diffusion coefficient is given by the Stokes-Einstein expression,
DB = BkT = CkT/(6irna) (27)
where B is the mobility of the particle (Hidy and Brock, 1970).
Eddy diffusivity varies with turbulence intensity. According to Liu
and Ilori (1974), particle eddy diffusivity can be expressed as the sum of the
fluid eddy diffusivity Df and a component from the product of the square of
the root mean square velocity and particle relaxation time, x.
De Df + v2 T (28)
Particles can also be captured by the presence of rear eddies (Beard, 1974;
Wang, 1978). For drops, eddies form at about a drop Reynolds number of 20.
For Reynolds number over 300, particle capture is impeded by the fast shed-
ding of the eddies.
Electrostatics
The force on the particle near a charged conducting collector sphere due
to the electrostatic force can be expressed as
Fe = 6Trna/C(U0 E k^f/ + ffi8)) (29)
where U0 is the free stream velocity, ke-j are the dimensionless constants
resulting from the Coulomb, image, and dipole forces, and fer and fee are the
dimensionless radial and angular components, respectively (Nielsen and Hill,
1976). The expressions for the electrostatic parameters are shown in Table 3
(Nielsen and Hill, 1976). The dominant force when both particle and collector
are charged is the Coulomb force which is
F = -^- (30)
4ire r
a
For the case where the collector is a spherical water drop the above equations
are also applicable (Davis, 1969).
29
-------
TABLE 3. DEFINITIONS OF THE DIMENSIONLESS PARAMETERS AND THE VARIATION IN THE
RADIAL AND ANGULAR COMPONENTS (Nielsen and Hill, 1976)
e Force Fe Description Parameter" Ke Radial component // Angular component ff°
c Coulombic force Both collector ^,Q Q
and particle Kc= — I/ft2 0
are charged. 247rJefftpftc2/jC/0
ic Charged-particle Particle only is
image force charged. Charge __ ,
separation in- v ^c ^P \Ritp* i\»_i/p3i n
ducedincol- X|C' 24ir'efRpfleWo '
lector.
ip Charged-collec- Collector only
tor image is charged. „ gQ 2^ :
force Charge sepa- # = _1E £—E— —I//?5 o
ration induced 127rJefftc5jJt/0
in particle.
ex External elec- Particle only is
trie field force charged. Charge QQ p.
separation in col- KSK = P " (1 + 2Tc/ft3) cos 0 -(I- Tc//j') sin 0
Co lector induced 67rftpjuC/0 "•
° by external elec-
tric field.
icp Electric dipole Neither body is
interaction charged. Charge
force separation in 2ycypefCRp*E0* -[2(1 + 2yc/R>) cos' 0 -[(2 + 7c/ft')sin 0 cos#]
both bodies in- K-lco = K *
duced by exter- P RC^O -(1 —ycIR3) sin2 0 ]/R< R'
nal electric field.
"The parameters Kc, K-IC, and K-lp are identical to K^, K^, and K\ defined by Kraemer and Johnstone (1955).
Subscripts f, c, and p relate to air, the collector, and particle, respectively.
Q, C, R, e, y, U0,andY are the charge, slip coefficient, radius, dielectric
constant, viscosity, free stream velocity, and polarization coefficient, respectively.
-------
Thermophoresis
Particles in a temperature gradient move down gradient with a thermo-
phoretic velocity which can be expressed as
VT = -KT(AT/Ax) (31)
where Kj is a function of the physical and thermal properties of the par-
ticles and properties of the fluid (Leong, 1980). The temperature gradient
is assumed to be uniform. When the Knudsen number, Kn, which is the ratio of
the mean free path of the fluid to the radius of the particle, is much larger
than one (free molecular regime)
KT = 157rcX/(16yiT) (32a)
t
where c is the mean molecular speed of the molecules, A the mean free path,
and
y. = 8 for specular reflection (33a)
y. = 8-hr for diffuse reflection (33b)
In the slip regime, where the Knudsen number is much smaller than one
KT = vkT(YT + ctKn)/(T(l + 3cmKn)(l + 2yT + 2ctKn)) (32b)
where v is the kinematic viscosity of the fluid, Y]- is the ratio of the
thermal conductivity of the fluid to that of the particle, and ky, c^, and
cm are the thermal slip, thermal accommodation, and momentum accommodation
coefficients, respectively. The values of these coefficients in air are
approximately 1.1, 1.6, and 1.2, respectively (Leong, 1980). In the transi-
tion regime, where the Knudsen number is of order one, no adequate theoreti-
cal formula exists.
Diffusiophoresis
As in thermophoresis, particles have a diffusiophoretic velocity in the
presence of a vapor concentration gradient. The diffusiophoretic velocity
can be expressed as
VD = -KD (Apv/Ax) (34)
where the vapor gradient is assumed to be uniform (Leong, 1980). In the free
molecular regime for a dilute vapor
31
-------
KD = Dvg/(mg mv)'
where DVg is the diffusion coefficient of the vapor in the gas, and trig and mv
are the molecular masses of the gas and vapor, respectively (Leong, 1980).
In the slip regime
KD = (kDC/(l + 3cmKn))(mgDvg/(mvp)) (35b)
where RQ is the diffusion slip coefficient and p is the fluid density. In
the transition regime no satisfactory theory exists. In addition to the dif-
fusiophoretic velocity, there is also a Stefan flow of the fluid due to the
diffusion of the vapor. This velocity due to Stefan flow is
vs = -(Dvg/p)(Apv/Ax) (36)
Gravity Effect
The settling speed of small spherical particles is given by Stokes law as
vco= 2a2 ppgc/(9n) (37)
where g is the gravitational acceleration. Larger particles will have a
higher settling speed. For the case of particle collection by falling drops,
the effect of gravity is to decrease the relative inertia between particle
and drop and hence to decrease the efficiency.
Inertia Effect
Particle velocities are usually different from fluid velocities, due to
the inertia of the particle. The inertia can be characterized by the Stokes
parameter, defined by
K. = CmV/(6irnaL) (38)
o p
where m is the mass of the particle, V, the characteristic of free stream
velocity, and L, a characteristic length. For a sphere
Ks = C2a2ppv/(9nA) (39)
For a spherical collector with a « A, the collision efficiency by inertia!
impaction is given by Rimberg and Peng (1977) as
32
-------
e.m = (1+0.75 ln(2Ks)/(Ks-1.214)) 2 for K$ > 1.214 and viscous flow (40a)
e. = (K 0.2 and potential flow (40b)
in j o o
Interception Effect
If a particle follows the stream lines of the fluid, it will have a col-
lision efficiency due to its size. For the case where the collectors are
drops, Rimberg and Peng (1977) give this interception efficiency as
2
e- = 1.5(a/A) for viscous flow (41a)
ein = 3a/^ for P°tential f1ow (41b)
Sonic Agglomeration
Sonic or acoustic agglomeration is a method for inducing coagulation of
particles with high intensity sound waves (Shaw, 1978). Particles smaller
than a particular size are set into oscillation by high intensity acoustic
vibrations, while larger particles are unaffected. This promotes collision
of the smaller with the larger particles. The optimum frequency for agglomer-
ation decreases for larger particles. The sonic agglomeration constant anal-
ogous to the coagulation constant is directly proportional to the amplitude
of the sonic waves. Depending on the intensity of the acoustic wave, the
particle agglomeration can be increased by more than an order of magnitude
compared to Brownian coagulation, especially for particle sizes around 1 vim
(up to 3 orders of magnitude increase). Details can be found in a recent
review by Shaw (1978).
Comparison of Forces or Mechanisms
Collision efficiencies by different mechanisms for different particle
sizes for a 100 ym drop are shown in Figure 11, which illustrates the impor-
tance of each mechanism. In the estimation of electrostatic collection effi-
ciency, the particle charges used are those attained by unipolar diffusion
charging (Liu and Pui, 1977), while the drop charge is about one-tenth the
Rayleigh limit for drop stability. For particles less than 2 ym radius,
Coulomb attraction is the dominant collision mechanism. Inertia impaction
becomes the major mechanism for particles larger than 3 ym. For particles
larger than 10 ym, the settling speeds are over 1 cm/sec. Hence, settling is
an effective alternate means of removing particles. Gravity has the maximum
effect on particle collection by falling drops in the 1 ym radius particle
size region. It reduces or even nullifies the effect of interception. How-
ever, the absolute effect in terms of efficiency is less than 10~2.
For all practical purposes, Brownian diffusion can be ignored for all the
particle sizes shown, and interception can be ignored for particle sizes less
than 5 ym. Thermophoretic and diffusiophoretic forces have been shown to be
33
-------
O.I 1,0
PARTICLE RADIUS
0.01
Figure 11. Theoretical collision efficiencies for a 100 ym radius water /
drop falling at terminal velocity in air. 1) Coulomb force for
drop with one tenth Raleigh limit charge and particles charged
by diffusion charging only, 2) same as 1) except particles have
one electron charge, 3) inertia and interception effects only,
4) thermophoretic and diffusiophoretic forces only, 5) Browm'an
diffusion only.
34
-------
insignificant (less than 0.1% in overall collection) in the collection of
particles by drops (Pilat and Prem, 1977). In tubes or parallel plate systems,
phoretic forces can be significant, depending on the gradients used and the
residence time of the particle, e.g., passing a high temperature gas through
a cold wall tube (Byers and Calvert, 1969) or condensing steam in the system
(Azarniouch et al. , 1975). The effect of turbulence, in the case of drops,
is about the same order of magnitude as for thermophoresis (Lin, 1976). In
turbulent pipe flow, the eddy diffusivity can be several orders of magnitude
larger than Brownian diffusion and hence significant in the precipitation of
particles on the walls. However, compared to electrostatic forces, these
mechanisms are relatively inefficient for fine particles. The effects of
acoustic agglomeration would also be insignificant compared to Coulomb forces.
In the case of highly charged drops and particles, Kraemer and Johnstone (1955)
and Prem and Pilat (1978) have shown that collection efficiencies are over
100%. For neutral particles, a collection efficiency of about 10"2 is obtained
by image forces for drops charged to the Rayleigh limit (Grover and Beard,
1975). The above comparisons were made for a 100 ym radius drop at the
terminal velocity of 0.7 ms"1.
In Venturi-type scrubbers very high drop velocities are used. With a
typical velocity of 100 ms"1 the collection efficiency from inertia impaction
for a 100 ym radius drop using the efficiency equation for potential flow is
larger than 0.9 for 1 ym radius particles. However, for 0.1 ym radius
particles the collision efficiency is only 0.4. Increasing the velocity
by a factor of 10 will only increase the efficiency to 0.5. Hence collision
efficiencies can be maximized most effectively by maximizing the Coulomb
attraction between particle and drop. For cases where use of water drops may
be suitable, acoustic agglomeration offers a viable tool for pretreating fine
particles. The larger particles formed after agglomeration can then be
removed effectively by other methods.
Comparison Between Theory and Experiment
Numerous experiments have been conducted to measure the collection effic-
iency of liquid and solid collectors for particles of different size and
composition where one or more collision mechanism is operative. For a valid
comparison between theory and experiment all collision mechanisms involved
have to be identified and extraneous effects modifying the collection
efficiency have to be accounted for. These effects include particle non-
adhesion and assemblage of collectors instead of single collectors. Formation
of a coating of particles on the collector (Wang et al. , 1977) can change the
collecting characteristics dramatically by changing the size and shape of the
collector, as shown in Figure 12. The efficiencies increased as more particles
were collected due to the formation of dendrites. Particle bounce-off from
the coating may occur (Stulov et al., 1978) and dendritic structures may arise
(Bhutra and Payatakes, 1979).
Robig et al. (1978) obtained good agreement between theory and experiment
for the collection of 0.02 to 2 ym radius particles by metal spheres for
Brownian diffusion interception and inertia! capture. The experimental effic-
iencies of Robig et al. are shown in Figure 13 with the theoretical Brownian
diffusion collision efficiencies predicted by the convective diffusion theory
35
-------
13
II
>-
o
z
UJ
o
U-
UJ
o
h-
O 7
LJ
O
O
fe 5
O
<
I
0 10 20 30
NUMBER OF PARTICLES CONSIDERED
Figure 12. Ratio of collection efficiency taking into account previous
particles collected on the collector surface compared to the
efficiency computed when the collector surface has no adhered
particles (Wang et aJL., 1977)
36
-------
10
-I
o
UJ 10
o
U.
Lu
LJ
Z
O
I-
o
-2
10
-3
o
o
O
0,0
CL
-4
10
-5
i i r i 11
A, mm
X 0.175
o 0.3
• 1.0
A 3.5
Re
8.75
25
218
1099
(I)
(2)
(3)
(4)
0.01
CONVECTIVE DIFFUSION
THEORY
X
X
w
XX
I I I I 1
O.I I
PARTICLE RADIUS (/im)
10
Figure 13. Collection efficiencies of metal spheres by Brownian diffusion,
interception and inertial impaction. Experimental data for
different drop and particle radii are from Robig &t at. (1978).
Convective diffusion theory is from Wang (1978).
37
-------
used by Wang (1978). The efficiencies due to interception and inertial
impaction are within the bounds predicted by Stokes and potential flow.
Confirmation of the theory for interception and inertial capture of particles
has also been obtained by several investigators for collection by liquid drops,
and cylindrical and spherical shape collectors, e.g., Ranz and Wong, 1952;
Goldshmid and Calvert, 1963; Leong, 1980. The good agreement between experi-
ment and theory which included gravitational effects in the 1 ym radius part-
icle size region demonstrates the accuracy of the trajectory method in comput-
ing collision efficiencies (Robig et al. , 1978; Leong, 1980). For smaller
particles where inertia is insignificant and gravity has negligible effect,
the convective diffusion method has been proven to be applicable (Robig et al. ,
1978).
Particle collection by drops due to turbulence has been modelled by
De Almeida (1975) and Lin (1976). De Almeida used a stochastic model where
the collection was expressed in terms of a probability function. Lin used
boundary layer theory for turbulent collection by drops neglecting inertia of
the particles. However, no definitive data exist to verify either of the
above theories. The increase in particle collection by drops due to rear
eddies was shown experimentally by Beard (1974) and Wang (1978) but is less
than 1% in efficiency.
Excellent agreement between theory and experiment (Figure 14) has been
obtained for electrostatic collection by metal spheres when the Coulomb force
is dominant (Robig and Porstendorfer, 1979). Figure 15 shows the data of
Kraemer and Johnstone (1955). In contrast to the data of Robig and. Porsten-
dorfer there is substantial scatter in these data, probably a consequence of
the charge on the particles being not well controlled. The effect of image
forces at low drop and particle charge when the Coulomb force was not dominant
was also obtained. Image forces were significant only when the collection
efficiencies were less than or equal to approximately 10~2. In addition Robig
and Porstendorfer demonstrated that all particles that collided adhered with
or without a grease layer on the sphere.
In contrast, Lai et. al. (1978) found that collection efficiencies of
submicron silver chloride particles by liquid drops did not increase monoton-
ically with increasing drop charge but had a maximum value. This suggests
that collection by a liquid surface is different than for a solid surface.
For water drops in a nonsaturated environment, thermophoretic and diffus-
iophoretic forces are present. Leong (1980) obtained significant disagreement
between experiment and theory for particle collection by evaporating water
drops. The phoretic collection efficiencies did not decrease as rapidly with
large particles as theorized. This is shown in Figure 16 where significant
collection was obtained for 1 to 2 ym radius particles in contrast to the
theory which predicted no collection. His results indicated that the theory
used which was derived for uniform vapor or thermal fields may be inappropriate'
for the nonuniform fields encountered in the vicinity of evaporating drops.
Improved theory is difficult due to the mathematical complexities for the case
of nonuniform fields. Several experiments have been conducted using water
drops with low charge (Coulomb force not dominant) in a subsaturated environ-
ment (e.g. Adam and Semonin, 1970; Beard, 1974; Lai, et al. , 1978).
38
-------
10-0
10-1
LU
>•'
CJ
z
UJ
o
10-2
o 10
h-
UJ
_l
_l
O
-3
10-5
" ' ' ' ' ' ' ITI 1 i i i i i i n 1 1 — i i i i i u ; 1 — i i i i n
y
/ ijm 0 (JjriCfvO
; „/ • 0.036 Ag 0.4
; y* x Q44 OES 0.4
/> o 049 OES 0.4
/f + 0.41 DES 0.4
/ O 0.031 AgCl 0.4
/ 0.68 DES 0.4
: / > 0.68 DES 0.4
; / ~ 0.26 DES 0.4
Y * 0.03 AgCl 0.4
O 0.036 AgCl 0.4
• 0.2 NaCI 0.4
, 0.04 Cluster 0.4
1 _l 1 1 1 1 I J_L i. 11111111 L .,111111 , 1,11111
1 1 1 1 1 1 • ' !
Re
^-^ = 120-3200 :
2363 -
2363 :
2363
112
112
32 -
1 12
2133.533.1333
2363
39
1333. 44
i . - . , . i
10'4 10'3 10-2
COULOMB-PARAMETER -KE
Iff'
Figure 14. Collection efficiency of charged particles on a charged sphere
(Robig and Porstendorfer, 1979).
39
-------
100
10
u
z
u
o
z
o
H 10-1
o
u
10
,-2
10*
LEGEND
0-COLLECTOR CHARGED,
AEROSOL CHARGED BY CORONA,
PARAMETER,(KC- *E)
a-COLLECTOR CHARGED,
AEROSOL WITH NATURALLY
OCCURRING CHARGE.
PARAMETER,^! -Kf)
•-COLLECTOR GROUNDED,
AEROSOL CHARGED BY CORONA,
PARAMETER,(KC) •
THEORY
I I
I I
I 1 I
10-4
I0~3 IO~2
COLLECTION PARAMETER,
10"'
!" KE)
10
Figure 15. Collection efficiencies of charged particles by charged and
uncharged spheres (Kraemer and Johnstone, 1955).
40
-------
10°
10"
UJ
o
2
UJ
O
U_
U_
UJ
LU
rr
10"
CL
<
O
10"
.-4
Observed Efficiency
Minimum Detectable
Efficiency
Theory
I I
_QD_
0,4 0.6 0,8 I 2
PARTICLE RADIUS
10
Figure 16. Collection efficiencies of manganese hypophosphite particles by
a 66 ym radius drop (Leong, 1980).
41
-------
Significant disagreements were obtained due to omission of phoretic forces
in the theory or the lack of measurement of charge on the particles.
The theory has been adequate in predicting particle collection effic-
iencies larger than 10~2 when extraneous effects are negligible. This range
of efficiencies higher than 10~2 is usually the result of inertia capture for
particles larger than 2 ym radius and Coulomb attraction for smaller particles.
In this region of minimum collection efficiencies between 0.1 and 1 ym radius,
good agreement between theory and experiment is difficult for efficiencies
less than 10~2. Contributing factors include experimental errors and inexact
theory. For the purpose of particluate control, the most efficient collection
mechanism is Coulomb attraction. Hence, collection by highly charged drops
and particles will be examined in detail in the next section.
PARTICLE COLLECTION BY CHARGED DROPS
With charge collection as the dominant particle collection mechanism,
the collision efficiency for particles with negligible inertia by charged drops
can be computed as follows. The particle flux to the drop surface is given by
Equation (24), where
JA+a nvF = nBFC = -CQqn/(24Tr2naea(A+a)2) (42a)
where B is the electrical mobility of the particles. For a « A
JA+a = JA = -CQqn/(24Tr2naeaA2) (42b)
Since the drop is falling through the aerosol cloud at a velocity u » v, the
particle concentration n is relatively constant. Hence, the collision effic-
iency is computed using Equation (1)
= 47rA2JA/(irA2un) -4KC (43)
where K~ is the Coulombic electrostatic parameter.
Limits in Charged Particle Collection
Kraemer and Johnstone (1955) showed that single collector collision
efficiencies of over 1000% can easily be achieved by the adequate charging of
collector spheres and particles. Even with a value of the single collector
efficiency of 160% in the penetration formulae for electrostatic scrubbers
(Calvert et aZ., 1978) and charged droplet scrubbers (Pilat, 1975), the over-
all theoretical efficiency values obtained are over 99.9%. However, in prac-
tical applications, overall collection efficiencies attainable are well below
99%. For example, in electrostatic scrubbers (Calvert et aZ., 1978) charging
of the particles increased the collection efficiency of collection for 0.5 ym
radius particles from about 80 to 90%. Pilat (1975) obtained an increase
from 35 to 87% for 0.3 ym radius particles in a charged droplet scrubber in
which both the droplets and the particles were charged. The efficiencies
obtained for both the above cases are significantly below the theoretical
efficiencies (greater than 99%) for fine particles. These theoretical values,
however, did not take into account the particle-drop surface interactions which
42
-------
may lead to nonadhesion and hence lower efficiencies. This will be especially
true for nonwettable particles where particle nonadhesion may occur. Nonwet-
table particles tend to form a coating on the drop surface and this increase
bounces off and reduces effective electrostatic collection of particles.
Another consideration is that the maximum negative charge that a hydrodynami-
cally stable drop can possess is defined by the Rayleigh limit (Rayleigh 1882,
Hendricks and Schneider, 1963) which is given by
Q2 64TT2A3e a (44)
a
Above this limit, drops become unstable and charged droplets are ejected
(Abbas and Latham, 1967). For positively charged drops corona discharge
occurs before the Raleigh limit is reached. If drops are produced with
negative charge near the Rayleigh limit, evaporation in the low humidity
environment of particulate control devices will decrease drop size and cause
instability. Hence, maximization of the charge on the drops may not maximize
collection efficiencies. In addition, the maximum charge is controlled by
the surface tension. Decreasing the surface tension may help in particle
adhesion, but collision efficiency may be decreased.
Charge neutralization of charged particles by a highly charged drop may
also decrease the expected collection efficiency. Lai et al. (1978) found
that collection efficiencies for drops increased with higher charge to a
maximum value and then decreased for still higher charged drops for relatively
uncharged 0.24 urn radius particles. The decrease in efficiencies was attrib-
uted to charge transfer to the particles that came close to the drop for a
drop charge above a certain limit. The particles were possibly either neu-
tralized or acquired a charge of the same sign as the drop. Hence, the
electrostatic attraction of the particles to the drop would decrease or even
be reversed, leading to lower efficiencies. This explanation seems plausible
considering that a charged particle may induce an opposite charge on the drop,
increasing the charge density on the surface of the oppositely charged drop.
If this increase is large enough to cause a local Rayleigh instability charge
transfer may occur. In addition, the decrease in efficiencies occurred at a
lower drop charge density for a smaller drop. This is in agreement with the
trend for Rayleigh instability. However, the charge on the particles was not
measured by Lai et al. and the limited data do not conclusively define this
effect of charge transfer. In contrast, no decrease in efficiencies was
found when the charge on a metal sphere was increased (Kraemer and Johnstone,
1955; Robig and Porstendorfer, 1979) to much higher than that used by Lai
et al. Also, good agreement with theory and experiment was obtained, indicat-
ing no adhesion problems for metal spheres.
43
-------
SECTION 5
PROPOSED STUDIES
EXPERIMENTAL STUDIES
Adhesion Efficiency
Figure 17 shows the schematic of the proposed experiment to determine the
adhesion efficiency of different wettability particles to charged drops.
Widely spaced charged or uncharged drops of uniform size are generated and
fall through a cloud of monodispersed charged or uncharged particles at a
known temperature and humidity. The drops are collected at the bottom of the
chamber and analyzed for the mass of particles collected determining the
collection efficiency. For highly charged drops and particles, the dominant
collision mechanism is the Coulomb charge attraction. Robig and Porstendorfer
(1979), using a metal sphere, determined that no particle bounce-off occurs
in electrostatic collection and excellent agreement was obtained between
Coulomb attraction theory and experiment. Hence, the adhesion efficiency will
be determined by the ratio of the measured collection efficiency of the charged
drop to the computed collision efficiency. The theoretical collision efficiency
is easily obtained by measuring particle and drop charge and size since elec-
trostatic collection is independent of the flow regime. Drop sizes from 50
to 200 ym radius which correspond to sizes in scrubbers will be used. Particle
sizes tested will be in the 0.1 to 1 ym radius range, where collection effic-
iencies are minimum.
Effects of the addition of surfactants to the drops, the use of drops of
volatile (water) and nonvolatile (oil) liquids, and particles with different
wettability and physical characteristics (shape and roughness) will be studied.
Ionic (e.g., alkyl sulfates and sulfonates) and nonionic (e.g., aliphatic,
lauramide and coconut amide) surfactants will be used to determine their
efficacy. For proper control, pure surfactant compounds will be used initially.
Later, commercial preparations will also be applied.
The main components of the experiments (Figure 17) will be the aerosol
generator, aerosol conditions system, chamber, particle concentration detector,
hygrometer, charge detectors, and drop generator. Each component is described
below.
Aerosol Generator
Particles which are nonwettable or partially wettable are insoluble in
water. The Sinclair-LaMer type of generator is suitable for the generation
of this type of particles. The technique involves vaporization of the material
and subsequent condensation to form the required particle. This method of
44
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AEROSOL
GENERATOR
AEROSOL
CONDITIONER
DROP
GENERATOR
AEROSOL
CHAMBER
CN
COUNTER
HYGROMETER
FILTER
CLEAN AIR
DROP COLLECTOR
AND ELECTROMETER
Figure 17. Experimental design for determining adhesion efficiency of
particles to drops.
45
-------
generation and its variations are readily available in the literature, e.g.,
Kerker, 1975. Figure 18 shows an outline of the aerosol generating system
which can produce both insoluble particles and soluble particles.
Aerosol Conditioning System
The aerosol conditioning system will enable the selection of an aerosol
of a specified size, charge, and concentration. The system (Figure 19) will
consist of an electrostatic aerosol classifier (TSI 3071), a corona charging
device, a humidifier, and a dilution control. The classifier produces a mono-
disperse aerosol with singly charged particles from a polydispersed source.
Size is selectable and monodispersity is 5% of mean size. Independent sizing
will also be carried out with electron microscopy. A monodisperse aerosol is
necessary to differentiate any effects of size on the adhesion efficiency.
The corona charging device will be used to increase the charge on the aerosol
particles for examining effects of increased charge. The humidifier will
provide humidification of the aerosol for studying humidity effects on the
adhesion efficiency. Aerosol concentration can be decreased by the addition
of clean dilution air.
Drop Generator
An Abbott-Cannon type drop generator (Abbott and Cannon, 1972) will be
used to generate 50 to 200 pm radius drops. Uniform drops in a wide range of
sizes can be produced at a specified rate. The size of the drops produced
can be measured by a microscope after collecting the drops in a dish filled
with silicon oil (Wang, 1978). Drops can be charged to approximately the
Rayleigh limit by induction charging and the individual charge measured by
an electrometer.
Aerosol Chamber
Figure 20 shows an outline of the aerosol chamber. The aerosol is intro-
duced continuously near the top-of the chamber and flows out near the bottom.
This continuous flow method does not have the disadvantage of the closed
chamber method, where the particle concentration decreases with time due to
losses by coagulation or diffusion to chamber walls. Slight positive pressure
in the collector and drop chambers will prevent contamination. A condensation
nuclei counter (CMC) will monitor the particle concentration continuously.
Temperature and humidity will also be monitored continuously by a hydrometer.
An electrometer connected to the conducting cup will monitor the charge on
each drop collected.
Particle Wettability
Present theories and experiments indicate that the primary effect on
particle adhesion to a liquid surface is the wettability of the particle.
Hence, to characterize the effects of particles with different physical or
chemical properties on the adhesion efficiency, the wettability of the part-
icals used needs to be determined. In addition, the surface tension of the
fluid will also be required. Surfactants will be used to vary (lower) the
surface tension of water.
46
-------
ATOMIZER
LIQUID AEROSOL
EVAPORATOR
CONDENSATION
SECTION
FURNACE
SOLID OR LIQUID
•AEROSOL
CONDENSATION
SECTION
-*• AEROSOL
Figure 18. Aerosol generating system.
AEROSOL
GENERATOR
ELECTROSTATIC
CLASSIFIER
SINGLY CHARGED
MONODISPERSE
AEROSOL
CORONA
CHARGING
, —
DILUTION
SECTION
/TO AEROSOL
"CHAMBER
HUMIDIFIER
Figure 19. Aerosol conditioning system.
47
-------
DROP GENERATOR
1—
POSITIVE
PRESSURE
AEROSOL
IN
r
•CLEAN AIR
ELECTROMETER
»-
I
L--CLEAf
f\
i 3
i *«A/J;'.AJU «!iAAAyA
•CN COUNTER
-AEROSOL
ELECTROMETER
FILTER
CLEAN AIR
GROUNDED WIRE MESH
SHIELDING
CLEAN AIR
.S. CUP
Figure 20. Aerosol chamber design.
48
-------
Contact Angle
Direct measurements of the contact angle involve the interaction of a
liquid drop with a flat substrate or the interaction of the sphere with the
liquid. The latter method is the appropriate one for the case of particles
impacting on a drop. The particle sizes of interest are in the micrometer
and submicrometer range. However, due to engineering limits, spheres with
diameters larger than approximately 100 ym only are available. Hence, the
experiment will be done with "large" spheres and the effects will be inferred
for the particle sizes of interest.
Spheres of metals, plastics or glass of various sizes are readily avail-
able. Figure 21 illustrates the experimental technique for the determination
of the contact angle which is obtained by direct observation through a magni-
fying lens. Resolution can be achieved by adequate enlargement of a photo-
graphic print. The following effects on the pontact angle will be examined.
1. Surfactants: A range of surface tension values, obtained by the
addition of surfactants to the water, will be used.
2. Roughness or asperities on sphere surface: Different degrees of
roughness measured by height and spacing of asperities will be
studied. The roughness will be mechanically or chemically (etched)
produced.
3. Electrical charge: Effects of charge on the contact angle will be
studied by placing different potentials on the liquid and sphere.
In addition, following the method of Morishima and Kariya (1978), the
forces needed to push the sphere into or pull the sphere away from the fluid
will be determined with the above parameters. The results will be useful in
checking the theory developed for particle adhesion.
Wetlability
The primary concern is with nonwettable and partially wettable particles,
Wettability can be measured in terms of the contact angle. However, for most
substances a smooth sphere is impossible or extremely difficult to produce.
An alternate method of determining the relative wettability is by the rate
of rise of the liquid up a compacted bulk of the powder of the material used
to generate the particles (Weber, 1968; Glowiak and Kabsch, 1972). The
contact angle can be inferred (estimated) by reference to the rate of rise
for a powder of known contact angle such as glass, taking into account the
effects of size, shape and roughness obtained from the contact angle experi-
ment. Figure 22 shows an outline of the simple apparatus needed.
MODELLING STUDIES
Adhesion of Particles Impacting on a Drop
All previous studies (Pemberton, 1960; McDonald, 1963; Allen, 1975;
Emory and Berg, 1978) have considered only the case of particles impacting
49
-------
en
o
MAGNIFYING
LENS
CAMERA
VARIABLE
POTENTIAL
CONTACT ANGLE
VARIABLE \ /
HEIGHT Y
STAND /\
MICROBALANCE
Figure 21. Experimental design for determining contact angle of sphere.
-------
GLASS TUBE
COMPRESSED POWDER
LIQUID MENISCUS
LEVEL KEPT CONSTANT
FILTER PAPER FOR
RETAINING POWDER
Figure 22. Experimental design for determining wettability of powder.
51
-------
normally on a flat liquid surface. Particles were assumed to adhere once
coalescence occurred. These theories have been found to be inadequate in
light of experimental findings of Weber (1968, 1969) and Stulov et al. (1978).
Particles impacting on drops have different angles of impact. Particles
on a grazing or near grazing impact may have enough inertia to escape after
coalescence. The dynamics of the particle after coalescence has occurred may
be the decisive factor in determining if the particle adheres. Factors which
may affect coalescence include the shape of deformation of the liquid surface,
the curvature of the liquid surface (Morishima and Kariya, 1978), the condi-
tion of the particle or liquid surface (presence of contaminants), electrical
charges, and short range forces (Van der Waals, double layer forces). A
thorough analysis of the significance of the possible forces and conditions
and the modelling of more comprehensive dynamics of the particle-surface
interaction will be conducted to resolve the contradictions existing. In
addition, the proposed well-controlled experiments will yield data which will
verify the validity of the model.
Collision Efficiency
To characterize the data obtained from the above proposed experiments,
the collision efficiencies of drops for particles will be modelled taking
into account all significant mechanisms promoting particle capture. Electro-
static forces, inertial impaction, phoretic forces interception effects and
Brownian diffusion will be treated. Convective diffusion and trajectory
computations will be carried out to obtain the collision efficiencies in
Stokes and potential flow. Numerical flow fields available in the literature
will also be used.
Limiting Factors in Particle Collection by Charged Drops
Previous studies, e.g., Kraemer and Johnstone (1955) and Prem and Pilat
(1978), have indicated that increasing the .drop and the particle charges will
increase collection efficiencies. However, these works did not consider the
effect of charge on drop stability. A maximum in drop charging exists due
to the Raleigh limit (Hendricks and Schneider, 1963) for a hydrodynamically
stable drop. Due to the decrease in drop size by evaporation, a drop
generated at the.Raleigh limit will become unstable and eject highly charged
droplets. Hence, the effects of maximizing the drop charge on the particle
collection characteristics are not clear. A theoretical study will be carried
out to determine the conditions which maximize particle collection.
RESULTS AND/OR BENEFITS EXPECTED
The proposed studies will provide the following results:
1. Clarification and documentation of the various mechanisms affecting
the adhesion of particles impacting on drops.
2. Determination of the adhesion .efficiency of nonwettable, partially
wettable, and wettable particles impacting on drops.
52
-------
3. Elucidation of the role of surfactants in the collection of non-
wettable, partially wettable, and wettable particles.
4. Determination of the parameters for maximizing the collection of
charged particles by charged drops.
The results obtained will enable optimization of the collection effi-
ciency and operating costs of particulate control devices utilizing wet sur-
faces as collectors, e.g., electrostatic, Venturi, or charged droplet scrub-
bers and electrostatic precipitators with wet walls. Especially important
is the maximization of the fine particle collection efficiencies.
53
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REFERENCES
1. Abbas, M. A., and J. Latham, 1967. The Instability of Evaporating Charged
Drops. J. Fluid Mechanics, 30, 663-670.
2. Abbott, C. E., and T. W. Cannon, 1972. A Droplet Generator with Elec-
tronic Control of Size, Production Rate, and Charge. Rev. Sci. Instr.,
43, 1313-1317.
3. Adam, J. R., and R. 6. Semonin, 1970. An Experimental Determination of
the Collection Efficiencies of Raindrops for Submicron Particulates.
Precipitation Scavenging, AEC Symposium Series, No. 22, 151-160.
4. Allen, R. W. K., 1975. Collection of Hydrophilic and Hydrophobic
Particles by Suspended Water Drop. PhD thesis, McGill University,
Montreal, Canada.
5. Arbel, N., and Z. Levin, 1977. The Coalescence of Water Drops. Pageoph.,
115, 869-893.
6. Azarniouch, M. K., E. J. Farkas, N. E. Cooke, and A. J. Bobkowicz, 1975.
Removal of Micro-size Particles from Gases by Turbulent Deposition and
Diffusiophoresis. Can. J. Chem. Eng., 53, 278-285.
7. Beard, K.W., 1974. Experimental and Numerical Collision Efficiencies for
Submicron Particles Scavenged by Small Raindrops. J. Atmos. Sci., 31,
1595-1603.
8. Beard, K. W., and S. N. Grover, 1974. Numerical Collision Efficiencies
for Small Raindrops Colliding with Micron Size Particles. J. Atmos.
Sci., 31, 543-550.
9. Bhutra, S., and A. C. Payatakes, 1979. Experimental Investigation of
Dendritic Deposition of Aerosol Particles. J. Aerosol Sci., 10,
445-464.
10. Bowden, F. P., and D. Tabor, 1954. The Friction and Lubrication of
Solids, Clarendon Press, Oxford.
11. Bughdadi, S. M., 1973. Effect of Surfactants on Venturi Scrubber Particle
Collection Efficiency. MS thesis. Southern Illinois University at
Carbondale.
12. Butcher, S. S., and R. J. Charlson, 1972. An Introduction to Air
Chemistry. Academic Press, Inc., 230 pp.
54
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13. Byers, R. L., and S. Calvert, 1969. Particle Deposition from Turbulent
Streams by Means of Thermal Force. I & EC Fundamentals, 8, 646-655.
14. Calvert, S., S. C. Yung, H. Barbarika, and R. G. Patterson, 1978.
Evaluation of Four Novel Fine Particulate Collection Devices. EPA-600/
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