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Surfaces, Interfaces, and Colloids: Principles and Applications, Second Edition.
Drew Myers
Copyright
1999 John Wiley & Sons, Inc.
ISBNs: 0-471-33060-4 (Hardback); 0-471-23499-0 (Electronic)
13
Aerosols
The previous chapters have introduced several classes of colloids and some of
the important surface aspects of their formation, stabilization, and destruction.
Emulsions, foams, and dispersions are the most commonly treated and in-
tensely studied examples of colloidal systems. They constitute the majority of
practical and ideal systems one encounters. There exists one other class of
true, lyophobic colloids—the aerosols—which, although seemingly less impor-
tant in a theoretical or applied sense, are of great practical importance.
Aerosols are systems in which there exists a condensed phase of one mate-
rial (solid or liquid) that is dispersed in a gaseous phase and that has dimensions
that fall into the colloidal range. There are two subclasses of aerosols depend-
ing on whether the dispersed phase is a liquid or a solid. There cannot be, of
course, a dispersion of one gas in another. Where the dispersed phase is a
liquid, the system is commonly referred to as a ‘‘mist’’ or a ‘‘fog.’’ For solid
aerosols, one may commonly refer to a ‘‘dust’’ or ‘‘smoke.’’ Each class of
aerosol has its own characteristics of formation and stabilization and will be
discussed briefly below.
13.1. THE IMPORTANCE OF AEROSOLS
Aerosols, both liquid mists and solid smokes, have a great deal of technological
and natural importance. Technically they are usefully employed in coating
operations, firefighting, medical treatments (allergy and asthma sprays), chem-
ical production processes, spray drying, and other procedures. On the opposite
side of the ledger, of course, we have the smoke from industrial smokestacks,
smog and haze from industry and automobiles, forest fires, high-flying jet
contrails, chemical and biological weapons, and so on. However, the real
impact of aerosols (in purely massive terms) comes from natural sources:
clouds, smokes, and similar natural airborne particles.
A cloud (natural) is a large collection of water droplets or ice crystals
moving through the atmosphere and held together (loosely) by a variety of
forces to be discussed below. Other natural aerosols include: airborne pollen;
dust and sand (if high enough in the atmosphere causing beautiful red sunsets);
volcanic clouds of water, sulfur oxides (producing acids), and other solid and
liquid materials; natural ‘‘chemical fogs’’ produced by plant metabolism and
decomposition in dense forest areas (e.g., the Smoky Mountains in the south-
eastern United States); and many more.
317
318
AEROSOLS
Today, probably the most visible aerosols (to the general consciousness)
are those resulting from air pollution. Composed of an infernal mixture of
water, solid particulate materials, and liquid droplets, pollution aerosols can
literally represent the devils own chemical workshop. Under the influence of
the suns ultraviolet gaze, and aided by the effects of catalytic processes dis-
cussed in Chapter 9, the complex soups we produce daily can undergo continu-
ous chemical changes often leading to disastrous results for ourselves and our
environment. The effects of pollution on human health, on vegetation, on
materials and structures, and on the atmosphere itself are more apparent and
frightening ever day. To pretend that we, the human race, can simply take a
step back out of the industrial revolution and return to ‘‘better’’ days is pure
fantasy (and folly). Instead, we must improve our technology to reduce the
level of pollutants we produce and to control that which is unavoidable so
that it never reaches the open light of day. Today, using some of the simple
principles described below (and others more complex, of course), we have
the technological capability to greatly improve our situation. What are lacking
are the economic and political force of will to implement what we know and
continue developing new ways to control these inhabitants of the twilight zone
we call ‘‘aerosols.’’
13.2. COLLOIDAL PROPERTIES OF AEROSOLS
While aerosols are typical colloids in that they respond to the same forces
already introduced—that is, electrostatic and van der Waals interactions—the
special conditions that prevail in terms of the intervening gaseous medium
results in an apparent qualitative difference from colloids in liquid media.
The preceding chapters illustrated the importance of the intervening medium
to the character and interactions of colloidal particles due to the screening
effect of the continuous phase on particle–particle interactions. In aerosols,
although the fundamental rules remain the same, the screening effect of the
gaseous medium becomes relatively insignificant so that a number of adjust-
ments in thinking must be made in order to reconcile the apparent differences
between aerosols and emulsions, sols, and other colloidal systems.
In a first analysis, we can identify at least four basic differences between
aerosols and other colloids related to the dispersion medium: (1) buoyancy
effects, (2) the effects of movement of the dispersing medium, (3) particle
mobility in undisturbed conditions (i.e., free fall), and (4) modification of
interactions by the intervening medium. In emulsions, foams, and sols we
have seen that buoyancy can be important in determining the stability of a
system (i.e., matching the densities of dispersed and continuous phases can
retard creaming or sedimentation). In aerosols, where the density of the
continuous phase will always be significantly less than that of the dispersed
particle, such effects are practically nonexistent—the colloid is essentially left
to its own devices; the usual interactions found for all colloids, the ‘‘constant’’
13.2. COLLOIDAL PROPERTIES OF AEROSOLS
319
pull of gravity (assuming that we are not aboard the space shuttle or MIR),
and the whims of the winds.
13.2.1. Dynamics of the Aerosol Movement
Study of the dynamics of fluid flow is concerned with the forces acting on the
bodies in the fluid. In the earlier chapters on solid dispersions, emulsions, and
foams, fluid dynamics was largely ignored in favor of the ‘‘true’’ colloidal
interactions. In aerosols, the nature of the continuous medium makes the
subject of fluid dynamics much more important to the understanding of the
system, so that the following discussion will introduce a few basic relationships
that can be important in the study of aerosols.
‘‘Winds,’’ in the form of convection currents or other movements of the
medium, are generally more important in gases than liquids. Small temperature
differences or mechanical movements that would be damped out quickly in
a more viscous liquid may be translated over large distances in gases and
produce a much greater effect in aerosols. (Remember the famous Chinese
butterfly that can change the weather in Kansas according to chaos-based
theories of weather development?)
In a static system of relatively high viscosity (relative to that of gases),
inertial forces due to particle movement are seldom significant; specifically,
viscous forces dominate. In gases, the forces resulting from particle movement
become more important and must be considered in a dynamic analysis of the
system. In dynamic fluid flow analysis, the ratio of inertial forces (related to
particle mass, velocity, size, etc.) to viscous forces (a characteristic of the
medium and not the particles) in a system is a dimensionless number termed
the Reynolds number, Re, and is used to define the type of flow occurring in
the system (i.e., laminar or turbulent). For spherical particles of radius
R
and
density moving with a velocity
v
in a medium of viscosity , the Reynolds
number is given by
Re
2vR
(13.1)
When Re
1 the system is said to be in laminar flow (Fig. 13.1a) and the
Stokes equation [Eq. (10.20)] is found to apply. When Re 10
3
, the system
is in fully turbulent flow (Fig. 13.1b) and flow resistance is controlled by drag
forces due to the medium given by
F
d
0.2
m
R
2 2
v
(13.2)
In the region 1
Re
10
3
, a transition occurs from laminar (F
d
v)
to
2
turbulent flow (F
d
v
) and the relationship between
F
d
and
v
becomes more
complex. Also, since drag forces actually apply only to the relative velocity
320
AEROSOLS
FIGURE 13.1.
In the movement of aerosol particles, the type of flow in the gas phase
will significantly affect the fate of the particles. For Reynolds number, Re, 1, laminar
flow will prevail (a). However, since gases are usually of very low viscosity compared
to liquids, it is more common to encounter the situation where Re
1000. In that
case, turbulent flow is common and particle dynamics is much more difficult to model.
of the particle to the medium, the effects of drag or viscous resistance to flow
for a dispersed particle must be adjusted to take into consideration the flow
of the medium. Raindrops, for example, generally fall under turbulent flow
conditions, so analysis of their behavior should include extrapolation from
Equation (13.2).
Even under ideal conditions, the dynamic flow behavior of aerosols in
contrast to other colloids can be markedly different. In still air, the average
distance a particle will travel before colliding with another particle, the mean
free path, , is given by
[(
8)
N
R
2
]
1
(13.3)
where
N
is the particle number density. For an aerosol containing 10
8
particles
0.11 cm. Thus, a particle in random motion
cm
3
and radius 10
4
cm,
would travel an average of 0.11 cm before colliding with a neighboring particle.
Such collisions may result in changes in the characteristics of the system—
momentum changes in the case of elastic collisions and possibly size changes
for inelastic (‘‘sticky’’) collisions. The potential importance of sticky collisions
will be discussed below.
For aerosols of small radius ( 10
4
cm) and Re
10
3
, Equation (13.2)
should be adjusted to take into consideration the effects of particle collisions.
A correction factor,
C
c
(the Cunningham correction factor) can be incorpo-
rated into the Stokes equation to give
F
d
where
6
Rv
C
c
(13.4)
13.2. COLLOIDAL PROPERTIES OF AEROSOLS
321
C
c
1
R
1.26
0.4 exp
1.1R
(13.5)
Obviously, the correction given in this equation becomes more important for
aerosols of smaller particle radius, or in conditions of lower gas pressures
(e.g., high altitudes).
According to the Stokes equation, the velocity of free fall of a particle in
an undisturbed gravitational field,
v
f,
is given by
v
f
m
a
g
6
R
2R
2
g
9
(13.6)
For simplicity, it is assumed that the density of the gas phase is small compared
to that of the particle. For more accurate results, the density difference between
particle and gas (
p
g
) should be employed. At 20 C and atmospheric
pressure, the viscosity of air is 1.83
10
4
cP (centipoise or g cm
1
s
1
), so
3.0 g cm
3
(e.g., volcanic
that for an aerosol particle of
R
10
4
cm and
ash), the rate of fall will be approximately 0.04 cm s
1
. Particles from a plume
of ash thrown to an altitude of 10,000 m would (theoretically and neglecting
all complicating factors mentioned above) take about 290 days to reach the
ground! If the particle size grows to 10
3
cm radius by flocculation, its rate
of fall increases to 3.6 cm s
1
, and the same trip will take about 3.2 days. It
is easy to understand, then, why volcanic eruptions and other natural (and
unnatural) events that produce high-altitude aerosols can affect not only the
color of our sunsets but also other more vital global atmospheric interactions.
In water, with a viscosity approximately 50 times that of air, mineral particles
similar to those above would have sedimentation rates on the order of 1.6 m
day
1
and 23 m min
1
, respectively. Such calculations (estimations, really)
are important for modeling problems of sediment accumulation in dammed
reservoirs, for example.
13.2.2. Colloidal Interactions in Aerosols
Although the rules are the same, particle–particle (colloidal) interactions in
aerosols can seem to have significantly different quantitative and qualitative
characteristics than in liquid media. A gaseous medium, because of its very
different unit density, dielectric constant, and other properties, is very ineffec-
tive at screening the forces acting between colloidal particles. For that reason,
Hamaker constants in aerosols are large, usually falling in the range of 5–
20 10
20
J (see Table 4.5), resulting in strong attractive interactions between
particles and between particles and surfaces regardless of the materials in-
volved. If we use as a measure of the kinetic energy of an aerosol particle
the value of kT (Boltzmann’s constant
absolute temperature), at ambient
temperature, that energy will be about 4
10
21
J. The Hamaker constant

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