Chemistry Reference
In-Depth Information
where r
N
is the particle number density. For an aerosol containing 10
8
particles/cm
3
and radius 10
4
cm, l
¼
0.11 cm. Thus, a particle in random motion would travel
an average of 0.11 cm before colliding with a neighboring particle. Each such col-
lision may result in changes in the characteristics of the system—momentum
changes in the case of elastic collisions and possibly size changes for inelastic or
''sticky'' collisions.
According to the Stokes equation, the velocity of free fall of a particle in an
undisturbed gravitational field v
f
is given by
2R
2
gr
9Z
m
a
g
6pRZ
¼
v
f
¼
ð
8
:
20
Þ
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 par-
ticle and gas (r
¼
r
p
r
g
) should be employed. At 20
C and atmospheric pres-
sure, the viscosity of air is 1.83
10
4
cP (centipoises or g cm
1
s
1
), so that
0.92 g/cm
3
(e.g., a hydrocarbon) the
rate of fall will be approximately 0.011 cm/s. If the particle is emitted by an air-
plane flying at an altitude of 10,000 m, the hypothetical drop will reach the ground
after approximately 2.9 years! If the particle grows to a radius of 10
3
cm by coa-
lescing with other drops, its rate of fall increases to 1.1 cm/s, and the same trip will
take about 11 days. It is easy to understand why 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.
10
4
cm and r
¼
for an aerosol drop of R
¼
8.7.3.2. Colloidal Interactions in Aerosols
Although the rules are the same, particle-particle interactions in aerosols appear to
have characteristics significantly different from those of emulsions and dispersions
in liquid media. A gaseous medium, because of its very different density, dielectric
constant, and other properties, is very ineffective at screening the forces acting
between colloidal particles. For that reason, aerosol particles, whether liquid or
solid, will tend to have stronger attractive interactions among themselves and
with other contacting surfaces than will similar units in a liquid medium. The spon-
taneous formation of ''fuzzballs'' and dusty deposits (Figure 8.10) in the cleanest of
homes is an all-too-common manifestation of the affinity of dispersed particles in
aerosols. The illustration is, of course, for solid aerosols or dusts and smokes, but
the concept is the same for liquid aerosol deposits, even though electrostatic effects
may be reduced somewhat.
If we use as a measure of the kinetic energy of a aerosol particle the value of kT
(Boltzmann's constant times absolute temperature), at ambient temperature that
energy will be about 4
10
21
J. The colloidal forces in aerosols will be at least
an order of magnitude greater, indicating that the attraction between particles will
almost always overwhelm the kinetic energy of the particles and inelastic or sticky
collisions will commonly occur.
