Environmental Engineering Reference
In-Depth Information
Figure 6.1, the drift velocity of clusters
w
near the orifice is [60, 61]
0
3
c
s
tan
)
2/3
,
w
D
2.68
c
s
(
ντ
τ
D
,
(6.2)
α
where the relaxation rate
ν
is given by (6.1),
τ
is the time for variation of the flow
velocity, and
is the conic angle.
We consider also falling of a cluster or a particle under the action of their weight.
Taking the case of a dense gas (6.5) and equalizing the weight to the resistive force
that is given by the Stokes formula, we obtain the free-fall velocity
w
for a spherical
particle of radius
r
0
:
α
gr
0
9
2
w
D
,
(6.3)
η
where
g
is the free-fall acceleration and
is the gas viscosity. In particular, for a
water particle in air at atmospheric pressure and temperature
T
η
D
300 K, this
formula may be represented in the form
0.0118
r
0
a
2
w
D
,
(6.4)
where the velocity of the falling particle is given in centimeters per second and
a
D
1
μ
m. This formula holds true at small values of the Reynolds number Re
D
r
/
v
1, where
v
D
η
/
g
is the kinematic viscosity of the gas, and
g
is the gas
v
density. In the case of water drops in air this criterion is
r
0
30
μ
m.
6.1.3
Charging of Particles in a Dense Ionized Gas
When a cluster is in an ionized gas, electrons and ions may attach to its surface,
which leads to cluster charging and also produces a sink for electrons and ions of
an ionized gas. In considering the process of cluster charging in an ionized gas,
we will model clusters by a macroscopic spherical liquid drop (Section 2.1.3), so
its radius is large compared with the distance of interaction between the cluster
surface and atomic particles, and both large nanoclusters and microparticles are
identical in this consideration. Since a cluster is charged, a self-consistent field is
formed near it that influences the equilibrium cluster charge and the distribution
of electrons and ions near the cluster. We consider below charging processes for
an isolated cluster in an ionized gas that determine the cluster charge and the self-
consistent field near it.
Foradensebuffergas,whenthecriterion
r
0
λ
(6.5)
holds true (
isthemeanfreepathofionsinagas),wehavethefollowingexpres-
sion for the ion flux
J
C
(
R
) toward the cluster, which is the total number of positive
λ
