Environmental Engineering Reference
In-Depth Information
restricted by
r
0
<
22
μ
m .
(6.105)
We note also that the charge distribution function (6.15) for drops (aerosol parti-
cles) is wide. In particular, on the basis of the charge distribution function we have
for the width of this distribution function
18
r
0
a
.
(
Z
Z
)
2
D
One can see that for
r
0
20
μ
m the width of the distribution function is close to
the average drop charge.
We assume in this case an equilibrium between molecular ions in atmospheric
air and charged aerosols, and the formation of charged aerosols does not influence
the number density of molecular ions. Let us determine a typical time for aerosol
charging under these conditions. The charging time, that is, the time for establish-
ment of charge equilibrium between aerosols and molecular ions, is [60, 65]
T
1
τ
D
N
i
e
2
D
i
D
,
(6.106)
rec
4
π
4
π
N
i
eK
i
where
N
i
is the number density of molecular ions,
D
i
and
K
i
are the diffusion co-
efficient and the mobility for positive molecular ions, and this time is independent
of aerosol size. In accordance with the data in Table 6.10, we take
K
i
2cm
2
/(V s),
10
3
s at the number density of molecular ions
N
i
300 cm
3
.
which gives
τ
rec
This time is less than or comparable to the time for cloud formation.
We now analyze charging of clouds from another standpoint. Let us find the val-
ue of the total mass of water drops
per unit volume that provides the above spe-
10
10
C/g and the current density of falling
cific charge of drops
j
Z
j
e
/
m
D
1.3
10
16
A/cm
2
as is observed on average over the ocean [149].
We obtain on the basis of the above formulas that this value is independent of
the drop radius and is
charged drops 3.7
10
7
g/cm
3
, which corresponds to a water con-
tent in the atmosphere of 0.35 g/kg of air, whereas the average content of water
in the Earth's atmosphere is 7 g/kg of air [150], which relates to the temperature of
10
ı
C at which the saturated vapor pressure corresponds to the above water content.
These estimates show that a small part of atmospheric water is used for charging
the Earth.
For this water content we obtain the number density of water drops
N
dr
per cubic
centimeter:
D
4.6
10
4
a
r
0
3
N
dr
D
8.4
.
Thechargedensity
N
Z
Dj
Z
j
N
dr
per cubic centimeter is
10
5
a
r
0
2
N
Z
D
1.4
.
