Environmental Engineering Reference
In-Depth Information
This leads to the following estimate for a typical charge of aerosol particles after
collision of ice and liquid water aerosols:
r
r
0
T
e
2
D
r
r
0
a
Z
4
.
This charge corresponds to the width of the charge distribution function (6.15)
for particles if their charging results from attachment of molecular ions to their
surface.
We now compare the rate of this mechanismwith that due to molecular ions. We
take a typical time for this process on the basis of the Smoluchowski formula (6.8)
and this time coincides with the time for the coagulation process:
1
col
D
4
π
D
dr
N
dr
r
0
.
(6.108)
τ
According to (4.110), the diffusion coefficient of aerosols is [60, 65]
a
r
0
,
T
D
dr
D
η
D
D
0
4
π
r
0
where
is the air viscosity, and in air at room temperature and atmospheric pres-
sure we have
D
0
η
10
7
cm
3
/s. Next, taking the average water content in
the Earth's atmosphere to be 7 g/kg of air, that is, the water density in drops is
D
D
1.2
10
5
g/cm
3
, and assuming the drop radius to be identical for all drops,
we obtain for the number density of drops (expressing it in per cubic centimeter)
9.1
10
6
a
r
0
3
N
dr
D
2.2
.
As a result, we obtain a typical time for collision of a test water drop with other
drops, assuming collision as contact of two drop surfaces:
a
r
0
3
1
1
τ
col
D
,
τ
0
10
3
s. It is seen that the time for collision is large compared with
the lifetime of neutral drops in a cloud for typical drop sizes. From this it follows
that the mechanism of drop charging as a result of collision of ice particles and
liquid drops is not important for electric processes in the Earth's atmosphere.
A typical time (6.108) for collision of two drops characterizes also the time for
growth of neutral drops in atmospheric air. But because water drops are charged
by attachment of molecular ions, the process of drop growth results from collision
of charged drops of the opposite sign. We determine below a typical time for drop
recombination. Let us divide drops into two parts, positively and negatively charged
ones, and because the mobilities of positive and negative ions are similar, we take
in this estimate the average drop charge to be zero, and the number densities of
positively and negatively charged drops to be
N
dr
/2, where
N
dr
is the total number
where
τ
D
3.1
0
