Environmental Engineering Reference
In-Depth Information
If we require this charge density not to exceed a typical value of approximately
10
3
cm
3
,wefindthedropradiusmustbenotsmall:
r
0
>
10
μ
m .
(6.107)
One more estimate relates to the electric field strength on cloud edges if it is cre-
ated by a noncompensated charge of falling water drops. From the Poisson equa-
tion we have the following estimate for the electric field strength
E
and the electric
potential
U
of a cloud:
eN
Z
L
2
,
E
2
π
N
Z
L
,
U
D
2
π
10
3
cm
3
and the cloud depth
wherewetakeatypicalchargedensityof
N
Z
10MV, which correspond to observa-
tional values [152]. Thus, assuming that charge separation in clouds is determined
by falling of charged water drops, we obtain a noncontradictory picture of this phe-
nomena, but the radii of falling drops lie in a narrow range:
r
0
L
1km.Weobtain
E
100 V/cm and
U
D
10
20
μ
m.
6.5.4
Characteristics of Earth Charging
In considering Earth charging in atmospheric processes as a result of lightning
phenomena [151] which lead to charge transfer from clouds to the Earth's surface,
we find that the charge separation in clouds results from falling of charged water
drops under the action of the gravitational force. The origin of this process is evap-
oration of water from the Earth's surface, and condensation of water proceeds at al-
titudes of several kilometers, where the temperature is lower that that at the Earth's
surface. Therefore, the atmospheric electric phenomena are secondary phenome-
na with respect to water circulation in the Earth's atmosphere. The above estimates
show that the main contribution to the charge separation in clouds follows from
water drops with radius
r
0
m. We now consider these processes in detail
to convince ourselves of the reality of this picture of atmospheric electric processes.
In the above analysis we assumed that charging of water drops results from at-
tachment of positive and negative molecular ions, and this process does not influ-
ence the number density of molecular ions, which is
N
i
D
10
20
μ
10
3
cm
3
.Cosmicrays
are of importance for ionization of the Earth's atmosphere [159, 162, 163]. Indeed,
penetrating the Earth atmosphere up to altitudes of several kilometers and ioniz-
ing atmospheric molecules, cosmic rays (mostly protons) lead to the formation of
molecular ions. Let us determine the number density of molecular ions if they are
formed under the action of cosmic rays and are destroyed as a result of attachment
to water drops. We assume the mobilities of positive and negative ions to be simi-
lar and according to the data in Table 6.10 the mobility is
K
2cm
2
/(V s) at atmo-
D
0.05 cm
2
/s.
From this for the average water content in atmospheric air of 7 g/kg of air, we ob-
tain for the rate of destruction of molecular ions as a result of attachment to water
spheric pressure and the ion diffusion coefficient for
T
D
300 K is
D
D
