Environmental Engineering Reference
In-Depth Information
where
N
p
is the number density of aerosol particles,
Ze
is their mean charge,
w
is
the velocity of its falling, which is given by (6.3),
N
C
and
N
are the number den-
sities of positive and negative ions, and
K
C
and
K
are their mobilities. Taking the
regime when aerosol particles give a small contribution to the ionization balance,
that is,
N
C
D
N
D
N
, and the ion mobilities are nearby
K
C
D
K
D
K
,we
obtain from this balance the simple relation for the electric field strength:
ZN
p
w
2
KN
.
In particular, from this it follows that since for large aerosol particles
Z
E
D
r
0
ac-
r
0
according to (6.3), the electric field strength at a given
mass density of water in the atmosphere is independent of a typical size of aerosol
particles.
cording to (6.11) and
w
6.5.6
Prebreakdown Phenomena in the Atmosphere
We now analyze one more aspect of electric phenomena in the atmosphere. As
noted above, the electric field strength of a cloud during lightning is less by one
or two orders of magnitude than the breakdown strength at atmospheric pressure
of about
E
90 Td) between plane electrodes, or the break-
down strength due to propagation of a positive streamer (about 5 kV/cm). We shall
consider some reasons for this that extend our understanding of the nature of pro-
cesses that accompany electric phenomena in atmospheric air.
Consider a chain of processes that can lead to breakdown. We shall consider only
one of several mechanisms in order to demonstrate the character of these process-
es [178]. Assume that atmospheric air is subjected to an electric field of strength
E
,
and the elementary processes 11, 12, 17, 20, 23, 26, 40, and 41 in Table 6.6 are
the determining factors. These processes lead to balance equations for the num-
ber densities of electrons
N
e
,negativeoxygenions
N
, and ozone [O
3
]thatcanbe
stated as
D
25 kV/cm (
E
/
N
D
dN
e
dt
D
ν
at
)
N
e
C
N
[O
3
]
k
23
,
(
ν
ion
dN
dt
D
ν
k
17
N
2
at
N
e
N
[O
3
]
k
23
,
d
[O
3
]
dt
D
[O
3
]
τ
C
M
2
ν
26
N
e
.
(6.114)
We employ here the quantities
D
k
26
[O
2
]. We assume that process 17 in Table 6.6 gives the main contribution to
recombination of positive and negative charges and that the number density of
ozone molecules is relatively small, so the dissociation of an oxygen molecule leads
automatically to the formation of two ozone molecules as a result of processes 40
and 41. The rate of ozone formation is denoted by
M
,and
ν
D
k
11
[O
2
]
C
k
12
[N
2
],
ν
D
k
20
[O
2
], and
ν
ion
at
26
τ
is the lifetime of ozone
molecules.
