Environmental Engineering Reference
In-Depth Information
obtain from this
6.8
s
T
i
e
2
T
i
m
i
j
Z
j
r
0
R
0
N
0
N
p
.
ν
D
p
From this we find for the ratio of the attachment rates
s
T
i
s
T
i
ν
e
2
r
0
T
e
S
p
S
w
,
e
2
r
0
T
e
0.87
D
i
m
i
j
Z
j
0.14
D
i
m
i
j
Z
j
p
R
0
N
p
w
D
D
D
R
0
,
ν
(6.57)
r
0
N
p
R
0
is the total area of the particle surface per unit tube
where
S
p
D
4
π
π
e
2
/
r
0
T
e
length, and
S
w
D
2
π
R
0
is the wall area per unit tube length. Since
j
Z
j
1,
we have
isthemeanfreepathofionsinanionizedgas.
Thus, the particle surface is more effective than the tube walls for recombination
of electrons and ions.
ν
R
0
/
λ
1, where
λ
S
p
S
w
D
p
r
0
R
0
N
p
w
D
2
π
.
ν
As a demonstration of these results, we consider an example of an argon plasma
with ion temperature
T
i
1cm.
We find the reduced electric field strength in the absence of particles [60],
E
/
N
D
400 K and a gas discharge tube of radius
R
0
D
D
Figure 6.11
Dust particles in the positive column of gas discharge (a) and fluxes of electrons
and ions to the walls and particle surface (b). As a result, electrons and ions recombine on the
particle surfaces as well as on the surface of the gas discharge tube.