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.
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