Environmental Engineering Reference
In-Depth Information
where
D
is the electron diffusion coefficient in a gas according to (4.64). Since the
electron pressure
p
e
D
N
e
T
e
is constant in space, this expression may be written
as
D
T
e
.
d
dT
e
N
e
T
e
D
T
D
(4.76)
In particular, if the rate of electron-atom collisions does not vary in space,
ν
D
n
we have
const, this equation gives
D
T
D
0. In the case of the dependence
ν
v
D
T
D
nN
e
D
.
(4.77)
This means that the direction of the electron flux with respect to the temperature
gradient depends on the sign of
n
.
4.3.5
Cross-Fluxes in Electron Thermal Conductivity
A characteristic property of the electron thermal conductivity is such that cross-
fluxes can be essential in this case. In the case the electron thermal conductivity
of a weakly ionized gas in an external electric field, when a temperature gradients
exist, we have the following expressions for fluxes
j
D
N
e
K
E
D
T
N
e
r
ln
T
e
,
q
D
r
T
e
C
α
e
E
.
(4.78)
e
We first consider the case of electron transport when displacement of electrons
as a whole cannot violate the plasma quasineutrality that corresponds to plasma
regions far from electrodes and walls. Then the mobility
K
in (4.78) is the elec-
tron mobility, and one can ignore the ion mobility including the ambipolar diffu-
sion. The expression for the electron thermodiffusion coefficient is given by (4.76),
and (4.70) gives the thermal conductivity coefficient. Below we determine the coef-
ficient
in (4.78) by the standard method by means of expansion of the electron
distribution function over the spherical harmonics, similar to (3.10). Then the first
equation of the set that is analogous to (3.25) yields
α
f
1
D
eE f
0
/(
ν
T
e
), and the
coefficient
α
is
v
7
2
,
4
m
e
N
e
6
T
e
4
T
e
N
e
3
p
π
n
2
α
D
D
0
Γ
(4.79)
ν
m
e
ν
0
/
p
2
T
e
/
m
e
n
where we take
ν
D
ν
.For
n
D
0thisgives
v
5
T
e
N
e
2
m
e
α
D
,
ν
and for
n
D
1, when
ν
D
v
/
λ
,thisformulayields
s
2
T
e
N
e
3
v
T
m
e
λ
2
λ
α
D
3
p
π
D
,
