Chemistry Reference
In-Depth Information
By the systematic dimension analysis of (4.14)
ten dimensionless characteristic
numbers
can be derived, beside the Reynolds number, Gay-Lussac number, Froude
number, and Peclet number.
4.5.3 P
LASMA
C
HEMICAL
S
IMILARITY
:P
OSITIVE
C
OLUMN
OF
G
LOW
D
ISCHARGE
The derivation of the relevant similarity parameters here will be demonstrated for
the plasma chemistry in the
positive column of a glow discharge model reactor
.In
this case the most important version of (4.14) is the particle balance equation of
the different chemical species (4.1) written once again in modified manner [17]. For
particles of kind
i
we have
∂
n
i
∂
t
+
div
(
v
·
n
i
)
−
div
(
D
i
·
grad
(
n
i
))
−
S
i
=
0.
The thermal energy balance of the neutral gas requires
∂
ρ
c
p
T
∂
div
v
ρ
c
p
T
−
+
div
(
λ
W
·
grad
(
T
))
−
H
=
0
(4.15)
t
andthebalanceequationsofparticlenumbersandenergyoftheelectrons. Theparticle
balance equation of electrons is given by
∂
n
e
∂
t
+
div
(
n
e
v
e
)
−
S
e
=
0
(4.16)
μ
e
n
e
E
with
n
e
v
e
=−
−
grad
(
n
e
D
e
)
and μ
e
=
m
e
τ
e
. The energy balance of electrons
e
0
reads [18]
div
n
e
U
e
v
e
+
2
∂
3
3
2
·
v
e
E
n
e
U
e
)
+
n
e
+
n
e
H
e
=
t
(
0,
(4.17)
∂
where
n
i
,
e
is the particle number density of heavy particles
i
and electrons
e
, respectively
v
the gas flow velocity
v
e
the drift velocity of electrons (subscript “
∗
” is the corresponding velocity for
the flux of energy)
D
i
,
e
the diffusion coefficients of heavy particles and electrons, respectively
T
the gas temperature
ρ the density
c
p
the specific heat
λ
W
the heat conductivity
U
e
the mean energy of electrons
E
the electrical field strength
μ
e
and τ
e
are mobility and mean lifetime of electrons
effective source terms
S
i
,
e
of heavy particles and electrons,
H
of heat production,
H
e
of electron energy
