Environmental Engineering Reference
In-Depth Information
which is
exp
,
z
0
e
2
R
R
r
D
j
U
(
R
)
jD
where the Debye-Hückel radius
r
D
is given by (1.9), and
z
0
follows from combining
this formula and (6.36) in an intermediate region.
The criterion for gas rareness has the form
σ
N
a
R
0
1,
σ
is the diffusion cross section of ion-atom scattering, which is assumed
to be independent of the collision velocity. Because this ion scattering proceeds
through the resonant charge exchange process, where an ion and an atom move
along straight trajectories, we have
where
σ
D
2
σ
res
[179], so the criterion for gas
rareness takes the form
2
N
a
R
0
σ
1 .
(6.38)
res
In this case the electron and ion currents originate at distances of approximately
λ
from the particle where interaction of ions with the particle field is negligible.
In particular, for the above example we have the cross section of resonant charge
exchange involving an argon atom and its ion to be
83 Å
2
at a collision
energy of 0.01 eV [76]. Criterion (6.38) for argon pressure
p
takes the form
σ
D
res
p
1Torr.
We now consider one more aspect of ion-cluster interactions. If a cluster or a
particle is moving in a rareness gas with a low velocity
w
compared with a thermal
velocity of atoms, the frictional force
F
is determined by atom scattering by this
particle, and on the basis of (6.1) we have for this force
r
8
T
π
4
3
σ
v
T
F
D
N
a
mw
,
D
m
,
(6.39)
v
T
where
N
a
is the number density of gas particles,
m
is the mass of these atoms, the
diffusion cross section of atom-particle scattering is
r
0
(
r
0
is the particle
radius), and the velocity
v
T
is of the order of the average atom velocity. We now
consider this problem from another standpoint: if a flux of ions passes through an
ionized gas containing particles. Then the frictional force for ions due to particles,
the drag force [4]), by analogy with (6.39) is given by
σ
D
π
σ
v
T
F
D
N
p
mw
,
(6.40)
where
N
p
is the number density of gas atoms and
m
is the ion mass. If an ion is not
captured by the particle, it is scattered elastically, and the diffusion cross section of
this scattering is
l
2
because of strong ion interaction with a self-consistent
particle field at distances
R
from its center,
R
σ
π
l
. From this it follows that although
the number density of particles
N
p
in an ionized gas is small, the large radius of
action of its field (
l
<
r
0
) may compensate for this smallness, and interaction of
ions with particles may be of importance for their braking in an ionized gas.
