Geoscience Reference
In-Depth Information
free molecule expression for the ion-particle recombination does not work. On the
other hand, no modifications related to the Coulomb interaction appear in the case
of repulsive potential. The free molecule formula works for small particles (a
l
c
)
and only when the particle size becomes comparable to the Coulomb distance do
the corrections become perceptible.
In the case of repulsion nothing interesting appears. Equation
3.185
reproduces
the well-known free molecule limit
˛.a/
a
2
v
T
e
ˇU.a/
:
(3.189)
Indeed, at small particle sizes ˛
fm
has the form
˛
fm
.a/
a
2
v
T
e
ˇU.a/
e
ˇU.R/
:
(3.190)
On substituting this expression into Eq.
3.185
, one comes to Eq.
3.189
.
At large
a
,Eq.
3.185
always reproduces the diffusion limit
4D
˛
diff
.a/
D
:
(3.191)
a
r
2
e
ˇU.r/
dr
3.6.4
Recombination
The important role of charging processes in aerodisperse systems had been recog-
nized long ago (Natanson
1959
,
1960
). More or less reliable expressions for particle
charging efficiencies had been found only for neutral particles. The case of particle-
ion recombination remained, and still remains, open for further theoretical attacks.
The nature of the difficulty is the necessity for the incident ion to loose a part of its
kinetic energy. This process goes only in the presence of a third body (normally a
carrier gas molecule). The respective expression for the recombination efficiency
should thus depend on the density of the carrier gas. It is quite clear that the
recombination process goes at the distances not exceeding the ion mean free path.
Next, on colliding with a third body the ion should occupy sufficiently deep energy
levels; otherwise, the lifetime of a loosely bounded dipole (ion
C
particle) with
respect to the collisions with the molecules of the carrier gas becomes very short.
So far the parameters, the recombination distance, and energy have been introduced
by hand. The goal of this subsection is to demonstrate how this arbitrariness can be
removed. The flux-matching theory allows one to introduce and to define the radius
of the limiting sphere, which in the limit of very small particle sizes depends only
on the ion diffusivity in the carrier gas. This radius has the order of the ion mean
free path. Next, this theory allows for taking into account the contribution of the ion
