Geoscience Reference
In-Depth Information
˛
fm
.a;R/e
ˇU.R/
˛.a/
D
;
(3.185)
R
˛
fm
.a;R/e
ˇU.R/
4D
e
ˇU.r
0
/
dr
0
r
0
2
1
C
The numerical calculations were performed for the potential from Lushnikov
and Kulmala (
2004a
) that includes Coulomb
C
image forces with q
D
Q
D
1 and
l
c
D
l or l
c
D
3l.
The results are presented in Figs.
3.19
and
3.20
in terms of the correction factors
.a/, the ratios of the charging efficiencies found from Eq.
3.176
to their values in
the free molecule regime.
˛.a/
˛
fm
.a/
;
.a/
D
(3.186)
4.0
3.5
l
c
=1
l
c
=3
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
PARTICLE RADIUS
a
(in units of
l
)
Fig. 3.19
Correction factor .a/
D
˛.a/=˛
fm.a/
for ion-particle recombination as a function of
particle radius (in units of l
D
2D=
v
T
).
Solid and dotted curves
display R.a/ for l
c
D
1 and
l
c
3, respectively. It is seen that even at small particle sizes these curves deviate from unity; i.e.,
the free molecule approximation is noticeably corrected by ion-carrier gas interaction l
c
D
/
l
