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