Geoscience Reference
In-Depth Information
PARTICLE SIZE (in nm)
0
01
02
03
04
05
06
5
ε
=2
ε
=5
ε
=100
4
3
2
1
1
PARTICLE SIZE (in units of l
c
)
Fig. 3.8
Enhancement factor ".a/ as the function of particle size for charging a neutral particle.
Lower horizontal axis
shows particle size in units of the Coulomb length l
c
ˇe
2
D
The particle-ion recombination is again described by Eq.
3.146
. This formula
can be used directly for the estimations, but for many practical purposes it is enough
to use the simplified asymptotic result (Lushnikov and Kulmala
2004a
):
ˇe
2
2a
C
u
:::
".a/
.
u
/
"
1
"
C
1
Although this equation is derived for small particles a
l
c
, the numerical
analysis shows that it well reproduces the exact expression up to the sizes a
D
l
c
.
The dependence of the enhancement factor on the particle size is presented in
Fig.
3.9
for a number of values of the dielectric permeability and equal values of
