Geoscience Reference
In-Depth Information
In the case of evaporation of the host molecules, the consideration does not
change except that in this case we must take into account the changes of the particle
size and the dependence of the equilibrium pressure over the particle surface on the
particle size (see Friedlander
2000
, p. 257):
c
e
.a/
D
c
1
exp.2
v
m
=akT/
(3.101)
Here
v
m
is the volume per a molecule in the gas phase and is the surface tension.
3.5
Particle Charging in the Free Molecule Regime
Charging of small neutral and charged particles suspended in a weakly ionized
plasma is investigated under the assumption that the Coulomb
C
image forces affect
the ion transport in the carrier plasma and define the rate of charging processes. Our
approach is based on a solution of the collisionless kinetic equation describing the
ion transport in the presence of force fields created by the particle charge and the
image force. The exact free molecule ion distribution over coordinates and velocities
is used for calculating the rate of ion deposition onto neutral and charged dielectric
particles. Our approach easily reproduces well-known results for metallic particles
and allows us to derive rather simple expressions for the charging efficiencies of
dielectric particles. Our theory is applicable either for particles whose sizes are
much smaller than the ion mean free path (the charging of neutral particles) or
when the ion mean free path much exceeds the Coulomb length (the distance at
which the ion thermal and Coulomb's energy become comparable) (ion-particle
recombination).
3.5.1
Introduction
The problem of particle charging is not new and its importance is beyond any
doubt. Charged aerosol particles are met almost everywhere. The reason for this
is apparent: the energy excess of a charged aerosol particle becomes comparable to
the thermal energy kT already at particle size of the order of the Coulomb length
l
c
D
e
2
=kT.Here
e
is the electron charge,
T
is the temperature in K, and
k
is the
Boltzmann constant. At ambient condition this length is about 60 nm (for a singly
charged particle) and comparable to the mean free path
l
of air molecules (Seinfeld
and Pandis
2006
). On the other hand, there exist many sources of particle charging:
natural and artificial radioactivity, short-wave electromagnetic radiation, cosmic
rays, intra-atmospheric chemical reactions producing ions (Hodges
1969
;Marlow
and Brock
1975
;Marlow
1980
; Hussin et al.
1983
; Jensen and Thomas
1991
;
Beig and Brasseur
2000
). Cosmic rays generate ions deep within the troposphere
and control its electrical state down to the Earth's surface. The ions produced by
