Geoscience Reference
In-Depth Information
limiting sphere. This very ideology applies here for determining the efficiency of
trapping the reactant molecules by an aerosol particle as a function of the mass
accommodation coefficient.
3.3.1
Basic Equations
Below, an exact (formal) expression for the condensational efficiency is derived.
This expression eventually contains some parameters that can be defined only on
solving the full transport problem. However, it is possible to introduce simple
approximations and to restore these parameters approximately. This program is
performed in this section.
3.3.1.1
Trapping Efficiency
Let us assume that the reactant molecules (A molecules) move toward the particle
that captures them (see Eq.
3.30
). The further fate of reactant molecules depends on
the results of chemical processes that proceed inside the particle. Let us denote n
˙
as the concentration of A right beneath (n
C
) or right underneath (n
) the particle
surface. Already here we emphasize that the surface concentrations n
˙
depend on
the nature of physicochemical processes on the surface and inside the particle. Let
then n
1
be the number concentration of A molecules far away from the particle.
It is commonly accepted that the concentration difference n
1
n
C
drives a flux
of A toward the particle surface. The particle begins to grow and to change its
chemical composition. The rate of change in the number of A molecules inside
the particle is equal to the total molecule flux
J
minus the total number of molecules
deposited per unit time at the particle surface minus the rate of consumption of A
by chemical processes inside the particle. The A molecules are assumed to escape
from the particles. In steady-state conditions, the flux
J
can be written as
J
D
˛.a/.n
1
n
C
/;
(3.31)
Here ˛.a/ is the capture efficiency and
a
is the particle radius. Of course, ˛
depends on the mass accommodation coefficient S
p
. The latter is defined as the
probability for an A molecule to stick to the particle. For completely sticking
particles, S
p
D
1.
The interface and in-particle processes fix the value of n
C
. In the simplest case
of the first-order chemical reactions, n
C
is a linear function of
J
, n
C
D
J .a/and
thus
˛.a/n
1
1
C
˛.a/ .a/
;
J
D
(3.32)
