Geoscience Reference
In-Depth Information
to be very similar to condensation. The only problem is how to find the pressure of
the evaporating substance over the particle surface. There are two sorts of problem:
the evaporation of an admixed molecule and the evaporation of the molecules
of the particle host material. The commonly accepted approach to the latter problem
assumes that the pressure of the host material over the particle surface is equal to its
equilibrium pressure over the curved surface. The effects related to the curvature of
the particle surface are of importance for nanoparticles. We discuss this issue at the
end of this section and begin with the evaporation of an alien molecule.
The diffusion of the alien molecule inside the particle is described by the
diffusion equation
@c
@t
D
Dc
(3.94)
with the boundary condition
J.t/
D
4a
2
D
r
c
j
a
(3.95)
and the initial condition
c.r;0/
D
c
0
.r/
(3.96)
In what follows we assume that c
0
is independent of
r
. Next, the characteristic
diffusion time
diff
D
a
2
=D is much shorter than the evaporation time
ev
D
1=˛n.a/,wheren.a/ is the vapor concentration over the particle surface; this means
that the concentration profile inside the particle is always almost flat. Hence, we can
find the concentration beneath the particle surface:
N.t/
4a
2
c
.a;t/
D
(3.97)
The concentration over the particle surface is
c
C
.a;t/
D
Hc
;
(3.98)
where
H
is the dimensionless Henri constant. The conservation of the flux demands
dN
dt
D
˛.a/c
.a;t/
D
˛
3N.t/
(3.99)
4
Finally we have
N.t/
D
N
0
exp .
3˛.a/t=4/
(3.100)
A less primitive consideration may be seen in Ford and Harris (
2004
).
