Geoscience Reference
In-Depth Information
Here S
p
is referred to as the mass accommodation coefficient. The left-hand side
of this equation gives the distribution function of the molecules moving outward
from the particle surface. The part 1
S
p
of inward moving molecules specularly
rebounds from the particle surface (the first term on the right-hand side). The second
term describes the emission of the reactant molecules from the particle.
In the particular case when the reactant molecules do not experience chemical
transformations inside the particles, n
C
D
n
e
(equilibrium number concentration
over the particle surface), which means that all guest molecules trapped by
the particle thermalize and escape from it having the Maxwell distribution over
energies.
Let us write down the solution to Eq.
3.40
:
2
M.E/
r
˚
n
1
C
C
n
1
ı
s;1
C
.1
S
p
/ n
1
C
S
p
n
C
ı
s;1
: (3.43)
1
f
s
D
The first term describes all molecules flying past by the particles. They fly in
both radial directions, s
DC
1 and s
D
1. The second term describes the
molecules flying from infinity and hitting the particle. The third term describes
the motion of the molecules that flew from infinity and recoiled from the particle
surface and the molecules evaporated from the particle. Here we introduced n
1
.
The point is that free molecule concentration n
1
does not correspond to that of
the reactant in the diffusion zone and serves as a fitting parameter allowing us to
make the concentration n
fm
.R/ equal to n
c
.R/. Equation
3.43
can be cast into the
form:
2
M.E/
r
n
1
S
p
.n
1
n
C
/
ı
s;1
;
1
f
s
D
(3.44)
where ı
q;s
stands for the Kroneker delta and
M.E/
D
2.kT/
3=2
p
Ee
E=kT
(3.45)
is the Maxwellian. In deriving Eq.
3.44
the evident identities
ı
s;1
C
ı
s;1
D
1 and
C
C
D
1
(3.46)
were used.
Equations
3.26
and
3.44
yield:
2
S
p
.n
1
n
C
/
1
r
1
!
1
a
2
r
2
n
fm
.r/
D
n
1
D
n
1
.n
1
n
C
/b
.r/:
(3.47)
