Geoscience Reference
In-Depth Information
3.3.4
First-Order Chemical Reaction Inside the Particle
Here we give an example of the function .a/ appearing in Eq.
3.32
. To this end we
consider a steady-state diffusion-reaction kinetics inside the particle. The respective
equation has the form:
D
L
n
L
.r/
n
L
.r/
D
0
(3.65)
Here D
L
is the diffusivity of the reactant inside the particle, n
L
.r/ is the reactant
radial profile inside the particle, and is the reaction constant. We use
ˇ
ˇ
ˇ
ˇ
rDa
J
D
D
L
@n
L
@r
(3.66)
as the boundary condition to Eq.
3.65
. This condition provides the independence of
n
L
of time. The solution to this equation can be found elsewhere. The result is
J
4D
L
a.acoth a
1/:
n.a/
D
n
D
(3.67)
Next, n
D
Hn
C
(the Henri law) with H being the dimensionless Henri
constant. Finally we find
1
4D
L
aH .a coth a
1/
:
.a/
D
(3.68)
Here
D
p
=D
L
.
3.3.5
Results
Here we list the results of the present consideration.
The total flux J isgivenbyEq.
3.32
:
˛.a/n
1
1
C
˛.a/ .a/
:
J
D
This result is exact and thus does not depend on the approximations done in
calculating the trapping efficiency ˛.a/. The function .a/ is independent of
J
in the case of the first-order physicochemical processes at the surface and inside
the particle. In more complicated cases this function depends on
J
and the total
flux is no longer a linear function of n
1
