Environmental Engineering Reference
In-Depth Information
where
1
K
G
=
1
k
G
+
K
aw
k
L
.
(6.57)
The general equation for the rate of absorption in the case of an enhancement in the
liquid phase due to reaction is given by
1
(K
aw
/k
G
E))
C
G
i
,
r
1
=
(6.58)
((
1
/k
L
)
+
where
E
is the enhancement in mass transfer due to reaction
rate of uptake with reaction
rate of uptake without reaction
.
E
≡
(6.59)
+
→
For example, consider an instantaneous reaction given byA(g)
B(aq)
products;
(D
B,aq
/D
A,aq
)(C
B,aq
/C
in
A
)
.
The derivation of the two-film mass transfer rate at fluid-fluid interfaces can
be generalized to a number of other cases in environmental engineering such as
soil-water and sediment-water interfaces.
+
the enhancement factor
E
is 1
6.1.5 D
IFFUSION AND
R
EACTION IN A
P
OROUS
M
EDIUM
The lithosphere (e.g., soils, sediments, aerosols, activated carbon) is characterized by
an important property, namely, its porous structure. Therefore, all of the accessible
area around a particle is not exposed to the pollutants in the bulk fluid (air or water).
The diffusion of pollutants within the pores will lead to a concentration gradient from
the particle surface to the pore. The overall resistance to mass transfer from the bulk
fluid to the pore will be composed of the following: (a) diffusion resistance within the
thin-film boundary layer surrounding the particle; (b) diffusion resistance within the
pore fluid; and (c) the final resistance from that due to the reaction at the solid-liquid
boundary within the pores. This is shown schematically in Figure 6.12a and b.
If the external film diffusion controls mass transfer, the concentration gradient
is
C
A
C
A
, and the diffusivity of A is the molecular diffusivity in the bulk liquid
phase,
D
A
. If internal resistance controls the mass transfer, the gradient is
C
A
C
A
(r)
,
but the diffusivity is different from
D
A
. The different diffusivity results from the fact
that the solute has to diffuse through the tortuous porous space within the particle. A
tortuosity factor,
−
, is defined as the ratio of the actual path length between two points
to the shortest distance between the same two points. Since only a portion of the solid
particle is available for diffusion, we have to consider the porosity
τ
ε
of the medium.
ε
is defined as the ratio of the void volume to the total volume. Thus the bulk-phase
diffusivity
D
A
is corrected for internal diffusion by incorporating
ε
and
τ
.
D
A
ε
τ
D
eff
A
=
.
(6.60)
For most environmental applications,
ε
/
τ
is represented by the
Millington-Quirk
10
/
3
/
ε
2
, where
θ
is the volumetric content of the fluid
approximation
which gives
θ
(air or water).
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