Environmental Engineering Reference
In-Depth Information
E
XAMPLE
6.6 R
EACTION- AND
D
IFFUSION
-L
IMITED
R
EGIONS
The transport-limited mass transfer coefficient can be related to other system parameters
such as flow velocity, particle size, and fluid properties using correlations, for example,
the
Fröessling correlation
:
k
c
D
p
D
A
=
2
+
0.6
Re
1
/
2
Sc
1
/
3
,
Sh
=
(6.42)
where
Sh
is the Sherwood number,
Re
is the Reynolds number
(
=
uD
p
/
ν
)
, and
Sc
is
the Schmidt number
(
=ν
/D
A
)
.For
Re >
25, the above equation can be simplified to
obtain
Sh
=
0.6
Re
1
/
2
Sc
1
/
3
.
(6.43)
Thus we have the following equation for
k
c
:
k
c
=
0.6
D
2
/
3
u
D
p
1
/
2
A
.
(6.44)
1
/
6
ν
For aqueous solutions,
D
A
≈
10
−
10
m
2
/s,
ν =
1
×
10
−
6
m
2
/s, and
k
c
≈
1.2
×
10
−
6
(u/D
p
)
1
/
2
. Using a typical environmental reaction condition,
C
g
A
≈
10
−
5
mol/m
3
and
k
A
≈
0.1 s
−
1
, we obtain
(
1
×
10
−
6
)
1
+
(
8.3
×
10
4
/(u/D
p
)
1
/
2
)
.
r
=
(6.45)
10
-6
Reaction limited
10
-7
10
-8
10
-9
Diffusion limited
10
-10
10
-11
10
-12
10
4
10
4
6 × 10
4
10
4
10
5
1.2 × 10
5
0
2
×
4
×
8
×
1
×
(
U
/
D
P
)
(1/2)
FIGURE 6.10
Diffusion and reaction-limited regions for a heterogeneous reaction
involving transport of reactants to the surface.
continued
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