Biomedical Engineering Reference
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where
K
C
k
1
þ K
A
k
1
þ k
1
A
B
S
a ¼
(E9-4.45)
K
A
K
C
k
1
þ k
1
S
þ k
B
K
B
B
Fig. E9-4.8
shows the comparison between the full solutions and those from PSSH treat-
ment for the particular case of
k
A
¼
10
k
S
where we have also shown the
LHHW solutions. One can observe that bulk phase concentration solutions based on PSSH
are surprisingly close to the full solutions (
k
S
t
10
k
S
and
k
B
¼
0.02), better than the LHHW solutions as
shown in
Fig. E9-4.8
. Although we have used the argument that all the intermediates remain
at steady state (pseudo-steady state) and the solutions (of surface coverages,
Fig. E9-4.8
B) do
not appear to be the case, the computed fractional coverages agree quite well with the full
solutions. There is still an apparent shift of the dashed curves to the left but smaller than
that in
Fig. E9-4.6
.
To show the reasonable agreement with the solutions from the PSSH approximation to the
process,
Fig. E9-4.9
shows the comparison between the full solutions and those from PSSH
>
(a)
(b)
1.0
10
9
C
A
0.8
8
7
A
0.6
6
5
j
0.4
4
3
B
2
0.2
C
B
1
0
0.0
0.01
0.1
1
10
100
0.01
0.1
1
10
100
k
S
t
k
S
t
FIGURE E9-4.8
Variations of bulk phase concentrations and fractional surface coverage with time for
k
A
C
s
¼
10
k
S
;
k
B
C
s
¼
10
k
S
;
K
A
¼
1/
C
s
;
K
C
¼
4;
K
B
¼
1/
C
s
. The dashed lines are the predictions from PSSH kinetics, whereas the
solid lines are from the full solutions.
(a)
(b)
10
1.0
9
C
A
8
0.8
7
A
6
0.6
5
j
4
0.4
3
2
0.2
C
B
1
B
0
0.0
0.01
0.1
1
10
100
0.01
0.1
1
10
100
k
S
t
k
S
t
FIGURE E9-4.9
Variations of bulk phase concentrations (a) and fractional coverages (b) with time for
k
A
C
s
¼ k
S
;
k
B
C
s
¼
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