Biomedical Engineering Reference
In-Depth Information
½
P
2
T
¼½
P
2
þ½
P
E
5
(E10-3.34)
2
½
E
2
T
¼½
E
2
þ½
M
E
2
þ½
M
E
2
(E10-3.35)
1
3
½
E
3
T
¼½
E
3
þ½
M
E
3
(E10-3.36)
2
½
E
4
T
¼½
E
4
þ½
M
E
4
þ½
P
E
4
(E10-3.37)
4
1
½
E
5
T
¼½
E
5
þ½
M
E
5
þ½
P
E
5
(E10-3.38)
5
2
Further solution of these equations render identical solutions to the problem (for the interme-
diates) as compared with that from the reaction rate approach as shown in Example 10-2. The
fluxes can be obtained as
J
1
¼ J
2
¼ k
1
½
M
1
½
E
2
k
1
½
M
1
E
2
2
¼k
1c
K
1
½
¼ k
1c
½
M
1
E
M
1
½
E
2
(E10-3.39)
k
1c
½
M
1
½
2
T
E
¼
K
1
þ K
1
K
1
f1
½
M
3
þ½
M
1
J
4
¼ J
3
¼ k
2
½
M
2
½
E
3
k
2
½
M
2
E
3
M
2
E
3
¼k
2c
K
2
½
¼ k
2c
½
M
2
½
E
3
(E10-3.40)
¼
k
2c
½
M
2
½
E
3
T
K
2
þ½
M
2
4
¼k
3c
K
3
½
J
8
¼ J
7
¼ k
3c
½
M
3
E
M
3
½
E
4
(E10-3.41)
k
3c
½
M
3
½
E
4
T
¼
K
3
þ K
3
K
1
f2
½
P
1
þ½
M
3
J
9
¼ k
4c
½
M
4
¼J
8
¼ J
7
(E10-3.42)
k
5c
½
M
3
½
E
5
T
J
13
¼ J
12
¼
(E10-3.43)
K
5
þ K
5
K
1
f3
½
P
2
þ½
M
3
5
¼J
13
¼ J
12
(E10-3.44)
where the upper case K's are defined the same by Eqns
(E10-2.51) and (10-2.52)
. That is,
J
14
¼ k
6c
½
M
K
i
¼
k
i
þ k
ic
i ¼ 1; 2; 3;
and
5
(E10-3.45)
k
i
and
K
fi
¼
k
fi
k
fi
i ¼ 1; 2; 3
(E10-3.46)
Keeping the same notation with reaction rate expressions allows us to see the connections
between reaction expressions and the flux expressions.
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