Biomedical Engineering Reference
In-Depth Information
Figure 7.28
Reaction
A
+
B
®
C
on a diffusion front.
together with the initial conditions
t
=
0
c x
( ,0)
=
c
c x
( ,0) 0
=
for
x
<
0
A
A
,0
B
(7.56)
t
=
0
c x
( ,0) 0
=
c x
( ,0)
=
c
for
x
<
0
A
B
B
,0
The system of equations (7.55) can be transformed under a more symmetrical
form by using the following transformations
1
2
æ
ö
2
x
L
D
*
*
x
=
,
t
=
t D
,
=
D D
,
L
=
ç
(7.57)
÷
A B
L
D
k C C
è
ø
A
,0
B
,0
We obtain the equivalent system of equations
2
¶
c
¶
c
A
A
-
1
=
χ
-
β
c c
A B
*
*
2
¶
t
¶
x
(7.58)
2
¶
c
¶
c
B
-
B
1
=
χ
-
β
c c
A B
*
*
2
¶
t
¶
x
We see that the system depends only on the two nondimensional parameters
c
and
b
defined by
C
D
D
A
B
A
,0
,0
χ
=
,
β
=
(7.59)
C
B
Figure 7.29
Reaction
A
+
B
®
C
in one-dimensional geometry.
