Biomedical Engineering Reference
In-Depth Information
They solve the preceding equations to arrive at an expression for the curvature
(1/
R
) such that
2
3
−
2
d
1
φκ
j
1
2
E
1
−
exp
π
Dt
m
m
+
9
1
H
FD
d
11
eq
m
−
=
(6.89)
RR
Q
0
where 2
d
is the thickness of the strip,
D
m
=
k
m
E
m
/[3(1 +
H
eq
)] is the diffusion
coefficient (~4.5
10
-6
cm
2
S
-1
), and
Q
is the stiffness (i.e., the product of the elastic
modulus and the area moment of inertia of the bending strip).
Their presentation further gets more empirical and unclear. However, it is inter-
esting to note that expression (6.89) for the curvature is similar to our expression but
involves the current density
j
, which is unknown. The reader is referred to their paper
for further explanation and graphical representation of their solutions. Figure 6.20
depicts numerical simulation of these equations according to Asaka and Oguro (2000).
As can be seen, the trends that they observe are very similar to the trends observed
experimentally and simulated theoretically by the proposed model in this chapter.
×
10
30
Experiment
Experimental
8
Eq. (26)
Eq. (26)
20
a
a
b
6
b
10
4
0
2
-10
0
-2
-20
1
6
4
0.5
2
0
0
-2
-0.5
-4
-1
-6
-1
0
12345
-1012345
Time, t/s
Time, t/s
(a)
(b)
FIGURE 6.20
Numerical simulation of equation 6.89 by Asaka and Oguro (Asaka, K. and
K. Oguro. 2000.
J. Electroanalytical Chem
. 480:186-198.)
