Biomedical Engineering Reference
In-Depth Information
Figure 1. Sketch showing a cross-section of (a) a hemispherical electrode embedded
in an insulator and (b) a disk electrode recessed a distance l into the surface of the
insulator.
i
i
lim
(8)
1
e
f
K
(
Dk R e
/
0
)
(1
DK
)
f
Second, consider a disk electrode that is recessed a distance l
into the surface, as sketched in Fig. 1b . Solving the diffusion equa-
tion for this system yields 18
4
FDC R
b
S
FDC R
b
2
l >> R
i
R
|
R
(
l
R
)
(9)
￿
lim
14/
l
S
R
l
where the last simplification holds when l >> R . Substituting the
corresponding values A = S R 2 and b = S R 2 / l into Eq. (6) yields for
the current
i
l >> R
i
lim
(
l
R
)
(10)
￿
f
K
0
(1
D K
)
f
1
e
(
Dlk
/
)
e
While superficially very similar in form to Eq. (8), note that
this result is actually independent of the electrode radius R (!).
 
 
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