Biomedical Engineering Reference
In-Depth Information
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FIGURE 5.3
A possible charge redistribution configuration in ionic gels.
Then it can be shown that the component of the electric potential field per unit charge
at the point
,
Z
)
perpendicular to the row is represented in a series such that:
(r
i
i
∞
r
Z br
n
i
Rr Z
(, )
=
,
(5.3)
i
i
2212
]
(/ )(
s
+
1
)
[(
−
)
i
i
i
=−∞
, and is symmetrical about the origin.
It may therefore be represented in a Fourier series in the form
This function is periodic in
Z
, of period
b
i
i
∞
∑
Rr Z
(, ) (/ )
=
12
C
+
C
cos(
2
π
mZ
/ )
b
(5.4)
i
i
0
i
i
i
i
m
=
1
where
∞
α
r
cos(
2
π
mZ
/
b
)
∑
i
∫
C
=
(/ )
2
b
i
i
i
dZ
(5.5)
mi
i
i
(/ )(
12
s
+
1
)
(
)
0
2
2
Z b
−
+
r
n
=∞
i
i
i
Evaluating the coefficients
C
,
m
= 0, 1, 2,…
∞
in equation (5.5), for
m
= 0, then
mi
r
ΓΓ
(/ )()
,
(/)
12
1
i
C
=
(5.6)
oi
b
i
Γ
32
and for
m
> 0
[
]
(/ )
12
s
Cr
=
(/
4
b
( /
π
mb r
)
Γ
(/
1 2
)/
Γ
( / )(
1 2
s
+
1
)
mi
i
i
i
i i
(5.7)
Ks
(/ )(
12 2
π
r
/ )cos(
b
2
π
Z
/
b
)
ii
i
i i
i
