Biomedical Engineering Reference
In-Depth Information
+ Ve
on
- Ve charge
+ Ve charge
+ Ve
on
+ Ve charge
+ Ve charge
+ Ve charge
+ Ve charge
on
+ Ve
on
+ Ve
- Ve charge
+ Ve
on
+ Ve
on
+ Ve
on
+ Ve
on
- Ve charge
+ Ve
on
on
+ Ve
- Ve charge
- Ve charge
FIGURE 6.24
The simplest solution for a configuration with a few cations after activation.
since the net force along the length of the gel strip is a distributed force and should
give rise to a net Coulomb force of zero, the following equation holds:
L
o
/
2
(
)
∫
FZ Z
η
,
=
0
,
(6.104)
−
L
/
2
This implies that the spacing between the fixed charges (i.e.,
b
) obeys the equation
−
1
bmL
o
=
(6.105)
If equation (6.104) does not hold for a given strip of ionic gel, then some overall
movement of the gel strip occurs in addition to the bending. In fact, recent experimental
results (Shahinpoor and Kim, 2001) confirm this observation. Note that, from equation
(6.103), an average stress over the cross-section of the gel strip (width =
w
g
; thickness
=
t
g
) may be defined as
2
πη
(
)
=−
(
)
22
−
ση
,
Z
16
N
π
Q b
/
w t
K
cos
2
π
ZZ
/ ,
(6.106)
gg
1
b
where the negative sign ensures that the stress is negative when the gel is in a
contracted state.
Now, in order to find the curvature
λ
-
should be calculated. Assuming a neo-Hookean type of constitutive equation for
polymer elasticity, it is concluded that
κ
E
in equation (6.46), the difference
λ
+
-
