Biomedical Engineering Reference
In-Depth Information
Having found an explicit equation for
v
(
r, t
), we can now carry out numerical
simulations to compare the theoretical dynamic contraction of ionic polymeric gels
in an electric field with those of experiments. In order to compare the experimental
results and observations with the proposed dynamic model, a number of assumptions,
simplifications, and definitions are first made. Consider the ratio
W
(
t
)/
W
(0), where
W
(
t
) is the weight of the entire gel at time
t
, and
W
0
=
W
(0) is the weight of the gel
at time
t
= 0, just before the electrical activation. Thus,
r
t
0
∫
∫
Wt
()
=−
W
2
πρ
vrtrdrdt
( , )
(4.30)
0
0
r
i
This can be simplified to
t
r
∫
∫
o
=−
−
1
Wt W
()/
1
W
2
πρν
( , )
rtrdrdt
(4.31)
0
0
0
r
i
The initial weight of the gel is related to the initial degree of swelling
q
=
V
(0)/
V
p
,
where
V
(0) is the volume of the gel sample at
t
= 0 and
V
p
is the volume of the dry
polymer sample. Numerical simulations were carried out based on the assumptions
that the cross-section of the gel remains constant during contraction of the gel sample,
and that
ε
=
e
= 1.6
×
10
-19
C
(4.32)
T
= 300 K,
α
= 1,
D
= 80,
µ
= 0.8
×
10
-3
Pa.s
(4.33)
= 1000 kg/m
3
,
b
= 2.55
×
10
-10
m
(4.34)
ρ
k
= 1.3807
×
10
-23
J/K,
r
i
= 6.08
×
10
-10
m,
r
0
=
r
i
q
(1/2)
(4.35)
q
= 25, 70, 100, 200, 256, 512, 750
(4.36)
The initial length and cross-section of the sample are, respectively,
= 1 cm
0
and
S
= 1
m
2
, and the electric field is
E
= 5.7 V/cm.
The results of numerical simulation and experimental data are depicted in figure
4.119 and show reasonable agreement with our experimental results, as well as the
experimental results of Gong et al. (1994a, 1994b) and Gong and Osada (1994)
shown in figure 4.120.
µ
4.6.12
O
THER
A
SPECTS
OF
PAN M
USCLE
B
EHAVIOR
The behavior of the PAN fibers may also be explained based on the molecular inter-
action forces. The main interaction forces may be considered as the long-range elec-
trostatic (Coulomb) forces as well as the short-range van der Waals and double-layer
