Biomedical Engineering Reference
In-Depth Information
Jk
P
x
∂
∂
+
φκ
j
=−
m
(6.86)
m
F
where
k
m
is the water permeability constant, according to them
P
m
is the fluid pressure
κ
is the water transference coefficient in the gel network
is the water molar volume
j
is the current density
F
is the Faraday constant (96,500 C/kg-mol)
φ
They, then, consider a linear stress-strain law—rather than hyperelastic neo-
Hookean, as was proposed in our formulation—for the bending deformation of the
strip in the form of
p
m
=
E
m
ε
, where
p
m
is the swelling or osmotic stress,
E
m
is the
elastic modulus, and
ε
is the linear strain. They relate the strain
ε
to the hydration
H
and equilibrium hydration
H
eq
by
HH
H
−
+
eq
3
ε
=
(6.87)
1
eq
This appears to have an unnecessary factor of 3. They consider inertial effect to
be absent (slow motion) and assume a conservation of momentum in the form of
∂
∂
P
x
∂
∂
p
x
m
m
=
(6.88)
1
0.8
q = 25
0.6
q = 70
q = 100
0.4
q = 200
q = 256
0.2
q = 512
q = 750
0
0
2
4
6
8
10
Time/min
FIGURE 6.19
Computer simulation (solid lines) and experimental results (scattered points)
for the time profiles of relative weight of the gel sample for various degrees of swelling,
q
.
