
Engineering applications 325
where I and
ij
are the identity matrix and Cauchy stress tensor, respec-
tively, and
is the osmotic pressure computed by the concentration values
of the mobile ionic species across the interface between the hydrogel and
solution as
PRTC CC
os
refkk
k
0
1
3
∑
(7.32)
where
is nondimensionalized osmotic pressure, and
and
k
are the
nondimensionalized concentrations of the
mobile ion in the hydrogel
and solution domains, respectively. Equation (7.31) can be expanded as
Eu
x
u
y
v
xy
P
x
1
1
2
1
2
os
0
2
2
2
0
2
2
0
2
−ν
∂
∂
+
−ν
∂
∂
+
+ν
∂
∂∂
=
∂
∂
(7.33)
Ev
y
v
x
u
xy
P
y
1
1
2
1
2
os
0
2
2
2
0
2
2
0
2
−ν
∂
∂
+
−ν
∂
∂
+
+ν
∂