Biomedical Engineering Reference
In-Depth Information
anode electrodes, respectively. Some water will be riding with the cations and anions
as hydrated water and cause a corresponding stress on the cathode and anode sides.
Therefore, the contribution to the total pressures on the anode and the cathode sides
due to these charge redistributions can similarly be calculated such that
ΠΠ
=
+
Π Π Π
+
+
−
Π
,
(6.35)
1
1
,
M
1
,
P
1
,
H
1
,
OH
hw
ΠΠ
=
+
Π Π Π
+
+
+
Π
,
(6.36)
2
2
,
M
2
,
P
2
,
H
2
,
OH
hw
where
Π
hw
is the stress magnitude due to migration of hydrated water riding on the
cations as they migrate towards the cathode. It is assumed that, due to symmetry,
the magnitude of this stress, because it is compressive and negative in the anode
side and tensile and positive in the cathode side, is the same in the anode and the
cathode sides. In summation form, equations (6.35) and (6.36) can be written as:
∑
()
−
()
−
+
−
Π
=
RT
C
t
C
t
Π
,
i
=
M P H
,
,
,
OH
(6.37)
1
Gi
,
Ai
,
hw
i
∑
()
−
()
+
+
−
Π
=
RT
C
t
C
t
Π
,
i
=
M P H
,
,
,
OH
(6.38)
2
Gi
,
Ci
,
hw
i
where
()
=
()
−
(
)
Ct
C
01
ht
,
(6.39)
Ai
,
Ai
,
GAi
,
()
=
()
−
(
)
+
()(
)
Ct
C
01
ht
C
0
VVh
/
t
−
Gi
,
Gi
,
GCi
,
Ai
,
A
G
GA
i
(6.40)
()(
)
2
C
0
V
/
V
h
h
t
Ai
,
A
G
GV i GCi
,
,
(
)
(
()
=
()
−
()
)
()(
)
2
Ct
C
01
C
0
VVht
/
+
C
0
VVh h t
/
,
Ci
,
Ci
,
Gi
,
G
C
GCi
,
A
,
i
A
C
GA i
,
GC i
,
(6.41)
+
−
iMPHOH
=
,,
Due to neutrality, the following relations also hold:
()
=
()
Ct
C t
,
kAGC
=
,
,
,
(6.42)
kM
,
kOH
,
()
=
()
Ct
C t
,
KAGC
=
,
,
,
(6.43)
kP
,
kH
,
Thus, equations (6.37) and (6.38) simplify to
