Biomedical Engineering Reference
In-Depth Information
equations as suggested by Segalman and coworkers (1991, 1992a, 1992b, 1992c,
1993). The flux of hydrated cations is given by
Q
= [
ρ
M
+
(x,y,z,t)+
n
ρ
w
(
x
,
y
,
z
,
t
)]
ν
(
x
,
y
,
z
,
t
)
(6.129)
Thus, the equation of continuity becomes
∂
[
ρ
( , , , )
xyzt
+
∂
n
ρ
( , , , )]
xyzt
=−∇
M
+
w
Q
.
(6.130)
t
Equations 6.114 through 6.130 are the governing equations for the dynamics of
IPMNCs. Clearly, they are highly nonlinear and require careful numerical simula-
tions, which are currently under way and will be reported later.
Next, a linear steady-state version of the formulation is presented to obtain some
preliminary understanding of the complex ionic diffusion and drift in these electronic
materials.
6.6.2
L
INEAR
I
RREVERSIBLE
T
HERMODYNAMIC
M
ODELING
6.6.2.1
Introduction
Figure 6.27 depicts the general structure of the IPMNCs after chemical plating and
composite manufacturing. The structure bends towards the anode. The nature of
water and hydrated ions transport within the IPMNC can affect the moduli at different
frequencies.
6.6.2.2
Steady-State Solutions
Let us now summarize the underlying principle of the IPMNCs' actuation and
sensing capabilities, which can be described by the standard Onsager formulation
using linear irreversible thermodynamics. When
static conditions
are imposed, a
simple description of
mechanoelectric effect
is possible based upon two forms of
transport:
ion transport
(with a current density,
J
, normal to the material) and
solvent
FIGURE 6.27
General structures of an IPMNC or IPCNC film with near-boundary function-
ally graded electrodes and surface electrodes.
