Biomedical Engineering Reference
In-Depth Information
verified that this rate is inversely proportional to square of particle size. This finding
is in line with Tanaka's proportionality with square of the characteristic length of
the sample.
Shahinpoor and Osada (1995a) formulated a theoretical model for a cylindrical
gel sample describing dynamics of contraction of ionic polymeric gels in presence
of an electric field. Their model considered the dynamic balance between the internal
forces during the contraction. These forces are assumed to be due to the viscous
effects caused by the motion of the liquid solvent medium within polymer network,
the internal forces due to motion of the liquid in and out of the network, and the
electrophoretic forces due to the motion of the charged ions in the solvent as it
exudes from the ionic polymeric gel network. The effects of the rubber elasticity of
the network as well as ion-ion interactions were assumed negligible compared to
inertial, viscous, and electrophoretic effects.
The governing equations were then solved for the velocity of the liquid exudation
(water, ethanol, acetone, or mixture of other solvents) from the network as a function
of the time and radial distance in the cylindrical sample. The relative weight of the
gel was then related to the velocity by an integral equation. This can in turn be
solved numerically to obtain a relationship among the amount of the contraction as
a function of time, electric field, strength, and other pertinent materials and geomet-
rical parameters. The results of the numerical simulation in the case of PAMPS
polymer indicated close agreement with experimental data, as described later in
chapter 6.
Caldwell and Taylor (1989) of the University of Hull in the United Kingdom
attempted to describe the force-velocity relationship of the contraction-expansion
mechanism of the PVA-PAA copolymer gel. They simulated flexor and extensor
muscle pairs of humans to power a robot gripper. They used water and acetone for
expansion-contraction of the copolymer gel. In their experiment, they measured up
to 30 N/cm
2
of swelling and contractile forces of the gel. They proposed a two-part
theory for the contraction rate of the copolymer gel:
1.
The diffusion coefficient controls the rate of movement of chemicals
within the polymer strips and its effect is as important as chemical con-
centrations on the dynamic rate. The diffusion coefficient depends on the
solvent used, concentration, degree of cross-linking, and temperature.
2.
Film thickness has been shown experimentally to be proportional to
dynamic rate by an inverse square relationship:
K
Φ
∆
=+
C
(1.28)
2
where
Φ
= contraction rate,
∆
= thickness, and
K
,
C
= fixed constants.
Caldwell and Taylor measured a maximum contraction rate of 11%/sec for a
0.1-mm thick PVA-PAA strip as compared with animal muscle of 24-1800%/sec,
depending on the muscle. They approximated the force-velocity curve of their
