Biomedical Engineering Reference
In-Depth Information
Expulsed solvent
Y
X
FIGURE 6.1
Gel disk swelling problem.
0.9
0.6
Y
0.3
0
0
0.3
0.6
0.9
X
FIGURE 6.2
Finite element mesh on gel geometry.
of symmetry, only a quarter of the gel disk is modeled. The finite element mesh
having 11 elements is shown in figure 6.2.
In the problem presented, the physical parameters and state variables are chosen
to resemble typical values for a polyacrylamide gel system. Initially, the gel is
assumed to be equilibrated at a pH of 8 with a corresponding equilibrium solvent
mass fraction equal to 0.989. Then the gel's pH is changed to 3 (with a corresponding
solvent mass fraction equal to 0.775). This will cause the gel to expel solvent and
shrink. Physical model parameters were derived from experimental observations
(
K
a
= 6
10
-5
, and
N
= 4).
Figure 6.3 shows the displacement of the outer edge of the disk as a function
of time. As expected, the initial shrinkage is the fastest and then it slows until the
new equilibrium dimension is reached. The solvent concentration gradients for three
different time values (20, 200, and 500 sec) are shown in figures 6.4, 6.5, and 6.6.
×
10
-5
,
x
= 0.2,
L
sp
=
1
×
