
331Properties and Characterization of Natural Fiber
By integrating Equation 15.9 over time and space, the moisture uptake of the
specimen when exposed to a constant temperature and humidity environment can be
described as follows:
∑
=−
+π
∞
1
(2 1)
exp
2
0
2
M
n
h
t
n
x
(15.11)
where
= mass of absorbed moisture at time t,
is saturated mass of absorbed
moisture, h is thickness of the sheet in dry condition, and D is the diffusion coef-
cient or diffusivity.
Case II: In some polymer systems, there will be some sharp boundaries, which
move linearly with time, existing between the swollen and unswollen regions
characterized as a “Cas ...