Biomedical Engineering Reference
In-Depth Information
When the equilibrium is established (exponential term vanishes):
2
DC
L
L
D
Q
t
=
A
t
−
(5.10)
6
From the intercept of
Q
t
vs.
t
curve on
t
-axis, the effective diffusion coefficient could be
obtained from the slope, whereas
C
A
could be calculated from the
y
-axis intersection.
Another form of solution under the same condition (constant donor concentration, con-
stant diffusion coefficient, and perfect sink), flux (
g
/(
cm
2
·
t
)) at the donor side is given by
1
2
∞
∑
∂
∂
C
x
D
t
{
}
2
2
J t
( )
= −
D
=
2
C
exp (
−
2
m
+
1
)
l
/(
4
Dt
)
(5.11)
A
π
x
=
1
1
By taking only the leading term, the flux at the donor side of the membrane is simplified
to [6]
0 5
.
2
D
L
Dt
0 5
.
ln(
t
J
)
=
ln
2
C
−
(5.12)
t
A
π
4
According to this equation, the effect of partition and diffusion in the membrane can be
separately calculated.
Chen and Lee [7] ignored the partition effect and studied the drug distribution and
release behavior for the case where the core and the coating have different drug diffusiv-
ity. Their theoretical study showed that the ratio between the diffusivity of the drug in the
coating and the diffusivity in the core was a major factor that affects the release rate and
the lag time (the time between onset of the experiment and the instance when drug can be
detected in the medium): the higher the ratio, the higher the release rate and the shorter the
lag time. This finding has been intuitively applied in numerous coating designs.
Diffusivity Control Theory
The diffusion coefficient is extremely important in diffusion because it measures the
number of solute being transported through a unit cross-sectional area in a unit time,
so it tells how fast a solute molecule could travel in a given system. Because diffusion is
eventually a type of motion, any factors, that is, the interaction between solute molecules,
the interaction between solute and solvent, and barriers to move and infl uence the mobil-
inluence the mobil-
ity of a solute, would affect its diffusion coefficient. In drug delivery devices, where the
drug (solute) is often released (through diffusion) from membrane or matrix, the release
rate could be affected by all the factors that affect its diffusion coefficient. Control of the
drug release rate is one of the essential issues in drug delivery; therefore, it is the control
of the diffusion coefficient critical in the design of drug delivery devices. In this sec-
tion, limiting factors of the diffusion coefficient and their mathematical models will be
discussed.
The simplest case of diffusion in a solution is a binary system where solutes are nonelec-
interaction between solute and solvent, and barriers to move and infl uence the mobil-
and infl uence the mobil-
solution is a binary system where solutes are nonelec-
trolytes, and the interaction between solutes is ignored (dilute solution). By considering
a solution is a binary system where solutes are nonelec-
