Biomedical Engineering Reference
In-Depth Information
Figure 5.11
Radial diffusion from an initial spherical volume.
On putting [4]
u c r
(5.28)
(5.27) becomes
2
¶
u
¶
u
=
D
(5.29)
2
¶
t
¶
r
This equation is formally the same as the one-dimensional diffusion equation,
and can be solved by using the same methods.
5.3.6.1 Steady State Solution
In the case of a steady state problem, (5.29) becomes
d
æ
dc
ö
=
2
r
0
(5.30)
ç
÷
d r
è
d r
ø
of which the general solution is
A
c
=
+
B
(5.31)
r
where
A
and
B
are constants to be determined from the boundary conditions.
5.3.6.2 Transient Solution
In the case of a spherical surface with a constant concentration
c
1
(
r
=
a
) and an
external concentration
c
0
(
r
>
a
), the solution is derived directly from the one-
dimensional Ilkovic's solution
