B
is a distance sufficiently far away from the surface that we can assume that the drug con-
centration is zero there,
cx
,
B
)
= 0
. At the left “inlet” boundary
x
=
x
L
, we use the BC
(
L
,
y
)
= 0
. At the right “outlet” boundary, we use the BC
∂
c
⁄ ∂
x
(
= 0
. At the solid sur-
(
x
R
,
y
)
xL
and the remaining regions are imperme-
face
y
= 0
, the stent occupies the region
0
≤≤
able to the drug. At the stent surface, we use the boundary condition
c
(
0
≤≤
,
0
)
=
c
eq
,
where
c
is the drug concentration in the fluid that is in equilibrium with the stent. At all
eq
other regions on the impermeable surface, we use the no-flux BC
∂
c
⁄ ∂
y
= 0
.
(
x
,
0
)
,,,
,
,,
,
B
.
The parameters for this problem are
V
δ
b
Dc
eq
Lx
L
x
R
NOTE:
This problem was inspired by an actual numerical study performed by a student
here at MIT. In that case, she was looking at the spatial distribution of drug release
into the underlying tissue by solving a reaction/diffusion equation in the underlying
surface underneath the stent to model drug uptake. She also solved, coupled to
the convection/diffusion equation in the fluid stream, the Navier-Stokes equations
to compute the exact laminar velocity profile around the stent. In practice, the drug
release into the underlying tissue is not spatially uniform, but is concentrated just
below and downstream of the stent. Here, I have simplified the problem by making
the underlying surface impermeable to the drug and by neglecting any perturba-
tion in the flow field by the stent.
(
You wish to compute the steady state concentration profile
,
y
)
using finite differences.