Biomedical Engineering Reference
In-Depth Information
If the pore size is so small that the entrance of solvent molecules (radius:
b
) is hindered as
well, partition coefficient would be written as [15]:
2
a
r
1
−
A
eff
=
A
(5.24)
0
2
b
r
1
−
sol-
ute inside solvent-filled pore was described by Langevin equation for a sphere of mass
m
,
radius a with velocity
v
(Figure 5.7) [16].
A more rigorous and general derivation was reviewed by Deen [11]. Diffusion of the sol-
the sol-
d
d
v
t
m
= −
6
π
av F t
+
( )
(5.25)
The first term on the right-hand side of the above equation is also known as Stokes force
on the sphere in an unbounded fluid [17].
Substituting the expression for driving forces [18] to produce diffusion motion into the
above equation by considering only the concentration difference, we have
d
d
v
t
∂
ln
C
x
m
= −
6
π
av kT
−
(5.26)
∂
At equilibrium, the diffusion motion force (second term of the right-hand side) is exactly
balanced by the hydrodynamic force (first term of the right-hand side). A factor
K
is intro-
duced to account the effect of the sidewall:
∂
ln
C
x
(5.27)
0
= −
6
π
aKv kT
−
∂
r
z
z
x
2
a
a
r
z
r
λ =
β =
FIGURE 5.7
Solute in a pore.
