Biomedical Engineering Reference
In-Depth Information
d
L
FIGURE 5.6
Definition of tortuosity.
m
A t
∂
C
L
= −
D
(5.18)
eff
⋅
But in fact, solute has traveled a distance
d
, and the area for diffusion is only
A
eff
, so we
should have
m
A t
∂
C
= −
D
(5.19)
eff
⋅
L
⋅
τ
Therefore,
D
D
A
A
eff
eff
=
(5.20)
⋅
τ
Substituting Equation 5.17 into the above equation:
D
D
A
A
⋅
⋅
ε
τ
eff
eff
=
(5.21)
0
Therefore, the effective diffusion coefficient would be correlated to the diffusion coeffi -
the diffusion coeffi -
diffusion coeffi
cient in a pure solvent by the following equation
2
3
5
D
D
a
r
a
r
a
r
a
r
eff
=
1
−
1 2 104
−
.
+
2 09
.
−
0 95
.
ε
/
(5.22)
Due to the steric hindrance, the solute concentration in the membrane (mass of the solute
in the membrane divided by volume of solution in the membrane) is smaller than the
concentration outside. Therefore, the first term in Equation 5.22 is also known as partition
coefficient (
K
p
). Similarly, the second term is known as the fraction reduction in diffusivity
or hydrodynamic dragging factor (
K
d
). The above equation therefore could be written in a
compact form:
D
K K
ε
d
p
D
=
(5.23)
eff
τ
