Biomedical Engineering Reference
In-Depth Information
Law can be applied to each pore. For a
p
ore of length ∆
x
, radius
r
, and cross-
section
A=πr
2
we get, because
J
v
=
v
:
A
8
ηπ
∆
x
∆
P
J
v
=
(8.28)
where
η
denotes viscosity, ∆
P=P
2
−
P
1
is the pressure difference,
J
v
is the
volume flux. Since
J
v
=
L
p
∆
P
(8.29)
we get
A
8
ηπ
∆
x
L
p
=
(8.30)
For an inhomogeneous membrane of thickness ∆
x
we can write
A
1
8
ηπ
∆
x
J
v
1
=
∆
P
.
.
A
i
8
ηπ
∆
x
J
v
i
=
∆
P
(8.31)
.
A
N
8
ηπ
∆
x
.
J
v
N
∆
P
=
or after summation as
A
t
8
ηπ
∆
x
∆
P
J
v
t
=
(8.32)
=
N
1
where
J
v
t
J
v
i
is the total volume flux across the membrane,
A
t
=
N
1
A
i
=
N
1
πr
i
is the total cross-section area of all pores. From equation
(8.32) we obtain
A
t
8
ηπ
∆
x
L
pt
=
(8.37)
where
L
pt
denotes the total filtration coecient of all pores. Equation (8.36)
also gives
A
8
ηπ
∆
x
∆
P
J
v
=
(8.38)
N
A
t
is the mean cross-section area of one pore, and
J
v
=
N
J
vt
is
where
A
=
the mean volume flux through one pore.
8.4 Mechanistic Equations of Membrane Transport
We consider a membrane system shown in Figure 8.3. An inhomogeneous
porous membrane separates two compartments, containing solutions of the
Search WWH ::
Custom Search