Biomedical Engineering Reference
In-Depth Information
Δ −Δ
P
π
(2)
J
=
μ
R
to l
where ∆π is osmotic pressure.
According to equation (2), flux is dependent on the driven force, i.e. transmembrane
pressure and total resistance. In practice, if feed solution contains particular materials or
macromolecules, the permeate will decrease with filtration time to a level which is much
lower than initial flux. The decrease of flux is a result of the build-up of a concentration
gradient onto membrane surface caused by convective transport of solutes towards membrane
(concentration polarization), formation of macromolecule gel layer on membrane surface and
other membrane fouling (i.e. narrowing or blocking membrane pore by solutes).
The total resistance increases with filtration time due to the different types of membrane
fouling, leading to a decline of flux when a constant pressure is applied. Thus the total
resistance is the sum of all sub resistances (equation 3).
R
=
RR R
+
+
(3)
to l
m
cp
f
where,
R
m
is the membrane resistance, a membrane constant;
R
cp
is the resistance caused by
concentration polarization;
R
f
is the resistance caused by membrane fouling.
Dead -end filtration
Cross-flow filtration
1.
Feed
Feed
Retentate
Permeate
Permeate
Figure 2. Dead-end and cross-flow filtration..
There are fundamentally two different ways of running pressure-driven membrane
process, i.e. dead-end filtration and cross-flow filtration (Figure 2).
In dead-end filtration, feed solution is pressurized through the membrane. The pressure is
constant over the whole membrane surface. If the feed solution is contained in a batch cell,
the feed volume will decrease with filtration time. In cross-flow filtration, the feed solution is
pumped tangentially along the membrane surface. By the pressured applied, the permeate is
induced. However, there is a pressure drop along the membrane because of the tangential
flow over the membrane. Thus, the pressure is not constant over the whole membrane surface.
Cross-flow filtration has several advantages comparing to dead-end filtration. Particularly, the
