Environmental Engineering Reference
In-Depth Information
Figure 9.7
Basic filtration processes.
Pure H
2
O (unfouled membrane)
Increasing
Reynolds number (
Re
)
J
∆
P
Figure 9.8
Solvent flux vs pressure drop.
The filtration process can operate in two basic modes, dead-end or cross-flow. These
modes are shown in Figure 9.7.
In dead-end filtration, retained particles form a cake layer. The cake-layer thickness
changes with time. As the thickness increases, the solvent flow decreases. In cross-flow
operation, a large portion of the solvent passes parallel to the membrane without per-
meating through the membrane. The advantage of cross-flow operation is that the shear
forces generated by the flow push the particles along the membrane, reducing fouling.
The solvent flux (
J
) is typically described by the equation
J
=
P
/
R
T
. The total
resistance to flow (
R
T
) is expressed as the sum of two resistances,
R
m
+
R
c
, where
R
m
is the resistance due to the membrane and
R
c
is the cake-layer resistance. The resistance
R
m
can be determined by measuring the pure-water flux on an unfouled membrane, one
limiting case corresponding to maximum solvent flux. This case is independent of feed
flowrate. As
R
c
increases, the flux becomes independent of
P
. This is illustrated in the
Figure 9.8.
For a membrane that has been exposed to a feed solution, the solvent flux decreases
compared to the pure-water value. As
P
increases, the flux reaches a plateau value and
becomes independent of
P
. The plateau value is a function of the feed flowrate (shown
by
Re
in Figure 9.8).
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