Biomedical Engineering Reference
In-Depth Information
permeate flux is said to be membrane controlled and the flux is pressure dependent and is
governed by the above equation.
At high transmembrane pressures, a significant gel layer of the rejected solutes
accumulates on the membrane and restricts flow. At this point, mass transfer is no longer
controlled by the operating parameters of cross-flowand transmembrane pressure. In this
region, permeate flux is said to be gel layer controlled and the flux is independent of
pressure. In this region, there is a balance between the rate at which solute is deposited at
the membrane due to convection by the solvent flow through the membrane and diffusion
of the solute from the membrane to the bulk liquid. Here, permeate flux is governed by
themass transfer coefficient and the relative solute concentration in the gel layer and bulk
solution (feed concentration), as shown in the following equation for the film theory
model that predicts that flux decreases exponentially with feed concentration
J
filtrate
¼ k ln
C
G
C
B
bulk stream concentration.
The optimal operating point is in the transition region between the membrane
controlled region and the gel layer controlled region. In this region, the beneficial effect
of increasing transmembrane pressure on permeate flux becomes nonlinear, yet flux is
still controlled by TMP. Here, both transmembrane pressure and cross-flow flux are
important. Cross-flow provides turbulence and shear that improve the mass transfer of
solutes from the membrane surface back to the bulk liquid. The agitation and mixing
provided by the cross-flow turbulence effectively sweeps accumulated solute from the
membrane and reduces the gel layer thickness by controlling concentration polarization.
Increasing cross-flow initially has a linear effect on reducing the gel layer thickness
and moves the gel layer controlled region to higher transmembrane pressure as shown
in Fig. 6.7. In the transition region, cross-flow affects filtrate flux by extending the
where C
G
¼
gel layer concentration and C
B
¼
Gel layer controlled
Membrane controlled region
Constant CFF
3
=
∆
P
3
Process fluid
Water
Constant CFF
2
=
P
2
∆
Constant CFF
1
=
P
1
∆
Maximum TMP
Transmembrane pressure
Figure
6.7.
Effect of cross-flow rate on permeate flux.
