1. Rejection and Mass Transport in Membranes
Michael J. Semmens

2. Rejection of hard particles that are smaller than the pores in the membrane
Flexible macromolecules.

3. Deformable or Flexible Solutes
When colloids or large molecules are flexible they can interact more favorably with the membrane and reduce the effective pore size.

4. Solution Composition can effect the apparent size of charged macromolecules.
e.g. pH and Salt effects -
Polyelectrolytes in dilute solution experience
charge repulsion between groups.
Low pH conditions may neutralize the charges and
result in a more compact configuration - +
High salt concentrations and divalent cations tend to cause the electrolyte to shrink and fold back on itself - - + - + - + - + + - + + - -

5. Size exclusion of large organic molecules such as NOM
The size of large organic molecules can be related to the molecular weight.
Where ap is the hydrodynamic radius
is the molecular weight
Z1 and Z2 are constants.

6. Example illustration
Figure 3:  B-Type Membrane Retention of Nonionic Organics All solutes tested individually Saccharides:  Sepa ST stirred cell, 100 psig, 150 rpm (0.4 m/s at outer edge) PEGs:  Sepa CF radical flow cell, 50 psig, 0.9 m/s crossflow
Ref:

7. Rejection
Global Rejection R is based upon the bulk concentrations of the feed water and permeate concentrations.
We can also take into account the volume of permeate collected and base rejection on the mass of solute rejected.

8. Measuring rejection
Add feed solution of known concentration and volume
Apply pressure
Collect permeate as a function of time
Measure permeate concentration

9. Determining Rejection
Initial conditions =
volume of 200mL and and initial concentration of 150 mg/L
Time
Volume collected
Concentration 1 20 18 2 40 16 3 58 5 90 14
Calculate Rejection of the membrane

10. Characterizing Rejection
As membrane filtration continues the concentrations change in the system
and the concentration changes with time may change R
Pressure
Pressure
Pressure

11. Rejection in continuous flow modules
Note that the concentration will change along the length of a membrane in
a flowing system as well. This means that the .
FEED
RETENTATE
Membrane
PERMEATE

12. Local Rejection Pressure
Concentration at the membrane (Cwall) is higher than the bulk concentration

13. Permeate flux as a function of transmembrane pressure.

14. Transport across the membrane
The membranes is selective.
When we examine the impact of membrane filtration on the dissolved organic compounds and particles we see that when they are rejected they are concentrated at the membrane surface.

15. Consider fluxes across the membrane
Clean water flux =
Let s = the fraction of the membrane area that is occupied by pores big enough to allow the solute molecules to pass.
The water flux passing through these pores will transport the solute, thus we can calculate the transport of solute
Solute flux =
Note the feed concentration of the solute on the concentrate side of the membrane may increase somewhat because of rejection as noted above.

16. But the solute flux is equal to the permeate flux times the permeate concentration
NOTE
s is a function of pore size distribution, molecular size, shape, charge etc.

17. Bulk
Suspension
Pore
Blockage
Adsorption
Concentration
Polarization
Cake/Gel / Particle
Layer
Membrane
Resistance
Solids accumulate with time on the membrane. Note that the concentration at the concentration reaches a maximum value at the membrane surface. Note that the concentration gradient encourages back diffusion into the bulk. We could add a mixer and help this back transport.

19. UF for dissolved species MF for suspended particles
Crossflow Filtration
UF for dissolved species
MF for suspended particles Cm Cp Cb
Concentration polarization

20. Consider a steady state analysis
When the system is operating at a steady state the rate of delivery of the solute to the membrane by convection must be balanced by back transport mechanisms.
The concentration gradient will encourage diffusive transport back to the bulk water.

21. 1-D Mass balance Cm Cb Cp d

22. Let
has units of m/s or velocity and is equivalent to a mass transfer coefficient.

23. Permeate flux as a function of transmembrane pressure.
Mass transfer limited
Permeate
flux
Permeate flux approx. independent of pressure
Transmembrane Pressure

24. Film Model

25. What factors affect k
Temperature
Module configuration
velocity

26. Calculating k
The most commonly used equations include the Leveque correlation [3]:
the Chilton-Colburn correlation [17]
and the Dittus-Boelter correlation
Note as velocity is increased, Re increases and Sh increases too so k will increase as we increase the velocity of the water

27. Effect of increasing velocity on permeate flux?
Higher velocity
Permeate
flux
Transmembrane Pressure

28. How would the initial feed concentration affect Membrane flux behavior?
Note the effect is very like that observed for the effect of velocity on the gel model
How can we prove that this effect is predicted by the gel model?

29. How would the initial feed concentration affect Membrane flux behavior?

30. How would the initial feed concentration affectMembrane flux behavior?
J = k log Cm – k log Co
J = a – k log Co
Slope = -k J
Log Co

32. Accounting for concentration polarization In rejection measurements.