Rejection and Mass Transport in Membranes Michael J. Semmens

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

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.

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 - - + - + - + - + + - + + - -

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.

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: http://www.gewater.com/library/tp/765_Practical_Characterization.jsp

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.

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

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

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

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

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

Permeate flux as a function of transmembrane pressure.

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.

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.

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.

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.

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

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.

1-D Mass balance Cm Cb Cp d

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

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

Film Model

What factors affect k Temperature Module configuration velocity

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

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

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?

How would the initial feed concentration affect Membrane flux behavior?

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

Accounting for concentration polarization In rejection measurements.