## Ultrafiltration Principles And Theory

During UF, pressure (retentate pressure) is applied on the upstream side of the membrane that forces the filtrate to flow through the membrane. The flow rate per unit area, or flux, J, is

Figure 17.5 Industrial-scale ultrafiltration systems for concentration of proteins produced in cell culture fluid. (Reproduced by permission of Millipore Corporation.)

described by equation (2). Modifying equation (2) to include the effect of osmotic pressure (AP) yields:

where J is filtrate flux, Lp is membrane permeability, AP is transmembrane pressure and a is the osmotic reflection coefficient (Belter et al. 1988). For solutes that completely pass through the membrane, a = 0 and for solutes that are completely retained by the membrane, a = 1. The osmotic pressure can be determined using the McMillan-Mayer (1945) theory for aqueous solutions:

where C is the protein concentration and a,b and c are the first, second and third coefficients, respectively. Equation (5) can be simplified to include only the first two coefficients for most protein concentration applications. Additionally, this equation can be expanded to include the contributions of multiple components if needed; however, determining the individual coefficients for multicomponent solutions can be difficult.

Another key equation in the description of ultrafiltration is the rate of solute transport in the fluid near the membrane surface. Figure 17.6 shows that as filtrate flows through the membrane,

CONCENTRATION POLARIZATION AND MEMBRANE FOULING

CONCENTRATION POLARIZATION AND MEMBRANE FOULING

Feed

### Membrane

Figure 17.6 Concentration profiles in the bulk solution and at the membrane wall during ultrafiltration. (See text [pages 336-341] for explanation of terms.)

Feed

### Membrane

Figure 17.6 Concentration profiles in the bulk solution and at the membrane wall during ultrafiltration. (See text [pages 336-341] for explanation of terms.)

the retained molecules collect close to the membrane surface leading to an increased concentration of those molecules at the wall (Cw). Meanwhile, away from the membrane surface in the bulk solution, the concentration of these molecules (Cb) is lower due to the tangential flow of the retentate. When the protein concentration builds up within a boundary layer at the membrane surface, the resulting effect is called concentration polarization, and this leads to a reduction in the filtrate flux (J) which has been described by the stagnant-film model (Michaels 1968; Blatt et al. 1970):

where k is the solute mass transfer coefficient, Cw, Cb and Cf are the concentrations at the membrane wall (surface), in the bulk feed solution, and in the filtrate, respectively. Concentration polarization is described further in the following section.

Concentration polarization and membrane fouling are inherent issues in any ultrafiltration process. They are often confused and difficult to distinguish between during processing, especially since both may occur rapidly and both result in flux decline. Basically, concentration polarization refers to the collection of retained solute particles near the surface of the membrane that can result in a lowering of the filtrate flux. On the other hand, membrane fouling is associated with the formation of a cake layer, which could be the result of protein adsorption to the membrane or formation of aggregates, precipitates or denatured proteins that deposit on the membrane surface. Membrane fouling has also been described as a change in the membrane performance as a result of specific interactions between the membrane and the feed components, and membrane regeneration is the

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### Responses

• lidya
What is ultrafiltration theory?
2 years ago