Ultrafiltration theory

Ghosh, R. (2003). Protein Bioseparation Using Ultrafiltration Theory, Applications and New Developments, Imperial College Press, London, 166 pp. 

In reverse osmosis membranes, the pores are so smaH, in the range 0.5— 2 nm in diameter, that they ate within the range of the thermal motion of the polymer chains. The most widely accepted theory of reverse osmosis transport considers the membrane to have no permanent pores at aH. Reverse osmosis membranes are used to separate dissolved microsolutes, such as salt, from water. The principal appHcation of reverse osmosis is the production of drinking water from brackish groundwater or seawater. Figure 25 shows the range of appHcabHity of reverse osmosis, ultrafiltration, microfiltration, and conventional filtration. 

In addition to excess sodium intake, abnormal renal sodium retention may be the primary event in the development of hypertension, and it includes abnormalities in the pressure-natriuresis mechanism. In hypertensive individuals, this theory proposes a shift in the control mechanism preventing the normalization of blood pressure. The mechanisms behind the resetting of the pressure-natriuresis curve may include afferent arteriolar vasoconstriction, decreased glomerular ultrafiltration, or an increase in tubular sodium reabsorption.4 Other theories supporting abnormal renal sodium retention suggest a congenital reduction in the number of nephrons, enhanced renin secretion from nephrons that are ischemic, or an acquired compensatory mechanism for renal sodium retention.9... 

Bowen, W. R. and Williams, P. M. Chem. Eng. Sci. 56 (2001) 3083. Prediction of the rate of cross-flow ultrafiltration of colloids with concentration-dependent diffusion coefficient and viscosity-theory and experiment. 

The theory of permeation through microporous membranes in ultrafiltration and microfiltration is much less developed and it is difficult to see a clear path forward. Permeation through these membranes is affected by a variety of hard-to-compute effects and is also very much a function of membrane structure and composition. Measurements of permeation through ideal uniform-pore-diameter membranes made by the nucleation track method are in good agreement with theory. Unfortunately, industrially useful membranes have nonuniform tortuous pores and are often anisotropic as well. Current theories cannot predict the permeation properties of these membranes. 

Theory of Ultrafiltration. Ultrafiltration is a membrane process with the ability to separate molecules in solution on the basis of size (Ghosh, 2003). Particles are separated with the use of pressure and specially designed semipermeable membranes (Figure 13.5). An ultrafiltration membrane acts as a selective barrier. It... 

Singh R. and Tembrock J., Effectively controlled reverse osmosis systems. Chemical Engineering Progress 95 1999 57-66. Koltuniewicz A. and Nowor)fta A., Dynamic properties of ultrafiltration systems in light of the surface renewal theory. Industrial Engineering and Chemical Research 33 1994 1771-1779. 

Danckwerts P.V., Significance of liquid film coefficients in gas absorption. Industrial Engineering and Chemistry 43 1951 460-1470. Denisov C.A., Theory of concentration polarization in cross-flow ultrafiltration Cel-layer model and osmotic-pressure model. Journal of Membrane Science 91 1994 173-187. 

In theory, ultrafiltration is a rather simple process (Cross and Strathmann, 1973 Michaels, 1968). Under hydrostatic pressure, solute molecules, within the molecular weight cutoff of the membrane, pass, along with solvent, through the micropores of the membrane. Larger solutes are retained and concentrated. The separation is made in a cell (see Fig. 6, Chapter 15) with constant stirring to prevent concentration polarization and clogging of the membrane. 

Perhaps because much attention has centered on reverse osmosis membranes, the fine pores present in their skins were observed prior to the discovery of the functionally larger pores of ultrafiltration (UF) membranes. Recently, pores of v30 A have been observed by Zeman (35) in the skins of UF membranes. Their density, uniformity and diameters leave no doubt that these are actually the pores which function during UF. Our ability to actually "see" the intermicellar defect pores (the population of larger size pores) in the skins of RO membranes extends to the 10 X range. Therefore, it is reasonable to expect that at some point we shall be able to extend this ability to the population of smaller sized pores, whose existence is predicted by Sourlrajan s pore theory (36). 

Blatt et al.(29) developed what has become known as the "gel polarization" theory for ultrafiltration, in which the amount of macromolecular material in the fouling layer is controlled by its back-diffusion rate into the feed stream. The gradual decline in flux observed in some practical systems was explained in terms of an irreversible consolidation of the gel layer with time, leading to a reduction in the layer s permeability. Kimura and Nakao (,1) used Blatt s approach to model the fouling of reverse osmosis... 

Boundary Layer Theory. The Reynolds number for flow-through hollow fibers during our experiments was at most about 0.02 cm (diameter) x 4 cm/sec (velocity) x 1.0 g/cm (density)/ 0.007 poise (viscosity) 11 therefore, a boundary layer theory is needed for laminar flow in tubes. Because of its simplicity, the most attractive available theory is an approximate result of thln-film theory. This theory is restricted to a description of boundary layers that are thin in comparison to the tube radius. Furthermore, the ultrafiltrate velocity, J, must not vary along the tube length (uniform-wall-flux theory). At the centerline or axis of the fiber, the impermeable solute concentration C = C... 

For experiments with proteins, this theory, together with data for osmotic pressure, also aids in explaining the rather unusual response of ultrafiltration rate to pressure and the virtual Independence of this response from fiber length and axial flow velocity. Osmotic pressure data are available in the literature for bovine serum albumin at pH 7.4 ( ), and osmotic pressure measurements of moderate accuracy were made by the authors on bovine calf serum. 

Ultrafiltration Experiments. There is no boundary layer theory for ultrafiltration of proteins in tubes for the general case of applied pressures comparable to reverse osmotic pressures. The process involves complete rejection of protein, and most... 

No exact theory for protein ultrafiltration is available to test the asymptotic theory against therefore, its validity can only be inferred by how well it correlates data. The test of the data used only one adjustable parameter, the protein dlffusivity. The value calculated for D for BSA systems was compared with that in the literature. For calf serum there are no published diffusion data, and internal consistancy of results was the primary criterion for success. A patterned ear h program was used to find the least value of the sum Z[(P - several sets of... 

The parameter, D, calculated is probably strongly related to a true protein diffusivity, but an exact boundary layer theory for protein solutions is needed to accurately establish that relationship. However, irrespective of a theoretical explanation, the observed Independence of graphs of J versus P from axial velocity and fiber length is a new region of Xhe protein ultrafiltration process that should be investigated further. 

Gel polarized ultrafiltration was recently analyzed for cross flow and unstirred batch cell systems by Trettin and Doshi (1980 a,b). We have shown in these papers that the widely used film theory does not predict the limiting flux accurately. The objective of this paper is to derive an expression for the permeate flux when the pressure independent ultrafiltration of macro-molecular solutions is osmotic pressure limited. We will also attempt to distinguish between gel and osmotic pressure limited ultrafiltration of macromolecular solutions. 

An early work considering osmotic pressure in the ultrafiltration of macromolecular solutions was done by Blatt, et al,. (1970), who employed a theory which had been developed for cross flow reverse osmosis systems. They essentially suggested that the film theory relationship given by Eq. (2) could be solved simultaneously with Eq. (1) to predict permeate rates, where the... 

Osmotic pressure limited ultrafiltration data were analyzed by using Eq. (92) and the osmotic pressure data of Vllker (1975) for 0.15M Saline BSA solutions at pH 7.4. Vilker s data are reproduced in Fig. 5 for BSA in both 7.4 and 4.5 pH 0.15M saline solution. The comparison between theory and experiment is quite good as shown in Table I where the value of D was taken as 6.91 x 10 cm /sec. 

When the assumption of constant wall concentration is justified, data for the unstirred batch cell and thin channel systems may be interpreted using models presented in Trettln and Doshi (1980a, 1980b). Such an analysis is performed where agreement is shown to be very good between theory and osmotic pressure limited ultrafiltration experiments. 

In macromolecular ultrafiltration, 2is pressure is increased, permeate flux first Increases and then In a large number of cases levels out and remains more or less pressure Independent. This could be due to the increase In solute concentration at the membrane surface such that either gel formation occurs or the corresponding osmotic pressure approaches the applied pressure. Limiting flux for the gel polarized case was recently analyzed for cross flow and unstirred batch cell systems by Trettln and Doshi (1980,a, b). In this paper we have analyzed the osmotic pressure limited ultrafiltration for the two systems. Our unstirred batch cell data and the literature cross flow data agree quite well with the theory. We have further shown that an unstirred batch cell system can be used to determine whether pressure Independent ultrafiltration of macromolecular solution is gel or osmotic pressure limited. Other causes for the observed pressure Independence may be present but are not considered in this paper. 

Rivas BL, Moreno-Villoslada I. Binding of Cd2+ and Na+ ions by poly(sodium 4-styrenesulfonate) analyzed by ultrafiltration and its relation with the counterion condensation theory. J Phys Chem B 1998 102 6994-6999. 

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