Standard filtration model, membranes

As the membrane pores become smaller, the standard blocking law is no longer valid (Figure 6.55B). The cake filtration model remains valid, which indicates prevention of the ferric hydroxide precipitates from entering pores and subsequent internal deposition. Membrane pore radii were tabulated in Table 6.1 as 2,6, 4.8, and 9.1 nm for the 10, 30 and 100 kDa membranes, respectively. Lo and Waite (1998) reported iron hydroxide precipitates to be as small as 10 nm. Nevertheless, complete blocking (pore blocking by the particulates) is not a valid mechanism. Possibly cake formation prevents pore blockage. 

Humic Acid Fractionation. The two different size fractions of humic acid used in this study were obtained by ultrafiltration of previously characterized HA from Lake Bradford, FL. An Amicon ultrafiltration cell (model 8050) was used for fractionation with a filtration membrane of the desired pore size. Molecules exceeding that pore size were retained above the membrane. The nominal molecular weight cut-off (MWCO), or pore sizes, were reported by the manufacturer (Amicon), and are based on globular protein standards. Membranes used in this study were XM300 (MWCO 300,000 daltons, lot number AI), YMIOO (MWCO 100,000 daltons, lot number AT), and XM50 (MWCO 50,000 daltons, lot number AG). A 5 liter fiberglass reservoir (Amicon model RG5) was filled with the solution to be fractionated. The solution was ultrafiltered under pressure (50 psi) with constant stirring. 

Nagesha et al. [71] evaluated the selectivity of membranes with dense silica and PI as the active layer and support, respectively, on the permeation of tocopherols. They used samples of deodorized distillate of soybean oil (DDOS), diluted or not in hexane and DDOS oil ester, without dilution. For comparison, model systems consisting of mixtures of oleic acid and tocopherols in different proportions (80 20 and 50 50), diluted or not in hexane, were selected. In a standard model, (free of hexane) was added to a mixture of fatty acids methyl esters (FAMEs) from soybean oil and tocopherols (90 10). Experiments were conducted on a pressurized filtration unit with nitrogen at 30 bar, 30 C, and 800 rpm. The study revealed that preferential permeation of tocopherols in relation to other constituents of low molecular weight (fatty acids and FAMEs) occurs. The selectivity of the membrane to tocopherols increased with the esterifled DDOS. 

The mechanisms of membrane fouling can be predicted with empirical mathematical models, which are generally a function of TMP and flux [34, 35]. The fouling models, such as cake filtration, pore, standard, intermediate and complete blockage, are derived from Darcy s law [34, 36, 37]. Those fouling models can be applied for either constant flux [38, 39] or constant TMP [36, 40] operation. 

The Realizable k-e model ensures the positivity of normal stresses ( realizable ) by making the empirical constants of k-e turbulence model, C, a function of the mean flow (mean deformation) and the turbulence (/c, ) while the Boussinesq theory used in the standard and RNG k-e model allows for negative normal stresses. The Realizable k-e model is more accurate in the prediction of the spreading rate of both planar and round jets. Kang et al (2008) used a Realizable k-e model to simulate the hydrodynamics in the membrane filtration zone of pilot and full-scale MBRs. 

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