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One of the most broadly used models for membrane fouling is the Hermia model (HM), which separates this phenomenon into four blocking mechanisms, each with an associated parameter n. The original model is given by an Ordinary Differential Equation (ODE) dependent on n. This ODE is solved only for these four values of n, which limits the effectiveness of the model when adjusted to experimental data. This paper aims extend the original Hermia model to new values of n by slightly increasing the complexity of the HM while keeping it as simple as possible. The extended Hermia model (EHM) is given by a power law for any n ≠ 2 and by an exponential function at n = 2. Analytical expressions for the fouling layer thickness and the accumulated volume are also obtained. To better test the model, we perform model fitting of the EHM and compare its performance to the original four pore-blocking mechanisms in six micro- and ultrafiltration examples. In all examples, the EHM performs consistently better than the four original pore-blocking mechanisms. Changes in the blocking mechanisms concerning transmembrane pressure (TMP), crossflow rate (CFR), crossflow velocity (CFV), membrane composition, and pretreatments are also discussed.

Membrane fouling caused by complex greywater synthesized by personal care products and detergents commercially available for household applications was investigated using dead-end microfiltration (MF) and analyzed systematically by a multistage Hermia blocking model as a first attempt. The highest flux decline was associated with the smallest pore size of the membrane (0.03 μm). This effectiveness was more pronounced at higher applied pressures to the membrane. A cake layer was formed on the membrane consisting mainly of silica particles present as ingredients in greywater. Although organic rejection was low by the porous MF membrane, the organic compound contributed to membrane fouling in the filtration stage. With a 0.03 μm pore size of the membrane, dominant fouling mechanisms were classified into three stages as applied pressure increased, such as complete pore blocking, intermediate pore blocking, and cake layer formation. Specifically, during the early stage of membrane filtration at 1.5 bar, membrane fouling was determined by complete pore blocking in the 0.10 μm pore size of the membrane. However, the later stage of membrane fouling was controlled mainly by intermediate pore blocking. Regardless of the applied pressure, pore constriction or standard blocking played an important role in the fouling rate with a 0.45 μm pore size of the membrane. Our results also support that complex formation can occur due to the concentration of organic and inorganic species present in simulated greywater. Thus, strategic approaches such as periodic, chemically enhanced backwashing need to be developed and tailored to remove both organic and inorganic fouling from MF membranes treating greywater.

This paper aims to interpret the role of the soul as ontological, intellectual or cognitive and as the moral principle within the frame of the holistic conception of human psychosomatic health that emerges from the context of Zalmoxian medicine in the proemium of Plato’s Charmides. It examines what the ontological status of the soul is in relation to the body and the body–soul complex of man considered as a psychosomatic whole. By comparing the presentation of the soul as principle in the Charmides and the Phaedrus, the paper defends the thesis that in the former dialogue, Plato develops his own anthropological ontology, which paves the way for the salvation of human existence and health. The soul is bestowed with an ontological primacy that determines the philosophical and medical presuppositions for treating human illness under a holistic view. The interpretation of the ontological relation of the soul to the body and the entire human being in the context of Zalmoxian holistic medicine is based on Hermias Alexandrinus’ exegesis of the conception of the soul as principle in the Phaedrus. This paper demonstrates that, from both the medical holistic viewpoint and the anthropological philosophical perspective, the soul is the principle and πρῶτον with regard to the body and the body–soul complex without being the whole that the corresponding medical epistemology must apprehend.

A commercially available nanofiltration membrane, NF90, was modified using an in situ concentration polarization-enhanced radical graft polymerization method to improve the organic fouling resistance as well as the removal of pharmaceutical and personal care products (PPCPs), including ibuprofen (IBU), carbamazepine, sulfadiazine, sulfamethoxazole, sulfamethazine, and triclosan (TRI). 3-Sulfopropyl methacrylate potassium salt (SPM) and 2-hydroxyethyl methacrylate (HEMA) were used in various dosages for surface modification, and the extent of membrane modifications was quantified based on the degree of grafting. The modified NF90 exhibited a 15–40% lower flux during humic acid (HA) fouling and 25% greater NaCl rejection compared with the virgin membrane. PPCP rejection in the modified NF90 membranes before and after HA fouling was 20–45% and 5–20% greater, respectively, compared with that of the virgin membrane. Both SPM and HEMA increased the hydrophilicity of NF90 by decreasing contact angles. Scanning electron microscopy revealed lower amounts of foulants on the modified NF90 than on the virgin membrane. The main fouling mechanism for virgin NF90 was gel layer formation and those for modified NF90 were complete and intermediate blocking. Therefore, the modification of NF90 was effective for controlling organic fouling and strongly rejecting PPCPs.

Designing turbulence promoters with optimal geometry and using them for ultrafiltration systems has been a key challenge in mitigating membrane fouling. In this study, six different turbulence promoters were created using three-dimensional printing technology and applied in dead-end ultrafiltration. Three-dimensional-printed (3DP) turbulence promoter configurations were integrated into a classical batch ultrafiltration cell. The effects of these configurations and the stirring speeds on the permeate filtration flux, organic rejections, and membrane resistances were investigated. The fouling control efficiency of the 3DP promoters was evaluated using two polyethersulfone membranes in a stirred ultrafiltration cell with model dairy wastewater. The Hermia and resistance-in-series models were studied to further investigate the membrane fouling mechanism. Of the Hermia models, the cake layer model best described the fouling in this membrane filtration system. It can be concluded that the 3DP turbulence promoters, combined with intense mechanical stirring, show great promise in terms of permeate flux enhancement and membrane fouling mitigation. Using a well-designed 3DP turbulence promoter improves the hydrodynamic flow conditions on the surface of the stirred membrane separation cells based on computational fluid dynamics modeling. Therefore, the factors effecting the fabrication of 3DP turbulence promoters are important, and further research should be devoted to revealing them.

In this paper, nanofiltration (NF) of acid whey after isolation of proteins was studied. Two membranes were tested: NF-99 (Alfa Laval) and DL (Osmonic Desal). Based on previous measurements that determined the highest efficiency in separating lactic acid and lactose whey, the pH was adjusted to 3. First, the most appropriate transmembrane pressure (TMP) was determined based on the highest flux measured. The TMP range was 5–25 bar for the DL membrane and 10–30 bar for the NF-99 membrane. The temperature was kept at 4 °C using a thermostat. The mechanisms of membrane fouling were investigated. The Hermia models and the modified Tansel model were applied to study the fouling mechanism and to determine which membrane would foul earlier and more severely, respectively. The most suitable TMP was determined at 20 bar. Despite the 1.4 times higher flux of the sample at DL, the fouling rate was higher when NF-99 was used. The results showed that the Tansel model is suitable for predicting the fouling time of protein-isolated whey by nanofiltration.

Fouling mechanisms associated with membrane-based polysaccharide enrichment were determined using a dense ultrafiltration (UF) membrane. Dextran with different molecular weights (MWs) was used as a surrogate for polysaccharides. The influence of dextran MW on fouling mechanisms was quantified using the Hermia model. Flux data obtained with different dextran MWs and filtration cycles were plotted to quantify the more appropriate fouling mechanisms among complete pore blocking, standard pore blocking, intermediate pore blocking, and cake filtration. For 100,000 Da dextran, all four mechanisms contributed to the initial fouling. As the filtration progressed, the dominant fouling mechanism appeared to be cake filtration with a regression coefficient (R2) of approximately 0.9519. For 10,000 Da, the R2 value for cake filtration was about 0.8767 in the initial filtration. Then, the R2 value gradually decreased as the filtration progressed. For 6000 Da, the R2 values of the four mechanisms were very low in the initial filtration. However, as the filtration progressed, the R2 value for cake filtration reached 0.9057. These results clearly show that the fouling mechanism of dense UF membranes during polysaccharide enrichment can be quantified. In addition, it was confirmed that the dominant fouling mechanism can change with the size of the polysaccharide and the duration of filtration.

Membrane surface patterning is one approach used to mitigate fouling. This study used a combination of flux decline measurements and visualization experiments to evaluate the effectiveness of a microscale herringbone pattern for reducing protein fouling on polyvinylidene fluoride (PVDF) ultrafiltration membranes. Thermal embossing with woven mesh stamps was used for the first time to pattern membranes. Embossing process parameters were studied to identify conditions replicating the mesh patterns with high fidelity and to determine their effect on membrane permeability. Permeability increased or remained constant when patterning at low pressure (≤4.4 MPa) as a result of increased effective surface area; whereas permeability decreased at higher pressures due to surface pore-sealing of the membrane active layer upon compression. Flux decline measurements with dilute protein solutions showed monotonic decreases over time, with lower rates for patterned membranes than as-received membranes. These data were analyzed by the Hermia model to follow the transient nature of fouling. Confocal laser scanning microscopy (CLSM) provided complementary, quantitative, spatiotemporal information about protein deposition on as-received and patterned membrane surfaces. CLSM provided a greater level of detail for the early (pre-monolayer) stage of fouling than could be deduced from flux decline measurements. Images show that the protein immediately started to accumulate rapidly on the membranes, likely due to favorable hydrophobic interactions between the PVDF and protein, followed by decreasing rates of fouling with time as protein accumulated on the membrane surface. The knowledge generated in this study can be used to design membranes that inhibit fouling or otherwise direct foulants to deposit selectively in regions that minimize loss of flux.

Vibrio natriegens is widely used as a production host for biotechnological processes due to its superior maximum glucose consumption rate, high growth rate, and abundant ribosomes. Most bioprocesses also need a scalable biomass separation step. This can be achieved by cross-flow filtration with ceramic membranes, although the membrane pores are susceptible to fouling. However, the fouling characteristics of V. natriegens culture broth have not been investigated in detail. We therefore characterized membrane fouling during the separation of V. natriegens biomass from culture broth using a cross-flow filtration plant with ceramic membranes. The resistance in series model was used to quantify the fouling-induced resistance caused by the different components of the culture broth. The total fouling resistance was 4.1·109 ± 0.6·109 m−1 for the culture broth and 5.4·109 ± 0.7·109 m−1 for the summed broth components. Reversible resistance accounted for 86% and 81% of these totals, respectively. We then applied Hermia’s adapted filtration laws to determine the dominant fouling mechanism induced by the different broth components. In a further step, we established a setup to determine the compressibility index of the cells during cross-flow filtration, resulting in an estimated value of 0.55 ± 0.04. These results will facilitate the design of economic filtration plants and will help to establish V. natriegens as a production host for large-scale industrial processes.

In this paper the physicochemical characteristics and the flow decline occurring during the reverse osmosis of skim milk, were analysed. The flow decline was evaluated using the resistances in series, the blocked pore models and a second conjugated model that combined the blocked pores with the development of a filter cake. The main resistance found was the concentration by polarization, which was mainly influenced by the complete blocking of the pores. The conjugated model was capable of predicting the flow decline of the process. With respect to the physicochemical properties, more than 98% of the lactose, protein, oils and fats were retained, demonstrating the efficiency of the process.