Critical Flux Values Research Articles

Determination of Sustainable Critical Flux through a Long-Term Membrane Resistance Model.

A long-term membrane resistance model (LMR) was established to determine the sustainable critical flux, which developed and simulated polymer film fouling successfully in a lab-scale membrane bioreactor (MBR) in this study. The total polymer film fouling resistance in the model was decomposed into the individual components of pore fouling resistance, sludge cake accumulation and cake layer compression resistance. The model effectively simulated the fouling phenomenon in the MBR at different fluxes. Considering the influence of temperature, the model was calibrated by temperature coefficient τ, and a good result was achieved to simulate the polymer film fouling at 25 and 15 °C. The relationship between flux and operation time was simulated and discussed through the model. The results indicated that there was an exponential correlation between flux and operation time, and the exponential curve could be divided into two parts. By fitting the two parts to two straight lines, respectively, the intersection of the two straight lines was regarded as the sustainable critical flux value. The sustainable critical flux obtained in this study was just 67% of the critical flux. The model in this study was proven to be in good agreement with the measurements under different fluxes and different temperatures. In addition, the sustainable critical flux was first proposed and calculated in this study, and it was shown that the model could be used to predict the sustainable operation time and sustainable critical flux, which provide more practical information for designing MBRs. This study is applicable to polymer films used in a wide variety of applications, and it is helpful for maintaining the long-term stable operation of polymer film modules and improving the efficiency of polymer film modules.

Maillard reaction products between whey powder and water-soluble tempeh protein extract: membrane-based fractionation

Whey powder, an industrial by-product, has the potential to be transformed into functional ingredients using the Maillard reaction. In this study, this chemical reaction occurred between whey powder and tempeh protein extract, resulting in increased antioxidant activity. This study aimed to isolate the Maillard reaction products (MRP) with the best antioxidant capacity using an ultrafiltration (UF) membrane by considering the fouling phenomenon that occurred on the membrane surface and critical flux for the filtration. MRP exhibited an antioxidant capacity of 0.09 mg ascorbic acid equivalent antioxidant capacity/mL, and the fractionation using a 5 kDa MWCO PES membrane showed the highest antioxidant capacity in terms of free radical reduction and metal chelating mechanisms. During MRP filtration, fouling on the membrane surface was observed, which could be attributed to the cake filtration model. The critical flux value was determined to be 4.23 LMH with a corresponding pressure of 0.75 bar. A long-term filtration below the critical flux showed stable performance, but filtration above the critical flux resulted in significant fouling. The permeate antioxidant IC50 value was 4.25 mg/mL. Based on the LC-MS analysis, 1,4-dihydroxy-2-methyl-anthraquinone and ilexin II were found as the potential contributors to the antioxidant activity of MRP. In summary, our study demonstrates that fractionating MRP using UF membrane-based filtration is an effective method for isolating MRP with high antioxidant capacity. Our findings also shed light on the critical flux value and fouling phenomenon during MRP filtration, which are important considerations for scaling up the production process.

Correlated insulating states in carbon nanotubes controlled by magnetic field

Recent experiments have shown that nearly metallic nanotubes remain insulating throughout magnetic field sweeps, in which the magnetic flux through the nanotube is expected to pass through a critical point where the single-particle band gap closes in one valley. Here, the authors investigate correlated insulating states of zigzag carbon nanotubes, which emerge from the interplay of electron-electron interactions, magnetic flux, strain, and spin-orbit coupling. They find that the gap for charged excitations generically remains open near the critical flux value, and predict a novel mirror symmetry breaking phase that may arise in the experimentally relevant regime of spin-orbit coupling.

Influence of different waveforms on peristaltic flows: a qualitative investigation

In this paper, we investigate the qualitative flow features of a peristaltic flow, in a planar channel, resulting by the action of sinusoidal, multisinusoidal, triangular, trapezoidal, and square waveforms. The results show that the vertical velocities are higher for the waveforms with sharp curvatures in the wave interface, e.g. the square waveform and the multisinusoidal (n = 3) waveform. The dynamical system analysis show the presence of centers, under the crest, and saddles near the trough region. It is observed that for waveforms in which wave trough forms a plateau, the saddles are formed at the end of the plateau where the wave interface begins to rise. We identify two critical values of the flux parameter, i.e. ( and ) around which the behavior of the equilibrium point changes. We show that these critical flux values depend, linearly, on the amplitude parameter ϕ and numerically compute the curves and . The critical values are the same for all of the waveforms except the triangular waveform.

Protected Hybrid Superconducting Qubit in an Array of Gate-Tunable Josephson Interferometers

We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective $\cos2\phi$ elements that exchange `pairs of Cooper pairs' between the superconducting islands when gate-tuned into balance and frustrated by a half flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset charge and magnetic field fluctuations for a sizable window around zero offset charge and half flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition point sets the critical flux value at which protection is destroyed.

Extraction of density-layered fluid from a porous medium

We consider axisymmetric flow towards a point sink from a stratified fluid in a vertically confined aquifer. We present two approaches to solve the equations of flow for the linear density gradient case. Firstly, a series method results in an eigenfunction expansion in Whittaker functions. The second method is a finite difference method. Comparison of the two methods verifies the finite difference method is accurate, so that more complicated nonlinear, density stratification can be considered. Interesting results for the case where the density stratification changes from linear to almost two-layer are presented, showing that in the nonlinear stratification case, there are certain values of flow rate for which a steady solution does not occur. A spectral method is then implemented to consider cases in which there is a stagnant region beneath a sharp interface between two layers of different, but constant, density. In this situation, flows also exist only for flow rates beneath a critical flux value, consistent with the results for the continuous density stratification.

Impact of Particle Shape and Surface Group on Membrane Fouling.

Membrane fouling remains one of the most critical drawbacks in membrane filtration processes. Although the effect of various operating parameters—such as flow velocity, concentration, and foulant size—are well-studied, the impact of particle shape is not well understood. To bridge this gap, this study investigated the effect of polystyrene particle sphericity (sphere, peanut and pear) on external membrane fouling, along with the effect of particle charge (unmodified, carboxylated, and aminated). The results indicate that the non-spherical particles produce higher critical fluxes than the spherical particles (i.e., respectively 24% and 13% higher for peanut and pear), which is caused by the looser packing in the cake due to the varied particle orientations. Although higher crossflow velocities diminished the differences in the critical flux values among the particles of different surface charges, the differences among the particle shapes remained distinct. In dead-end filtration, non-spherical particles also produced lower flux declines. The shear-induced diffusion model predicts all five particle types well. The Derjaguin-Landau-Verwey-Overbeek (DLVO) and extended DLVO (XDLVO) models were used to quantify the interaction energies, and the latter agreed with the relative critical flux trends of all of the PS particles. As for the flux decline trends, both the DLVO and XDLVO results are in good agreement.

Critical Flux and Fouling Analysis of PVDF-Mixed Matrix Membranes for Reclamation of Refinery-Produced Wastewater: Effect of Mixed Liquor Suspended Solids Concentration and Aeration.

Fouling tends to cause a significant increase in hydraulic resistance, decreased permeate flux, or increased transmembrane pressure (TMP) when a process is operated under constant TMP or constant flux conditions. To control membrane fouling and maintain sustainable operation, the concept of critical flux has been discussed by several researchers. Various fouling mechanisms, such as macromolecule adsorption, pore plugging, or cake build-up, as well as hydrodynamic conditions, for example aeration, can take place at the membrane surface. This study aimed to investigate the effects of mixed liquor suspended solid (MLSS) concentration and air bubble flow rate (ABFR) on the critical flux and fouling behavior, when treating refinery-produced wastewater. To determine the critical flux values, the experimental flux-steps were the following: (1) the filtration began with a 30 min step duration at a low flux (10 to 20 L/m2h); (2) at the end of this step (after 30 min), the permeate flux was increased, (3) this step was repeated until the TMP did not remain constant at the constant permeate flux, (4) the critical flux was then achieved. A critical flux model with an R2 of 0.9 was, therefore, derived, which indicates that the particle properties were regulated by the suspended solids. The increase of MLSS concentration, from 3 mg/L to 4.5 mg/L, resulted in a decrease of the permeate flux by 18%. Moreover, an increase in ABFR, from 1.2 mL/min to 2.4 mL/min, increased the permeate flux, but this decreased with a greater flow rate of aeration. To assess the stability and reversibility of fouling during critical flux (Jc) determination using a mixed matrix membrane, flux-step methods were utilized. A step height of 14.3 L/m2h and 30 min duration were arbitrarily chosen. The flux increased to 32.5 L/m2h with a slight increase of trans membrane pressure (TMP), while the rate of increase became significant at a higher flux of 143.6 L/m2h, due to fouling. Overall, this study proved that the response of MLSS concentration and aeration affected the membrane performance, based on the critical flux and fouling behavior.

Quantifying the influence of divalent cations mass transport on critical flux and organic fouling mechanism of forward osmosis membrane

Understanding the insightful impact of divalent cations mass transport on the complex organic fouling of forward osmosis (FO) membrane is vital when seawater/brine is utilized in a FO hybrid process. Our works deeply focused on quantifying the influence of divalent cations on not only critical flux but also the organic fouling mechanism. The presence of divalent cations in aqueous solutions caused a decrease in critical flux values. The fouling mechanism is mainly governed by intermolecular and ion-mediated interactions. The findings suggested the interaction of divalent cations with organic matters close to the membrane surface is more noticeable than that in the feed solution. These interactions combined with an operation at the flux ≥30 LMH led to the formation of a compact and cohesive cake layer (4.8–9.1 μm) where the great divalent cations were deposited on membrane surface after 30 h operation (Ca2+: 162.13–256.72 g/m2, Mg2+: 182.60–374.38 g/m2). In contrast, 21 LMH below critical value exhibited minor fouling with a very thin cake layer (0.5 μm) and minimized deposited divalent cations (Ca2+: 79.47 g/m2, Mg2+: 46.65 g/m2). Overall, the extended operation of 30 h suggested 16–21 LMH were threshold values for FO fouling control.

Critical flux behavior of ultrathin membranes in protein-rich solutions

Critical flux defines the ideal operating conditions in tangential flow filtration (TFF). Below this value a TFF process can, in principle, proceed indefinitely without membrane fouling. The critical flux behavior of ultrathin membranes, which are particularly valuable for small volume processing, has not yet been explored. Here we investigate the critical flux behavior of ultrathin nanoporous silicon nitride (NPN) membranes in concentrated protein solutions using a microfluidic TFF device. We find that NPN (~19% porosity; 60 nm average pore size; 100 nm thick) has the ability to process bovine serum albumin (BSA) solutions as concentrated as 10 mg/mL at 30 μL/min without exceeding a critical flux threshold. At 30 mg/mL and 60 mg/mL, NPN enables 40% and 20% of the supply to be filtered without fouling. In these experiments, NPN membranes achieve critical flux values as high as ~1200 LMH, which is 5x larger than 0.2 μm polyethersulfone (PES) membranes processing 5 mg/mL BSA and an order of magnitude higher than track-etch polymeric membranes (10 μm thick; 80 nm pores) in direct comparisons. The effects of nanoparticle capture on critical flux are also studied here, simulating the capture of small extracellular vesicles (sEVs) in forthcoming diagnostic applications. Our work not only demonstrates the utility of ultrathin membranes for processing concentrated protein solutions, it illustrates the value of applying membrane science principles developed for macroscale systems (e.g. critical flux, TFF) to the micro/nano scale.

The relevance of critical flux concept in the concentration of skim milk using forward osmosis and reverse osmosis

Skim milk was concentrated at 10 °C using forward osmosis (FO), reverse osmosis (RO) and pressure-assisted forward osmosis (PAFO). A pressure of 40 bar, in the form of draw solution osmotic pressure (FO and PAFO modes) or transmembrane hydraulic pressure (RO mode) was applied; an additional hydraulic pressure of 2 bar was applied in the PAFO mode. More severe protein fouling was observed in RO, followed by PAFO and then FO. This was credited to the difference in the initial permeate flux, induced by the different effective driving pressures, with RO having a greater deviation of the initial flux from the critical flux value. The critical flux was determined for the FO and RO modes using a step-wise increase of draw solution osmotic pressure or hydraulic pressure, at a constant milk solids content. The critical flux was between 5.4 L/m2h (1.5 × 10−6 m3/m2s) and 7.2 L/m2h (2 × 10−6 m3/m2s) for both the FO and RO modes at a cross flow velocity of 0.2 m/s. The similarities in the critical flux for FO and RO suggests that the critical flux does not depend on the nature of pressure applied on the system (hydraulic or osmotic). Therefore, when operated at the same flux and crossflow velocity, FO would not fundamentally provide a lower fouling environment compared to RO. An increase of the solids content from 8.7% to 17.3% caused a reduction in the critical flux from 5.4 L/m2h to 3.1 L/m2h (8.5 × 10−7 m3/m2s).

Insight into organic fouling behavior in polyamide thin-film composite forward osmosis membrane: Critical flux and its impact on the economics of water reclamation

A strategy of using critical fluxes to control organic fouling of polyamide thin film composite (PA-TFC) forward osmosis (FO) membranes during wastewater reclamation was developed for FO mode. This work was a comprehensive investigation with various organic foulants covering complex mixtures as well as single foulants. The foulants were alginate (ALG), Humic acid (HA), and Bovine Serum Albumin (BSA) and the study covered different concentration (40; 80; 120; 160 mg/L). Our results indicated that there was a single value of critical flux, 35 LMH for 160 mg/L and single foulant. However the presence of mixed foulants i.e., ALG + BSA, ALG + HA, HA + BSA, at an overall foulant concentration of 160 mg/L gave rise to foulant-foulant-membrane interactions that caused a significant decrease in critical flux values to 25–30 LMH. Using these results as a guide, long-term tests in which there was no fouling or negligible fouling were successfully implemented. Operating below critical flux maintains a sustainable operation with the characteristic of full reversibility, which is vital if chemical cleaning is to be minimized. Characterization of fouling around critical values was made through physico-chemical analyses including SEM, EEM, aggregate size, zeta potential, and FTIR. It was found that FO fouling became irreversible when operated at a flux ≥35 LMH for single foulants and fluxes of 25 LMH and 30 LMH for ALG + BSA and HA + BSA foulants respectively, being a foulant concentration of 160 mg/L; such conditions are favorable for the formation of the cohesive and compact cake layer. Economic assessments based on specific energy consumption facilitated the production of guidelines for practical design and operation.

Application of dead-end ultrafiltration and hollow fibre transverse vibration systems as pre-treatment for the valorisation of bioethanol dunder

Valorisation of high-strength molasses spentwash (biodunder) was investigated using two-stage membrane processing for the recovery of moderate-to-high value organic acids. Conventional techniques relying on precipitation are often problematic, consuming large volumes of chemicals and have poor selectivity within complex sample matrices. Both stirred-cell and hollow fibre transverse vibration systems were compared and assessed in terms of transmembrane pressure stability, dissolved organic matter (DOM) fractionation, organic acid separation and fouling reversibility during long-term operation. For the same membrane material and effluent dilution (10 fold), stirred cell filtration with a UF 30 kDa membrane revealed a critical flux (Jcritical) value of about 6.2 L/m2h, markedly lower than that obtained with a larger MWCO (UF 100 kDa) counterpart wherein Jcritical was situated around 12.7 L/m2h. On the contrary, transverse vibration of submerged hollow fibres demonstrated a greater tenacity to withstand more aggressive feed solutions (i.e. 5 and 2 fold dilution) even at fluxes above Jcritical, coupled with almost 60% restoration of membrane resistance by simple deionised water rinsing following 6.5 h of constant flux filtration. Size exclusion chromatography (LC-OCD) findings highlight considerable rejection of biopolymers (proteins and polysaccharides) in addition to humic, building block and LMW neutrals content of the effluent DOM. Importantly, HPLC analyses indicated the transmission of selected moderate-to-high value organic acids was greatest during submerged hollow fibre vibration with minimal (5 fold) effluent dilution. Further concentration via nanofiltration suggested almost 80% transmission of succinic acid during the polishing of UF permeate. Recovery of such constituents may contribute to substantially improve the economic viability of bioethanol production.

Experimental Investigation of Two-Phase Subcooled Liquid Flow Structure under Preburnout Conditions

The article presents the results from experimentally investigating the occurrence conditions and evolution with time of large vapor agglomerates in a rectangular channel during subcooled water boiling. The experiments were carried out at atmospheric pressure with a mass velocity of up to 1200 kg/(m2 s) and subcooling equal to 30–75 K. Agglomerates emerge as a result of coalescence of small vapor bubbles, the merging of which becomes progressively more intense with increasing the heat flux density at the heating wall starting from approximately 0.75–0.80 of the critical flux value. Decreasing the boiling liquid subcooling value facilitates the occurrence of agglomerates. Nucleate boiling may take place, and burnout phenomena (dry spots) leading to wall burnout may emerge in the liquid film between the heating wall and the agglomerate surface. The vapor agglomerates emerging in the flow of subcooled boiling liquid in a channel are burnout onset precursors. When agglomerates emerge in a system of parallel channels with subcooled boiling liquid, the hydraulic stability of its operation is upset.

Analytical study on ignition time of PMMA exposed to time-decreasing thermal radiation using critical mass flux

This contribution addresses an analytical model to predict the ignition time of PMMA (Polymethyl methacrylate) subjected to a time-decreasing incident heat flux. Surface temperature, transient mass flux and ignition time of PMMA are thoroughly studied based on the exact solutions of in-depth temperature. Critical mass flux is utilized as the ignition criteria. An approximation methodology is suggested to simplify the unsolvable high order equations and deduce the explicit expressions of ignition time. A numerical model is employed to validate the capability of the developed model. The results show that no ignition occurs when the decreasing rate of heat flux increases larger than a critical value. The agreement of the transient mass flux between analytical and numerical models is good at high decreasing rate but turns worse as the decreasing rate declines. However, this enhanced discrepancy affects the ignition time prediction slightly. The inverse of the square root of the ignition time is linearly correlated with the decreasing rate of heat flux, and it becomes significantly sensitive to the decreasing rate when the decreasing rate approaching its critical value. Meanwhile, the value of critical mass flux has appreciable influence on the ignition time prediction.

Cluster dynamics simulation of the flux effect for neutron irradiated pure iron

ABSTRACTThe effect of flux in a wide range from 1.39×10−10 to 1.39 ×10−3 dpa/s has been studied by the cluster dynamics (CD) simulation for pure iron neutron irradiated at a temperature of 300°C for the two fluences. The critical flux values which mark the regimes of flux dependence of average size, number density and irradiation induced hardening for vacancy clusters (VC) and self-interstitial atoms clusters (SIAC) are found. It was found that the effect of neutron irradiation on average size of SIAC was similar for low and high fluxes in the case of the same fluence.

Critical flux-based membrane fouling control of forward osmosis: Behavior, sustainability, and reversibility

Membrane fouling is closely related to the concept of critical flux. Therefore, a fouling control strategy for forward osmosis (FO) membranes that is based on the critical flux is necessary. This study systematically investigated the critical flux behavior of FO membranes (CTA and PA-TFC) in the short-term using a stepping method (draw solution (DS) concentration stepping). In addition, to test the reliability of this method, long-term experiments were conducted to evaluate the influences of operational critical flux on the fouling behavior (sustainable operation and fouling reversibility/irreversibility), thereby determining the critical flux for reversibility. Our results showed that the DS concentration stepping could be applied for critical flux determination in FO. Both membranes exhibited higher critical flux values for alginate fouling compared to other single foulants such as colloidal silica or gypsum. The values were 15.9 LMH for a cellulose triacetate membrane (CTA) and 20.5 LMH for the polyamide thin-film composite (PA-TFC). Whilst these values should be adequate in FO applications they were determined for single foulants. The presence of multispecies of foulants caused a significant decline in the critical flux values. This study found 5.4 LMH for the CTA membrane and 8.3 LMH for the PA-TFC membrane for the combined foulants of alginate + gypsum. This indicates that the critical flux behavior in FO was dependent on the foulant type and membrane type. Importantly, the high restoration of water flux was achieved with the PA-TFC membrane at an operation either close to critical flux (92–98%) or below critical flux (98–100%) (i.e., with negligible irreversible fouling). The critical fluxes for reversibility obtained in this study will aid the efficient operation of practical FO processes.

Assessment of oil fouling by oil-membrane interaction energy analysis

Membrane-filtration is promising for treating the voluminous oily wastewater, especially when the oil emulsions are smaller than 20 µm. However, studies on the inevitable membrane fouling phenomenon by oil are rather scarce. In particular, a question that remained to be addressed was whether the DLVO or XDLVO model provides better predictions of the oil-membrane interfacial interactions and thereby the extent of fouling. Accordingly, this study investigated four oil types (namely, hexadecane, soybean oil, fish oil and crude oil) that were stabilized by the same non-ionic surfactant (namely, Tween 20) and had similar mean droplet diameters. The direct observation through the membrane (DOTM) technique was used to quantify the critical flux of the different emulsions, and both the XDLVO and DLVO models were used to quantify the foulant-membrane and foulant-foulant interactions. DOTM results indicated that the critical flux values were similar for all oils under the conditions tested, except crude oil. Although the XDLVO model appears to be more comprehensive than the DLVO in terms of accounting for the additional Lewis acid-base polar (AB) interaction that is acknowledged to be important in membrane-filtration, results indicate that the dominance of the AB component drowns out the other interactions like that of electrostatics (EL) in this case, which impedes accurate prediction of the different fouling tendencies by the different oil types.

Performance and activated sludge characteristics at short solid retention time in a submerged MBR: effects of C/N ratio of wastewater

ABSTRACTThis study investigated the effect of carbon to nitrogen (C/N) ratio of influent wastewater on performance and activated sludge properties at a sludge retention time of 5 d in a submerged membrane bioreactor. The chemical oxygen demand and ammonia–Nitrogen (NH3–N) removal efficiencies were found to be over 96.3% and 86.9% in the sMBRs having different C/N ratios. It was found that total extracellular polymeric substances and total soluble microbial products increased with an increase in C/N ratio. It was also observed that critical flux, relative hydrophobicity and zeta potential values decreased, and capillary suction time, particle size and viscosity of sludge increased as the C/N ratio increased.

Investigation of the effect of coagulation bath composition on PVDF/CA membrane by evaluating critical flux and antifouling properties in lab‐scale submerged MBR

AbstractUltrafiltration membranes were prepared from blends of poly(vinylidene fluoride) (PVDF)/cellulose acetate (CA) via phase inversion method. The effect of different coagulation bath compositions on the morphology and performance of the blend membrane prepared from casting solution of PVDF/CA with ratio of 80/20 was investigated using sewage wastewater. NaCl and ethanol were used as additives of coagulation bath. Fouling analysis was conducted with Bovine Serum Albumin solution and critical flux evaluation was performed using a lab‐scale membrane bioreactor. In terms of morphological structure, the macrovoids decreased and changed to finger‐like structure. The irreversible fouling reduced and the flux recovery ratio (FRR) of the modified membranes increased remarkably while the reversible fouling caused by deposition of foulants on the surface of the membranes increased. The maximum values of FRR and critical flux of irreversibility were reached by the membrane which was prepared in the coagulation bath containing the highest concentration of NaCl.