Stability of Viscoelastic Solutions: BrijL4 and Sodium Cholate Mixtures with Metal Ions Across a Broad pH and Temperature Range.

The impact of pH, temperature, and metal ions on the rheological and interfacial properties of aqueous mixed surfactant solutions composed of anionic NaC (sodium cholate) and nonionic BrijL4 [polyoxyethylene (4) lauryl ether] surfactants has been investigated. The various compound systems were analyzed, considering variations in each selected factor. The results highlight the unique characteristics of the BrijL4/NaC mixture, suggesting its potential as a viable alternative to other existing surfactants. The synergistic effect between BrijL4 and NaC significantly reduces the critical micelle concentration (CMC) and improves the wetting properties on hydrophobic surfaces, surpassing those of single-component solutions. Additionally, sodium, calcium, and magnesium ions enhance surface wetting and decrease the CMC. Besides, the BrijL4/NaC solutions exhibit viscoelastic fluid behavior at higher surfactant concentrations. These viscoelastic BrijL4/NaC solutions demonstrate stability over various pH and temperature variations, exhibiting lower flow activation and scission energy values than those of other viscoelastic surfactant solutions. Notably, the BrijL4/NaC mixture has potential applications in gel-based foliar fertilizers and drug delivery systems. Furthermore, the rheological studies examine the impact of humic acid on the rheological properties of BrijL4/NaC mixture solutions, revealing that incorporating additional humic acids can achieve stable rheological properties.

A versatile route for the fabrication of micro-patterned polylactic-acid (PLA)-based membranes with tailored morphology via breath figure imprinting.

Breath figure imprinting, based on surface instabilities combined with fast polymer evaporation in a humid environment, enables the creation of micro-patterned membranes with tailored pore sizes. Despite being a simple procedure, it is still challenging to fully understand the dynamics behind the formation of hierarchical structuring. In this work, we used the breath figure technique to prepare porous PLA-based (polylactic acid) membranes with two distinctive additives, polyvinylidene fluoride (PVDF) and zinc oxide nanoparticles (ZnO NPs). The selection of these additives was governed by their unique properties and the potential synergistic effects; when blended with PLA, the addition of NPs leads to more uniform structures with tunable characteristics and potential multifunctionality. This article sheds light on the multifaced interactions that intricate the interplays between PLA, PVDF, and ZnO, thus governing their assembly. Through a comprehensive investigation, we scrutinize the impact of blending PVDF and different concentrations of ZnO NPs on the morphology and chemical properties of the final self-assembled PLA membranes while presenting an advanced understanding of the potential applications of PLA-self-assembly porous membranes in various industrial sectors.

Innovative stimuli-responsive membrane MSF brine rejection dilution by tertiary treated sewage effluent.

In this study, treated wastewater and Multi-Stage Flash (MSF) brine were integrated into the Forward Osmosis (FO) system using pressure stimuli-responsive Nanofiltration (PSRNF) membranes to dilute magnesium, calcium, and sulfate MSF plant brine reject. The deposition of magnesium sulfate and calcium sulfate in the heat exchanger is one of the main issues affecting the performance and efficiency of MSF thermal desalination plants. Reducing the concentration of the divalent ions can minimize scale formation and deposition to a level that allows the MSF plant to operate at high top brine temperature (TBT) and without scale problems. The PSRNF membranes were chosen in the FO process because of their high water permeability, rejection of divalent and monovalent ions, small structure parameter (S), and inexpensiveness compared to commercial FO membranes. Three PSRNF membranes were tested in the FO process with the feed solution facing the active membrane layer to avoid active layer delamination. Although the PSRNF membrane exhibited negligible water flux at 0 bar, it increased when a 2-4 bar was applied to the feed solution. The wastewater temperature was set at 25 °C while 40 °C was the brine operational temperature to mimic the field situation. A maximum average water flux of 39.5 L/m2h was recorded at 4 bar feed pressure when the PSRNF membrane was used for the brine dilution, achieving up to 42% divalent ions dilution at 0.02 kWh/m3 specific power consumption. The average water flux in the PRSNF membrane was 35% higher than that in the commercial TFC FO membrane. Notably, the PSRNF membrane is ten times cheaper than commercial FO membranes. Notably, the PSRNF membrane is ten times cheaper than commercial FO membranes, achieving substantial cost reductions and pioneering advancements in FO purification technology.

Production of sustainable thermoplastic composites from waste nitrogen fertilizer-grown marine filamentous cyanobacterium Geitlerinema sp.

The global demand for petroleum-derived plastics continues to increase, as does pollution caused by plastic consumption and landfilling plastic waste. Recycling waste plastics by thermomechanical molding may be advantageous, but it alone cannot address the challenges associated with plastic demand and its widespread pollution. A more sustainable and cleaner approach for recycling plastic waste could be to produce thermoplastic composite blends of waste plastic and biobased alternative materials such as marine algal biomass. In this study, Geitlerinema sp., a marine cyanobacterium, was cultivated with waste nitrogen fertilizer as a nitrogen source, resulting in phycocyanin content and biomass density of 6.5% and 0.7 g/L, respectively. The minimum and maximum tensile strengths of thermoplastic blends containing Geitlerinema sp. biomass, recycled glycerol plasticizer, and waste plastic were 0.29-23.2 MPa, respectively. The tensile strength and Young's modulus of thermoplastic composites decreased as the Geitlerinema sp. biomass concentration increased. Furthermore, thermal analysis revealed that thermoplastics containing Geitlerinema sp. biomass have lower thermal onset and biomass degradation temperatures than waste polyethylene. Nevertheless, 35-50% of Geitlerinema sp. biomass could be a sustainable biobased alternative feedstock for producing thermoplastic blends, making the recycling of waste plastics more sustainable and environmentally friendly.

Enhancing the electrocoagulation process for harvesting marine microalgae (Tetraselmis sp.) using interdigitated electrodes.

Marketable value of algal biomass has been increasing in recent years due to its wide range of applications. This study investigates the performance of a novel cylindrical interdigitated electrode array in electrocoagulation for the harvesting of marine microalgae (Tetraselmis sp.). The new electrode array is expected to exert a dielectrophoretic (DEP) force which would assist in the harvesting of the microalgae in the electrocoagulation process. Through numerical investigation, the induction of dielectrophoretic force was confirmed in the new electrode array. In this study, 10 min electrolysis time was found to be sufficient to harvest 82.4% microalgae with 1 cm electrode distance and 50 mA/cm2 current density. Furthermore, decreasing the electrode distance to 0.5 cm increased the algal harvesting efficiency to 96.18%. Energy analysis showed that the proposed electrode array shows 38% lower specific energy consumption than the conventional flat sheet electrode array.

Effect of the induced dielectrophoretic force on harvesting of marine microalgae (Tetraselmis sp.) in electrocoagulation.

In this study, a new electrocoagulation electrode configuration has been investigated in order to induce dielectrophoretic (DEP) force for the enhanced harvesting of marine microalgae (Tetraselmis sp.). Asymmetrical aluminum electrodes with an alternative current power supply were used. The impact of electrode configuration, current density and electrolysis time were evaluated. A maximum algal harvesting efficiency of 90.9% was achieved using 7.1 mA/cm2 current density and 10 min electrolysis time. The energy consumption was found to be 4.62 kWh/kg of microalgae. The major significance of using the new electrode configuration was found in the aluminum content in the harvested biomass which decreased by 52% compared to the conventional symmetrical electrocoagulation electrodes.

Predicting the performance of multi-media filters using artificial neural networks.

The impact of flow rate and turbidity on the performance of multi-media filtration has been studied using an artificial neural network (ANN) based model. The ANN model was developed and tested based on experimental data collected from a pilot scale multi-media filter system. Several ANN models were tested, and the best results with the lowest errors were achieved with two hidden layers and five neurons per layer. To examine the significance and efficiency of the developed ANN model it was compared with a linear regression model. The R2 values for the actual versus predicted results were 0.9736 and 0.9617 for the ANN model and the linear regression model, respectively. The ANN model showed an R-squared value increase of 1.22% when compared to the linear regression model. In addition, the ANN model gave a significant reduction of 91.5% and 97.9% in the mean absolute error and the root mean square error, respectively when compared to the linear regression model. The proposed model has proven to give plausible results to model complex relationships that can be used in real life water treatment plants.

A fouling suppression system in submerged membrane bioreactors using dielectrophoretic forces.

A novel method was developed to suppress membrane fouling in submerged membrane bioreactors. The method is based on the dielectrophoretic (DEP) motion of particles in an inhomogeneous electrical field. Using a real sample of biomass as feed, the fouling-suppression performance using DEP with different electrical field intensities (60-160 V) and different frequencies (50-1000 Hz) was investigated. The fouling-suppression performance was found to relate closely with the intensity and frequency of the electrical field. A stronger electrical field was found to better recover the filtrate flux. This is because of a stronger DEP force acting on the biomass particles close to the membrane's surface. Above an intensity and frequency value of 130 V and 1 kHz, respectively the permeate flux was reduced due to an electrothermal effect.

Performance and analysis of kappa-carrageenan hydrogel for PFOA-contaminated soil remediation wastewater treatment.

Perfluorooctanoic acid is an emerging pollutant with exceptional resistance to degradation and detrimental environmental and health impacts. Conventional physical and chemical processes for Perfluorooctanoic acid are either expensive or inefficient. This study developed an environmentally sustainable and cost-effective gravity-driven kappa-carrageenan (kC)-based hydrogel for perfluorooctanoic acid (PFOA) removal from synthetic and actual wastewater. Two kC filters were prepared by mixing activated carbon (AC) or vanillin (V) with the kC hydrogel to optimize the hydrogel selectivity and water permeability. Experimental work revealed that the PFOA rejection and water permeability increased with the AC and V concentrations in the kC hydrogel. Experiments also evaluated the impact of feed pH, PFOA concentration, hydrogel composition, and hydrogel thickness on its performance. Due to pore size shrinkage, the AC-kC and V-kC hydrogels achieved the highest PFOA rejection at pH 4, whereas the water flux decreased. Increasing the PFOA concentration reduced water flux and increased PFOA rejection. For 2 cm hydrogel thickness, the water flux of 3%kC-0.3%AC and 3%kC-3%V hydrogels was 25.6 LMH and 21.5 LMH, and the corresponding PFOA rejection was 86.9% for 3%kC-0.3%AC and 85.7% for 3%kC-3%V. Finally, the kC-0.3%AC hydrogel removed 81.1% of PFOA from wastewater of 179 mg/L initial concentration compared to 79.3% for the kC-3%V hydrogel. After three filtration cycles, the water flux decline of 3%kC-0.3%AC was less than 10%. The gravity dead-end kC hydrogel provides sustainable PFOA wastewater treatment with biodegradable and natural materials.

Advances in functionalization and conjugation mechanisms of dendrimers with iron oxide magnetic nanoparticles.

Iron oxide magnetic nanoparticles (MNPs) are crucial in various areas due to their unique magnetic properties. However, their practical use is often limited by instability and aggregation in aqueous solutions. This review explores the advanced technique of dendrimer functionalization to enhance MNP stability and expand their application potential. Dendrimers, with their symmetric and highly branched structure, effectively stabilize MNPs and provide tailored functional sites for specific applications. We summarize key synthetic modifications, focusing on the impacts of dendrimer size, surface chemistry, and the balance of chemical (e.g., coordination, anchoring) and physical (e.g., electrostatic, hydrophobic) interactions on nanocomposite properties. Current challenges such as dendrimer toxicity, control over dendrimer distribution on MNPs, and the need for biocompatibility are discussed, alongside potential solutions involving advanced characterization techniques. This review highlights significant opportunities in environmental, biomedical, and water treatment applications, stressing the necessity for ongoing research to fully leverage dendrimer-functionalized MNPs. Insights offered here aim to guide further development and application of these promising nanocomposites.

Iron slag/activated carbon-electrokinetic system with anolyte recycling for single and mixture heavy metals remediation.

The electrokinetic process has been proposed for in-situ soil remediation to minimize excavation work and exposure to hazardous materials. The precipitation of heavy metals in alkaline pH near the cathode is still challenging. Reactive filter media and enhancement agents have been used in electrokinetics to enhance the removal of heavy metals. This study investigated coupling industrial iron slag waste and iron slag-activated carbon reactive filter media with electrokinetic for a single and mixture of heavy metals treatment. Instead of using acid enhancement agents, the anolyte solution was recycled to neutralize the alkaline front at the cathode, reducing the operation cost and chemical use. Experiments were conducted for 2 and 3 weeks at 20 mA electric current. Copper removal increased from 3.11 % to 23 % when iron slag reactive filter media was coupled with electrokinetic. Copper removal increased to 70.14 % in the electrokinetic experiment with iron slag-activated carbon reactive filter media. The copper removal increased to 89.21 % when the anolyte solution was recycled to the cathode compartment. Copper removal reached 93.45 % when the reactive filter media-electrokinetic process with anolyte recirculation was extended to 3 weeks. The reactive filter media- an electrokinetic process with anolyte recycling was evaluated for removing copper, nickel, and zinc mixture, and results revealed 81.1 % copper removal, 89.04 % nickel removal, and 92.31 % zinc removal in a 3-week experiment. The greater nickel and zinc removal is attributed to their higher solubility than copper. The results demonstrated the cost-effectiveness and efficiency of the electrokinetic with iron slag-activated carbon reactive filter media with anolyte recirculation for soil remediation from heavy metals.

Recent advances in nanocellulose-based two-dimensional nanostructured membranes for sustainable water purification: A review.

Nanocellulose (NC), a one-dimensional nanomaterial, is considered a sustainable material for water and wastewater purification because of its promising hydrophilic surface and mechanical characteristics. In this regard, nanostructured membranes comprising NC and two-dimensional (2D) nanomaterials emerged as advanced membranes for efficient and sustainable water purification. This article critically reviews the recent progress on NC-2D nanostructured membranes for water and wastewater treatment. The review highlights the main techniques employed to fabricate NC-2D nanostructured membranes. The physicochemical properties, including hydrophilicity, percent porosity, surface roughness, structure, and mechanical and thermal stability, are summarized. The key performance indicators such as permeability, rejection, long operation stability, antifouling, and interaction mechanisms are thoroughly discussed to evaluate the role of NC and 2D nanomaterials. Finally, summary points and future development work are highlighted to overcome the challenges for potential practical applications. This review contributes to the design and development of advanced membranes to solve growing water pollution concerns in a sustainable manner.

Microalgae: A potential bioagent for treatment of emerging contaminants from domestic wastewater.

Water crisis around the world leads to a growing interest in emerging contaminants (ECs) that can affect human health and the environment. Research showed that thousands of compounds from domestic consumers, such as endocrine disrupting chemicals (EDCs), personal care products (PCPs), and pharmaceuticals active compounds (PhAcs), could be found in wastewater in concentration mostly from ng L-1 to µg L-1. However, generally, wastewater treatment plants (WWTPs) are not designed to remove these ECs from wastewater to their discharge levels. Scientists are looking for economically feasible biotreatment options enabling the complete removal of ECs before discharge. Microalgae cultivation in domestic wastewater is likely a feasible approach for removing emerging contaminants and simultaneously removing any residual organic nutrients. Microalgal growth rate and contaminants removal efficiency could be affected by various factors, including light intensity, CO2 addition, presence of different nutrients, etc., and these parameters could greatly help make microalgae treatment more efficient. Furthermore, the algal biomass harvests could be repurposed to produce various bulk chemicals such as sustainable aviation fuel, biofuel, bioplastic, and biochar; this could significantly enhance the economic viability. Therefore, this review summarizes the microalgae-based bioprocess and their mechanisms for removing different ECs from different wastewaters and highlights the different strategies to improve the ECs removal efficiency. Furthermore, this review shows the role of different ECs in biomass profile and the relevance of using ECs-treated microalgae biomass to produce green products, as well as highlights the challenges and future research recommendations.

Iron slag permeable reactive barrier for PFOA removal by the electrokinetic process.

The efficacy of the Standalone Electrokinetic (EK) process in soil PFAS removal is negligible, primarily due to the intersecting mechanisms of electromigration and electroosmosis transportation. Consequently, the redistribution of PFAS across the soil matrix occurs, hampering effective remediation efforts. Permeable reactive barrier (PRB) has been used to capture contaminants and extract them at the end of the EK process. This study conducted laboratory-scale tests to evaluate the feasibility of the iron slag PRB enhanced-EK process in conjunction with Sodium Cholate (NaC) biosurfactant as a cost-effective and sustainable method for removing PFOA from the soil. A 2 cm iron slag-based PRB with a pH of 9.5, obtained from the steel-making industry, was strategically embedded in the middle of the EK reactors to capture PFOA within the soil. The main component of the slag, iron oxide, exhibited significant adsorption capacity for PFOA contamination. The laboratory-scale tests were conducted over two weeks, revealing a PFOA removal rate of more than 79% in the slag/activated carbon PRB-EK test with NaC enhancement and 70% PFOA removal in the slag/activated carbon PRB-EK without NaC. By extending the duration of the slag/AC PRB-EK test with NaC enhancement to three weeks, the PFOA removal rate increased to 94.09%, with the slag/AC PRB capturing over 87% of the initial PFOA concentration of 10 mg/L. The specific energy required for soil decontamination by the EK process was determined to be 0.15 kWh/kg. The outcomes of this study confirm the feasibility of utilizing iron slag waste in the EK process to capture PFOA contaminants, offering a sustainable approach to soil decontamination. Combining iron slag PRB and NaC biosurfactant provides a cost-effective and environmentally friendly method for efficient PFOA removal from soil.

Microalgal bioremediation of brackish aquaculture wastewater.

Rapid aquaculture industry development contributed to a major increase in aquaculture wastewater generation. In the context of a circular economy, aquaculture wastewater treatment should simultaneously recover nutrients from the wastewater. Among many treatment methods, bioremediation using microalgae could be a cost-effective and environmentally friendly system that can be applied to treat aquaculture wastewater and simultaneously produce high-value microalgal biomass. This study explored the feasibility of treating brackish wastewater (0.8 % NaCl) generated from a Qatari commercial tilapia farm by microalgae. At first, 10 strains were grown using wastewater from the local farm in an indoor experiment. Based on nitrogen assimilation, biomass yield, biomass quality, and ease of harvesting, 4 candidate strains (Haematococcus sp., Neochloris sp., Monoraphidium sp., and Nostoc sp.) were shortlisted for outdoor growth experiments. Although Nostoc sp. could not grow outdoor in the wastewater, the other three strains were able to assimilate at least 70.5 % of the total nitrogen in the wastewater. Haematococcus sp. and Neochloris sp. could be harvested using self-settling, whereas Monoraphidium required an energy-intensive tangential flow filtration membrane process. Hence, the overall energy requirement for bioremediation, including biomass dewatering, for Haematococcus sp., Neochloris sp., and Monoraphidium sp. were determined as 0.64, 0.78, and 5.68 MJ/m3, respectively. Neochloris sp. had almost twice the biomass yield compared to Haematococcus sp. - suggesting that Neochloris sp. could be a potential candidate for aquaculture wastewater treatment.

Desalination by the forward osmosis: Advancement and challenges.

Forward osmosis (FO) has become a promising membrane technology for desalination and water treatment due to its simplicity, low energy consumption, and low fouling tendency compared to pressure-driven membrane processes. Therefore, the advancement in FO process modelling was one of the main objectives of this paper. On the other hand, the membrane characteristics and draw solute type represent the main FO process factors determining its technical performance and economical perspectives. Thus, this review mainly highlights the commercially available FO membrane characteristics and the development of lab-scale fabricated membranes based on cellulose triacetate and thin-film nanocomposite membranes. These membranes were discussed by considering their fabrication and modification techniques. Additionally, the novelty of different draw agents and their effects on FO performance have been analyzed in this study. Moreover, the review touched upon different pilot-scale studies on the FO process. Finally, this paper has stated the overall FO process advances along with its drawbacks. This review is anticipated to benefit the research and desalination scientific community by having an overview of the major FO components that require additional attention and development.

Industrial sludge valorization and decontamination via lipid extraction and heavy metals removal using low-cost protic ionic liquid.

Sludge is a heterogenous organic-rich matter that comprise of highly valuable biopolymers along with various contaminants including heavy metals. Sludge valorization as a renewable resource and inexpensive feedstock is key for sludge realization in circular economy context. This study presents the use of low-cost protic ionic liquid (PIL) as an integrated process medium to decontaminate heavy metal contaminated industrial sludge while selectively extract the lipid content. The treatment process focused on the use of 1-methylimidazole chloride for its higher heavy metal extraction performance compared to other screened ionic liquids (ILs). The treatment was also able to selectively extract lipids from industrial sludge, leaving a protein/carbohydrate rich solid product. Process temperature was shown to have a key impact on the biopolymers' fractionation. Operating at temperatures above 120 °C resulted in higher recovery of proteins in the lipid-rich fraction, compromising the quality of the lipid stream. Variation of the PIL acid/base (a/b) ratio also had a significant impact on the deconstruction of the sludge biopolymers, with a/b ratio of 1 resulting in highest recovery of all biopolymers. Optimal water concentration as co-solvent was found at 30 wt%, with lipid recovery reaching 60% and heavy metals extraction ranging between 29 and 89%.

A comparative physicochemical property assessment and techno-economic analysis of biolubricants produced using chemical modification and additive-based routes.

Several edible and non-edible oil sources are currently being developed as renewable basestocks for biolubricant production. However, these feedstocks possess undesirable physicochemical properties limiting their lubricant applications. Chemical modification and additive-based routes could be used to modify their properties -suitable for different biolubricant applications. The first part of this study compares how the selected modifications affect the properties of the basestocks. Next, the techno-economic analysis (TEA) was conducted to study 4 selected biolubricants and a potential biolubricant derived from marine microalgae biomass. Oxidative stabilities of chemically modified biolubricants followed the order of epoxidation> triesterification> estolide. Pour points of triesters showed minimal increments and reduced for estolides, whereas epoxidation increased pour points. Estolides exhibit maximum kinematic viscosity increment among chemical modification routes, followed by TMP-transesterification and epoxidation. The oxidative stability of chemically modified biolubricants was higher than additized biolubricants; conversely, the viscosity increments and pour point reductions for additized biolubricants were higher than chemically modified biolubricants. TEA results show that the unit cost for producing 1-kg estolide was the highest among the chemical modification routes. The unit cost per kilogram of jatropha biolubricant produced using the additive-based route was lower than chemically modified biolubricants. Due to a high microalgal oil feedstock cost, the unit cost per kilogram of additized microalgae oil biolubricant was more than the unit cost of additized Jatropha oil. The techno-economic feasibility of biolubricant production from marine microalgal oil could be improved by adopting a biorefinery approach.

MXene (Ti3C2Tx)/Cellulose Acetate Mixed-Matrix Membrane Enhances Fouling Resistance and Rejection in the Crossflow Filtration Process.

Obstacles in the membrane-based separation field are mainly related to membrane fouling. This study involved the synthesis and utilization of covalently crosslinked MXene/cellulose acetate mixed matrix membranes with MXene at different concentrations (CCAM-0% to CCAM-12%) for water purification applications. The membranes' water flux, dye, and protein rejection performances were compared using dead-end (DE) and crossflow (CF) filtration. The fabricated membranes, especially CCAM-10%, exhibited high hydrophilicity, good surface roughness, significantly high water flux, high water uptake, and high porosity. A significantly higher flux was observed in CF filtration relative to DE filtration. Moreover, in CF filtration, the CCAM-10% membrane exhibited 96.60% and 99.49% rejection of methyl green (MG) and bovine serum albumin (BSA), respectively, while maintaining a flux recovery ratio of 67.30% and an irreversible fouling ratio at (Rir) of 32.70, indicating good antifouling performance. Hence, this study suggests that covalent modification of cellulose acetate membranes with MXene significantly improves the performance and fouling resistance of membranes for water filtration in CF mode relative to DE mode.

Modeling and Sensitivity Analysis of the Forward Osmosis Process to Predict Membrane Flux Using a Novel Combination of Neural Network and Response Surface Methodology Techniques.

The forward osmosis (FO) process is an emerging technology that has been considered as an alternative to desalination due to its low energy consumption and less severe reversible fouling. Artificial neural networks (ANNs) and response surface methodology (RSM) have become popular for the modeling and optimization of membrane processes. RSM requires the data on a specific experimental design whereas ANN does not. In this work, a combined ANN-RSM approach is presented to predict and optimize the membrane flux for the FO process. The ANN model, developed based on an experimental study, is used to predict the membrane flux for the experimental design in order to create the RSM model for optimization. A Box-Behnken design (BBD) is used to develop a response surface design where the ANN model evaluates the responses. The input variables were osmotic pressure difference, feed solution (FS) velocity, draw solution (DS) velocity, FS temperature, and DS temperature. The R2 obtained for the developed ANN and RSM model are 0.98036 and 0.9408, respectively. The weights of the ANN model and the response surface plots were used to optimize and study the influence of the operating conditions on the membrane flux.