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Semipermeable membrane

A semipermeable membrane, also known as a selectively permeable membrane, is a thin barrier that permits the passage of certain molecules and ions—such as water, oxygen, and carbon dioxide—while restricting others, like larger polar molecules and charged particles, based on factors including size, charge, and lipid solubility.^[1] This selective permeability is fundamental to various functions, enabling processes like osmosis, where water moves across the membrane from areas of lower solute concentration to higher ones to maintain equilibrium.^[2] The structure of a biological semipermeable membrane, such as the plasma membrane of eukaryotic cells, consists of a phospholipid bilayer embedded with proteins, cholesterol, and carbohydrates, forming a fluid mosaic model that allows dynamic interactions.^[1] Phospholipids arrange with hydrophilic heads facing outward toward aqueous environments and hydrophobic tails inward, creating a nonpolar core that repels water-soluble substances but facilitates the diffusion of nonpolar molecules.^[1] Integral membrane proteins, including channels and carriers, further enhance selectivity by providing specific pathways for ion and solute transport, while peripheral proteins assist in signaling and structural support.^[1] Semipermeable membranes play critical roles in biological systems for homeostasis, nutrient uptake, waste removal, and cellular communication, as well as in artificial applications like water purification and medical filtration.^[2] For instance, in physiology, they regulate osmotic balance in kidneys to filter blood and concentrate urine, support nerve impulse transmission via ion gradients, and protect cells from environmental fluctuations in tonicity, preventing swelling or shrinkage.^[2] Disruptions in membrane permeability can lead to conditions like edema or cell lysis, underscoring their essentiality in health and disease.^[2]

Fundamentals

Definition and Properties

A semipermeable membrane is a selective barrier that permits the passage of certain molecules or ions while restricting others, primarily based on properties such as molecular size, electric charge, or solubility within the membrane material.^[1] This distinguishes it from fully permeable barriers, which allow unrestricted flow of all substances, and impermeable barriers, which prevent any passage.^[3] The selective nature enables the membrane to regulate transport, maintaining distinct compositions on either side.^[4] The concept originated from the work of Scottish chemist Thomas Graham, who in 1861 described experiments using parchment paper as a barrier for separating crystalloids from colloids through diffusion, a process he termed dialysis.^[5] Graham's observations highlighted the membrane's ability to allow small solutes like salts to pass while retaining larger particles, laying the foundation for understanding selective permeation.^[6] Over time, the terminology shifted from "dialysis membrane" to "semipermeable membrane" as researchers recognized its broader applicability beyond just dialysis setups.^[7] Key properties of semipermeable membranes include porosity, which governs the exclusion of larger molecules based on pore size; surface hydrophilicity or hydrophobicity, influencing the solubility and partitioning of solutes; thickness, often ranging from 5 to 10 nm in biological contexts; and composition, typically involving amphiphilic lipids in natural forms or synthetic polymers like cellulose acetate.^[8]^[9] These attributes collectively determine the membrane's selectivity and efficiency in transport. Natural examples, such as phospholipid bilayers, exemplify these traits in living systems.^[8] The rate of substance transport across a semipermeable membrane is quantified by the permeability equation, which describes the steady-state flux under a concentration gradient. The total flux J (in mol/s) is given by:

J = P \cdot A \cdot \Delta C

where P is the permeability coefficient (in m/s), A is the membrane area (in m²), and \Delta C is the concentration difference across the membrane (in mol/m³).^[10] This equation arises from Fick's first law of diffusion, j = -D \frac{dC}{dx}, where j is the areal flux (mol/m²·s), D is the diffusion coefficient (m²/s), and \frac{dC}{dx} is the concentration gradient. For a thin, homogeneous membrane of thickness L, assuming linear gradient and solute partitioning, the gradient approximates \Delta C / L, and the permeability coefficient incorporates the partition coefficient K (dimensionless, reflecting solubility in the membrane) as P = \frac{D K}{L}, yielding the areal flux j = P \Delta C; multiplying by area gives the total flux.^[11] The units ensure dimensional consistency: m/s × m² × mol/m³ = mol/s.^[12] This model provides a foundational framework for predicting membrane behavior across diverse materials.^[13]

Mechanisms of Permeability

Semipermeable membranes enable selective transport through passive and active mechanisms, allowing solutes to cross based on concentration gradients or energy input while restricting others. Passive mechanisms rely on the natural tendency of molecules to move from higher to lower concentrations without energy expenditure, primarily through diffusion, facilitated diffusion, and osmosis. Diffusion across the membrane follows Fick's first law, which states that the flux J of a solute is proportional to the negative concentration gradient across the membrane: J = -D \frac{dC}{dx}, where D is the diffusion coefficient, C is the concentration, and x is the position. The diffusion coefficient D quantifies the solute's mobility and depends on factors such as molecular size, temperature, and the membrane's properties; smaller, nonpolar molecules like oxygen diffuse more readily through lipid bilayers due to higher D values, approximately $10^{-5} cm²/s in biological membranes.^[14]^[15] Facilitated diffusion enhances passive movement of polar or charged solutes through protein channels or carriers without direct energy input, relying on concentration gradients. For instance, aquaporins are integral membrane proteins forming water-specific pores that allow rapid facilitated diffusion of water molecules, increasing permeability by orders of magnitude compared to unassisted diffusion; each aquaporin channel can conduct up to 3 billion water molecules per second.^[16]^[17] Osmosis, a specific form of passive transport for water, occurs when a concentration gradient of solutes drives water across the membrane toward the higher solute side. The osmotic pressure \pi required to prevent this flow is given by the van 't Hoff equation: \pi = iMRT, where i is the van 't Hoff factor accounting for solute dissociation, M is the molar concentration, R is the gas constant, and T is the absolute temperature. This equation derives from the analogy between osmotic pressure in dilute solutions and the pressure of an ideal gas, as van 't Hoff established by treating solute particles as exerting pressure on the membrane similar to gas molecules on a container. In semipermeable systems, water permeability via osmosis can reach rates up to 10⁻³ cm/s in hydrated membranes, far exceeding simple diffusion for other solutes.^[18] Active mechanisms counteract gradients using cellular energy, such as primary active transport. Primary active transport, such as ATP-driven pumps, uses hydrolysis of ATP to move ions against gradients; the sodium-potassium pump (Na⁺/K⁺-ATPase) exemplifies this by exchanging three Na⁺ ions out for two K⁺ ions in per ATP molecule hydrolyzed, maintaining electrochemical balances essential for membrane function.^[19] Permeability is modulated by several factors, including molecular size, electrostatic interactions, and solubility in the membrane matrix. Many semipermeable membranes exhibit a size cutoff, typically allowing free passage of solutes below 500-1000 Da while restricting larger ones, as seen in ultrafiltration systems where pore diameters determine exclusion limits. Electrostatic interactions between charged solutes and membrane components, such as charged lipid headgroups or fixed charges in polymeric membranes, can either enhance or hinder transport; for example, repulsive forces between like charges reduce permeability for anions in negatively charged membranes. The partition coefficient, defined as the ratio of solute concentration in the membrane phase to the aqueous phase, governs solubility-driven permeability; higher lipophilicity (log P > 0) favors partitioning into hydrophobic membrane cores, increasing overall flux according to the solubility-diffusion model.^[20]^[21]^[22] Experimental measurement of permeability employs techniques like fluorescence recovery after photobleaching (FRAP) and dedicated permeability assays. FRAP involves bleaching a region of fluorescently labeled membrane components with a laser and monitoring fluorescence recovery via lateral diffusion of unbleached molecules, yielding diffusion coefficients and permeability estimates; this method has quantified lipid mobility in bilayers at rates of 1-10 µm²/s. Permeability assays, such as parallel artificial membrane permeability assays (PAMPA), measure solute flux across lipid-impregnated barriers using concentration gradients tracked by UV spectroscopy or mass spectrometry, providing apparent permeability coefficients (P_app) in the range of 10^{-6} to 10^{-4} cm/s for drug-like compounds. These approaches ensure quantitative assessment of transport kinetics in both model and native membranes.^[23]^[24]^[25]

Biological Contexts

Phospholipid Bilayer

The phospholipid bilayer forms the foundational structure of biological semipermeable membranes, primarily composed of amphipathic phospholipids such as phosphatidylcholine, which feature hydrophilic phosphate heads and hydrophobic fatty acid tails.^[26] These lipids self-organize into a bilayer with heads facing the aqueous environments on both sides and tails sequestered in the interior, while cholesterol molecules intercalate between phospholipids to modulate membrane fluidity and stability, preventing excessive rigidity or permeability at physiological temperatures.^[26] Integral proteins, embedded within the bilayer and often comprising up to 50% of the membrane's mass, contribute to its functional complexity by spanning the hydrophobic core.^[27] The organization of the phospholipid bilayer is best described by the fluid mosaic model, proposed by Singer and Nicolson in 1972, which portrays the membrane as a dynamic, two-dimensional fluid where lipids and proteins diffuse laterally within the plane.^[28] This model emphasizes the bilayer's fluidity, with lipid rafts—specialized microdomains enriched in sphingolipids and cholesterol—facilitating localized protein interactions, and a striking asymmetry in lipid distribution, such as phosphatidylserine predominantly localized to the inner leaflet.^[29] The asymmetry arises from enzymatic regulation and maintains the membrane's integrity and signaling capabilities.^[29] Physically, the bilayer exhibits a thickness of approximately 4-5 nm, determined by the length of the hydrocarbon chains and influenced by chain saturation.^[29] Lateral diffusion rates for lipids and proteins typically range around 10^{-8} cm²/s, reflecting the fluid state that allows rapid molecular movement without disrupting the barrier.^[29] The bilayer undergoes phase transitions from a gel to a liquid crystalline state, often between 20-40°C depending on lipid composition, which affects packing density and permeability; cholesterol broadens this transition to sustain fluidity across temperature variations.^[29] Self-assembly of the phospholipid bilayer is driven by the hydrophobic effect, where amphipathic molecules minimize unfavorable interactions with water by aggregating tails inward, leading to spontaneous bilayer formation that lowers the system's Gibbs free energy (ΔG = ΔH - TΔS), primarily through an increase in entropy (ΔS) as water molecules are released from ordered hydration shells around hydrophobic tails, with minimal enthalpic change (ΔH).^[30] This thermodynamic process ensures the bilayer's stability in aqueous environments without external energy input.^[30]

Cellular Transport and Communication

Semipermeable membranes in cells facilitate the selective transport of molecules essential for nutrient uptake, waste elimination, and maintenance of internal homeostasis. Simple diffusion allows small nonpolar molecules, such as oxygen (O₂) and carbon dioxide (CO₂), to cross the phospholipid bilayer directly down their concentration gradients without energy input or protein assistance.^[4] In contrast, facilitated diffusion employs carrier proteins for polar or larger molecules that cannot freely permeate the lipid bilayer; for instance, glucose enters cells via glucose transporter (GLUT) proteins, which undergo conformational changes to bind and translocate glucose across the membrane.^[31] Vesicular transport mechanisms, including endocytosis and exocytosis, enable the movement of macromolecules and particles by enclosing them in membrane-bound vesicles that fuse with or bud from the plasma membrane, bypassing the selective barrier for bulk transfer.^[4] Beyond basic exchange, semipermeable membranes play a pivotal role in intercellular communication by hosting receptor proteins and specialized junctions. G-protein coupled receptors (GPCRs), embedded in the membrane, detect extracellular signals like hormones and neurotransmitters, triggering intracellular cascades via G-protein activation upon ligand binding.^[32] Gap junctions, formed by connexin proteins, create direct cytoplasmic channels between adjacent cells, permitting the passage of ions and small metabolites to synchronize activities such as in cardiac muscle contraction.^[33] In neuronal communication, synaptic signaling occurs across the presynaptic and postsynaptic membranes, where neurotransmitter release from vesicles in the presynaptic neuron diffuses across the synaptic cleft to bind receptors on the postsynaptic membrane, modulating ion channels and propagating electrical signals.^[34] A key example of active transport across semipermeable membranes is the sodium-potassium pump (Na⁺/K⁺-ATPase), which maintains ion gradients crucial for membrane potential and cellular volume. This enzyme hydrolyzes ATP to actively export three sodium ions (Na⁺) from the cytoplasm while importing two potassium ions (K⁺), operating through a cycle of phosphorylation and dephosphorylation that alternates the protein's affinity for ions and its orientation in the membrane.^[35] In bacteria, quorum sensing exemplifies membrane-mediated communication, where membrane-bound sensor kinases detect accumulated autoinducer molecules, triggering coordinated gene expression for behaviors like biofilm formation once a population threshold is reached.^[36] Energy considerations in ion transport across semipermeable membranes are governed by electrochemical gradients, which combine chemical concentration differences and electrical potential. The Nernst equation quantifies the equilibrium potential (E) for a specific ion, beyond which net diffusion ceases:

E = \frac{RT}{zF} \ln \left( \frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}} \right)

Here, R is the gas constant, T is temperature in Kelvin, z is the ion's valence, F is Faraday's constant, and [ion] denotes concentration outside and inside the cell; for potassium (K⁺, z=1), typical mammalian values yield an E_K of about -90 mV, driving passive K⁺ efflux that contributes to the resting membrane potential.^[37] Active pumps like Na⁺/K⁺-ATPase counteract these gradients, consuming ATP to sustain nonequilibrium states essential for signaling and excitability.^[38]

Osmotic Pressure Management

In biological systems, semipermeable membranes facilitate osmosis, the passive movement of water across the membrane from regions of lower solute concentration to higher solute concentration, driven by osmotic pressure differences. In plant cells, this influx of water generates turgor pressure against the rigid cell wall, which can reach up to 1.0 MPa in well-hydrated tissues, maintaining structural integrity and driving cell expansion. In hypotonic environments, where external solute concentration is lower than inside the cell, water enters the cell, increasing volume and turgor; conversely, in hypertonic conditions, water exits, reducing turgor and potentially leading to plasmolysis in plants.^[39]^[2] Cells manage osmotic stress through regulatory mechanisms that adjust membrane permeability and intracellular solute levels. Aquaporins, water channel proteins embedded in semipermeable membranes, are dynamically regulated during osmotic shock; for instance, their trafficking to the plasma membrane increases under hypotonic stress to enhance water influx, while phosphorylation or endosomal internalization reduces activity during hypertonic stress to conserve water. Additionally, plants accumulate compatible solutes such as proline during drought-induced osmotic stress, which lowers cellular water potential without disrupting metabolism, thereby restoring osmotic balance and protecting against dehydration. Proline levels can rise dramatically, up to 100-fold in some species, aiding turgor maintenance and scavenging reactive oxygen species generated by stress.^[40]^[41]^[42] Pathological disruptions occur when osmotic imbalances overwhelm these mechanisms. In hypotonic environments, excessive water influx causes animal cells, such as red blood cells, to swell and lyse (hemolysis), rupturing the membrane due to unchecked volume expansion. In hypertonic conditions, water efflux leads to crenation, where red blood cells shrink and develop a spiky, contracted appearance as the cytoplasm condenses. In the kidney, semipermeable membranes in the loop of Henle employ a countercurrent multiplier system to manage osmotic gradients; the descending limb is permeable to water, allowing equilibration with the hypertonic medullary interstitium, while the ascending limb actively extrudes solutes, amplifying the gradient up to 1200 mOsm/L at the loop's tip to facilitate urine concentration without cellular damage.^[2]^[43]^[44] Quantitative analysis of osmotic effects on cellular volume relies on the van't Hoff equation, which relates osmotic pressure \pi to solute amount n, temperature T, and volume V:

\pi = \frac{nRT}{V}

Rearranging gives the ideal volume V = \frac{nRT}{\pi}, assuming dilute solutions and ideal behavior. For red blood cells in physiological saline (approximately 300 mOsm/L, \pi \approx 7.6 atm at 37°C), volume remains stable at about 90-100 \mum³. In hypotonic media (e.g., 150 mOsm/L, \pi \approx 3.8 atm), predicted volume doubles to roughly 180-200 \mum³, leading to swelling and potential lysis if exceeding 1.4 times original volume; in hypertonic media (e.g., 600 mOsm/L, \pi \approx 15.2 atm), volume halves to 45-50 \mum³, causing crenation. These changes highlight how semipermeable membranes dictate volume homeostasis under osmotic stress.^[2]

Artificial and Synthetic Applications

Reverse Osmosis

Reverse osmosis (RO) is a pressure-driven separation process that utilizes a semipermeable membrane to purify water by forcing solvent molecules, typically water, from a higher-concentration solution to a lower-concentration one, counter to the natural osmotic gradient.^[45] This requires applying hydraulic pressure exceeding the osmotic pressure of the feed solution, with typical operating pressures ranging from 10 to 100 bar depending on the feed water salinity—for instance, 55 to 85 bar for seawater desalination.^[46] The process effectively removes dissolved salts, organics, and particulates, producing high-purity permeate while concentrating contaminants in the reject stream.^[47] RO membranes are predominantly thin-film composite (TFC) structures, consisting of a selective polyamide active layer deposited on a microporous polysulfone support layer, which provides mechanical stability and high water flux.^[48] These membranes achieve salt rejection rates of 95-99% for sodium chloride (NaCl) under standard conditions, enabling efficient desalination of brackish or seawater feeds.^[49] The polyamide layer's nanoscale pores and negative charge selectively permit water passage while repelling hydrated ions, though performance can vary with pH, temperature, and feed composition.^[50] In applications, RO dominates seawater desalination, accounting for approximately 70% of global installed capacity as of 2024, or about 77 million cubic meters per day out of a total around 110 million cubic meters per day.^[51] It is also widely used in wastewater treatment to reclaim water from industrial effluents and municipal sources, recovering up to 75-85% of the feed volume in optimized systems. Energy efficiency has improved significantly, with specific energy consumption for seawater RO typically around 3 kWh per cubic meter, achieved through energy recovery devices like pressure exchangers that recycle energy from the high-pressure brine reject.^[52] A major challenge in RO systems is membrane fouling, which reduces flux and increases energy use over time. Scaling occurs due to mineral precipitation, such as calcium carbonate or silica, on the membrane surface under high recovery conditions, while biofouling results from microbial growth and extracellular polymeric substances that form biofilms.^[53] Maintenance involves periodic chemical cleaning, including citric acid soaks at low pH (typically 2-4) to dissolve inorganic scales without damaging the polyamide layer, often alternated with alkaline cleaners for organic and biological foulants.^[54] Pretreatment strategies, like antiscalant dosing and filtration, are essential to mitigate fouling and extend membrane life to 5-7 years.^[55] As of 2025, advancements in RO technology include the development of novel thin-film nanocomposite membranes and improved energy recovery systems, enabling specific energy consumption as low as 2.5 kWh per cubic meter in cutting-edge seawater desalination plants.^[56]

Dialysis and Filtration

Dialysis relies on the passive diffusion of solutes across a semipermeable membrane driven by concentration gradients, separating small molecules from larger ones without requiring external pressure.^[57] In laboratory settings, this process typically employs regenerated cellulose or cellulose acetate tubing with pore sizes ranging from 10 to 20 Å, allowing molecules below 500 Da, such as salts and urea, to pass while retaining proteins and macromolecules.^[58] This mechanism aligns with the fundamental principles of diffusion through semipermeable barriers, where solutes move from higher to lower concentrations until equilibrium is achieved. In medical contexts, hemodialysis uses artificial semipermeable membranes in dialyzers to treat kidney failure by removing waste products from blood.^[59] Blood flows through one side of the membrane while dialysate flows countercurrently on the other, facilitating the diffusion of small solutes like urea, with typical clearance rates of approximately 200 mL/min for urea under standard conditions of blood flow around 300-400 mL/min and dialysate flow of 500 mL/min.^[60] Peritoneal dialysis, conversely, leverages the natural semipermeable peritoneum—the abdominal cavity's lining—as the membrane, where dialysate is introduced into the peritoneal space to draw out solutes via diffusion across this biological barrier.^[61] This approach enables continuous ambulatory peritoneal dialysis, performed multiple times daily, providing a gentler alternative for patients unsuitable for hemodialysis. Laboratory applications of dialysis include equilibrium dialysis, which determines protein-ligand binding affinities by separating bound and free ligand across a semipermeable membrane until concentrations equilibrate, allowing calculation of dissociation constants.^[62] Ultrafiltration, a related technique, employs semipermeable membranes under mild pressure or centrifugation to concentrate samples by retaining macromolecules while permitting solvent and small solutes to pass, commonly used in protein purification workflows.^[63] To maintain performance, dialysis membranes undergo regeneration through chemical cleaning to remove biofouling and deposits, such as using dilute bleach solutions (e.g., 0.5-1% sodium hypochlorite) followed by rinsing to eliminate contaminants without significantly degrading the membrane structure.^[64] Backflushing, where fluid is reversed through the membrane, aids in dislodging particulates and extending usability, particularly in reusable systems.^[65] These techniques can prolong the operational life of hemodialysis membranes to 1-3 years in reprocessing programs, depending on material and usage frequency, by mitigating fouling and preserving permeability.^[66]

Other Membrane Types

Nanofiltration Membranes

Nanofiltration membranes represent an intermediate pressure-driven filtration technology positioned between ultrafiltration and reverse osmosis, characterized by pore sizes typically ranging from 1 to 10 nm.^[67] These membranes selectively reject multivalent ions such as Ca²⁺ and SO₄²⁻ while permitting the passage of monovalent ions like Na⁺ and Cl⁻, enabling targeted removal of organics and salts without complete demineralization.^[68] Flux rates for nanofiltration processes generally fall between 20 and 50 L/m²/h under operational pressures of 5 to 15 bar, depending on feed composition and membrane design.^[69] The selectivity of nanofiltration membranes is often enhanced by incorporating charged polymers, such as sulfonated polyethersulfone or sulfonated polyether ether ketone (SPEEK), which introduce electrostatic repulsion mechanisms.^[70] This charge-based functionality relies on Donnan exclusion, where the fixed charges on the membrane surface repel similarly charged ions, complementing steric hindrance from the pore structure to achieve high rejection rates for divalent species.^[71] Such materials allow for tunable permeability, making nanofiltration suitable for applications requiring precise ion fractionation. In practical applications, nanofiltration is widely employed for water softening by removing hardness-causing divalent ions, as well as in pharmaceutical purification to separate active ingredients from impurities and solvents.^[72] In the food processing sector, it facilitates the concentration and demineralization of whey, notably through lactose removal from ultrafiltration permeate, enhancing product yield and quality.^[73] The global market for nanofiltration membranes was estimated at approximately $1.2 billion in 2025, according to one analysis, though estimates vary across reports.^[74]^[75] Compared to reverse osmosis, nanofiltration offers significant advantages, including lower operating pressures of 5 to 15 bar that reduce energy consumption by up to 50% in suitable scenarios.^[76] This enables partial softening and organic removal without the need for full desalination, preserving beneficial monovalent salts and lowering overall costs for targeted treatments.^[77]

Gas Permeation Membranes

Gas permeation membranes are semipermeable barriers designed specifically for separating gas mixtures based on differences in gas solubility and diffusivity, enabling efficient industrial purification processes. These membranes operate primarily through the solution-diffusion mechanism, where gas molecules first dissolve into the upstream surface of the membrane according to their solubility coefficient S (often described by Henry's law), then diffuse across the membrane driven by a concentration gradient, with the rate governed by the diffusivity coefficient D. The overall permeability P is given by the product P = D \times S, which quantifies the flux of a gas through the membrane under a given pressure difference. This model applies to non-porous, dense membranes and is particularly effective for light gases like H2 and CO2, which exhibit high permeability due to their small molecular size facilitating rapid diffusion (D up to orders of magnitude higher than larger gases) and favorable solubility in certain polymers.^[78] Polymeric materials dominate gas permeation membranes for their cost-effectiveness and ease of fabrication, with polydimethylsiloxane (PDMS) serving as a representative example for O2/N2 separation due to its exceptionally high gas permeability—often exceeding 500 Barrer for O2—stemming from its rubbery, flexible structure that enhances both solubility and diffusivity. Inorganic membranes, such as those based on zeolites, offer superior selectivity for challenging separations like H2/CH4, achieving ideal selectivities greater than 100 through molecular sieving effects in their uniform micropores (typically 0.3–0.4 nm), which restrict larger CH4 molecules while allowing H2 to permeate freely. For instance, DDR-type zeolite membranes have demonstrated H2/CH4 selectivities up to 207 under practical conditions, far surpassing polymeric limits for this pair.^[79]^[80] Key applications of gas permeation membranes include natural gas sweetening, where they remove CO2 and H2S to meet pipeline specifications, with polymeric systems like cellulose acetate processing feeds up to 1200 million standard cubic feet per day (approximately 34 million m³/day) in large installations. Air separation utilizes these membranes to produce high-purity N2 (up to 99.9%) by selectively permeating O2, supporting applications in inerting and food packaging, while hydrogen recovery in refineries employs them to purify H2 from reformate streams, recovering over 90% of H2 with purities exceeding 99%, as an energy-efficient alternative to pressure swing adsorption. Globally, these applications have scaled significantly, with thousands of membrane units operational across industries by the 2020s.^[81]^[82]^[81] Despite their advantages, gas permeation membranes face challenges such as plasticization, where high-pressure exposure to penetrants like CO2 causes polymer chain swelling, increasing diffusivity and permeability but degrading selectivity by up to 50% over time. This issue is particularly acute in natural gas sweetening under elevated CO2 partial pressures (>10 bar), necessitating material modifications like crosslinking to mitigate swelling. Additionally, a fundamental trade-off exists between permeability and selectivity, encapsulated by the Robeson upper bound—an empirical correlation plotting selectivity against permeability for gas pairs like CO2/CH4 or O2/N2, where the 2008 upper bound reflects dual-mode sorption and diffusion limitations in glassy polymers, limiting most materials to below this line unless innovative structures like thermally rearranged polymers are employed. Overcoming this bound remains a key research focus to enhance efficiency in high-volume separations.^[83]^[84]

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A simple but very important formula, the Nernst equation, expresses the equilibrium condition quantitatively and, as explained in Panel 11-2, makes it possible ...
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Structure and Function of Na,K-ATPase-The Sodium-Potassium Pump
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Loss of Stability: A New Look at the Physics of Cell Wall Behavior ...
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Spatially variant red blood cell crenation in alternating current non ...
Red blood cells crenate in response to local medium hypertonicity, which indicates local ion concentration gradients in non-uniform electric fields, but not in ...
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Countercurrent multiplication in the loops of Henle generates the cortico-medullary osmotic gradient necessary for water reabsorption, and countercurrent ...
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Reverse Osmosis - an overview | ScienceDirect Topics
Reverse osmosis is a membrane-based, pressure-driven process where water moves through a semipermeable membrane from a concentrated to a weaker solution. It is ...
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Reverse Osmosis Desalination Process - Lenntech
Before entering the seawater reverse osmosis membranes, clarified seawater is pressurized by the High Pressure Pump typically between 55 and 85 bars, depending ...
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Reverse Osmosis - The Basics - Puretec Industrial Water
Reverse osmosis (RO) removes contaminants from water by pushing it through a semi-permeable membrane under pressure, removing dissolved solids.
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Advanced fabrication and characterization of thin-film composite ...
Apr 30, 2025 · The maximum salt rejection and water flux for the prepared thin film composite reverse osmosis membrane were 98.6% and 19.1 L/m2 h, respectively ...
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Feb 14, 2023 · The performance of RFRO membranes was evaluated by a cross-flow desalination test with a 2000 ppm NaCl solution as feed. Figure 4a shows the ...
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A comprehensive review of reverse osmosis desalination
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A comprehensive review of energy consumption of seawater reverse ...
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Reverse osmosis membrane biofouling: causes, consequences and ...
Sep 15, 2022 · An alkaline clean is often performed before or after an acid clean when targeting removal of both organic and inorganic foulants.
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[PDF] Evaluation of fouling and chemical cleaning of reverse osmosis ...
Jan 8, 2025 · Then the RO membrane was cleaned with citric acid for 45 min followed by rinsing with the RO permeate before commencing the permeability test.
[54]
Can I use citric acid to descale/clean a reverse osmosis (RO ...
Citric acid is only useful for calcium carbonate scaling and re-tightening membrane pores after high pH cleaning. It can worsen membrane performance and is not ...
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Nanofiltration Membranes for the Removal of Heavy Metals ... - NIH
Sep 12, 2023 · This sophisticated filtering method uses semi-permeable membranes with pore sizes of 1–10 nm, permitting the selective removal of heavy metal ...
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Nanofiltration as an advanced wastewater treatment technique
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Study on the nanofiltration membrane fouling control and cleaning ...
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PES/SPAES blend membranes for nanofiltration - ScienceDirect.com
The addition of SPEEK leads to a more open membrane structure and consequently higher solvent fluxes. Due to the Donnan exclusion, the blend membranes showed ...
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Optimizing Nanofiltration Membrane Layer-by-Layer Modification
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What Is Nanofiltration In Water Treatment? - Molewater
Sep 23, 2025 · Nanofiltration's ability to remove water hardness lies between that of softeners and reverse osmosis. It can partially remove calcium and ...
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NF Lactose Concentration Case Study - Synder Filtration
Nanofiltration technology is commonly used after ultrafiltration to further concentrate acid whey UF permeate for whey processing applications within the dairy ...
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The nanofiltration membrane market size is estimated at USD 1208.7 million for 2025, and it will grow by 11.0% during 2026–2032, to reach USD 2504.7 million by ...
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Nanofiltration operates at lower pressures than reverse osmosis, making it more energy-efficient for applications that don't require complete desalination.
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Dec 24, 2024 · By operating at lower pressures, they consume less energy than RO systems, translating to reduced operating costs and lower environmental impact ...
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The solution-diffusion model: a review - ScienceDirect.com
The solution-diffusion model has emerged over the past 20 years as the most widely accepted explanation of transport in dialysis, reverse osmosis, gas ...
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Membrane Basics - Liquid Contacting and Gas Separation
O2/N2 Enrichment ... Silicone, chemically known as polydimethylsiloxane (PDMS), is among the most gas permeable dense polymeric membrane materials available.
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[PDF] Adsorption and Separation in Small-Pore Zeolites - DiVA portal
The high permeance was paired with a H2/CH4 selectivity of 207, markedly higher than previously reported for DDR membranes. Furthermore, a mass transfer model ...
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Membrane gas separation applications in natural gas processing
This paper considers the current and future potential of polymeric membranes in acidic gas removal, heavy hydrocarbon recovery, water dehydration as well as ...
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Future Directions of Membrane Gas Separation Technology
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Physical Aging, Plasticization and Their Effects on Gas Permeation ...
Aug 29, 2015 · The first phase is documented and characterized by a rapid permeability decline over ∼15 days and driven by excess nonequilibrium free volume ...
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The upper bound revisited - ScienceDirect.com
The upper bound correlation can be used to qualitatively determine where the permeability process changes from solution-diffusion to Knudsen diffusion.