Spiral-wound Membrane Research Articles

Modeling of Spiral Wound Membranes for Gas Separations—Part IV: Real-Time Monitoring Based on Detailed Phenomenological Model

The present study presents, for the first time, the real-time monitoring of an actual spiral-wound membrane unit used for CO2 removal from natural gas in an actual industrial offshore platform, utilizing a detailed phenomenological model. An Object-Oriented Programming (OOP) paradigm was employed to simulate the offshore membrane separation unit, accounting for the diverse levels of the membrane separation setup. A parameter estimation procedure was implemented to fit the phenomenological model to the real industrial data in real-time, for the first time. In addition, estimated permeance parameters and calculated unmeasured variables (soft sensor) were used for monitoring Key Performance Indicators (KPIs), such as membrane selectivity, dew point temperature, and hydrocarbon loss. Finally, a reparametrization of the parameters was implemented to improve the robustness of the optimization procedure. Thus, the model variables presented good adjustments to the data, indicating the satisfactory performance of the estimation. Consequently, the good accuracy of the model provided reliable information to the soft sensors and KPIs.

Dissecting spacer induced membrane deformation and fluid hydraulic behavior in reverse osmosis

Feed spacer is a key component of the spiral wound membrane module. However, the membrane deformation induced by the feed spacer under high pressure presents a significant challenge to long-term operation of reverse osmosis (RO) membrane. This deformation alters the fluid hydraulic behavior within the feed channel and its underlying mechanism remains elusive. In this study, the computational fluid dynamics (CFD) simulation was conducted to illustrate the impact of the feed spacer geometry on membrane deformation under high pressure and the resultant changes in hydraulic performances. The simulated results revealed that an increase in the mesh angle and a reduction in the filament diameter and length, led to a higher degree of membrane deformation. In addition, larger mesh angles and filament diameters, and shorter the filament lengths could significantly enhance the performance of the spiral wound membrane (SWM) module. This study provides an insight for the design of feed spacer to optimize the performance of reverse osmosis membrane module.

A general modeling framework for FO spiral-wound membrane and its fouling impact on FO-RO desalination system

Modeling fouling in forward osmosis (FO) spiral-wound membrane (SWM) is challenging due to the time-dependent nature of fouling and the complex flow patterns induced by baffle. This necessitates the development of a general modeling framework for FO SWM module that prioritizes both accuracy and ease of implementation. This framework was validated against FO SWM experiment data from previous work, demonstrating a reasonable agreement with a maximum error of 13.1 % in FO permeate flux. This validated model was used to study the impact of fouling on feed recovery, a critical factor influencing specific energy consumption (SEC) in FO-RO desalination systems. While improved operating conditions and membrane parameters (A, Ss and Cf) initially lead to increased water flux, this effect was significantly counteracted by accelerated fouling. Consequently, performance improvements in terms of flux and SEC remained minimal (<1 %) under severe fouling conditions. The results show that for foulant cake with larger pore diameter (>10 nm), the contribution of hydraulic resistance is insignificant compared to osmotic resistance. However, the contribution of hydraulic resistance becomes important for foulant cakes with pore diameter smaller than 10 nm. This paper shows that modeling have evolved to a stage that they can be used to understand membrane fouling phenomena at the SWM module scale.

Experimental investigation and mathematical modelling of a spiral wound membrane module for osmotically assisted reverse osmosis applications

Osmotically assisted reverse osmosis (OARO) has gained interest for applications like desalination, wastewater treatment, and draw solution recovery in forward osmosis. Despite that, on the one hand limited experimental research on pilot- or industrial-scale modules is available, and on the other hand existing simulations are often theoretical and unsuitable for real OARO scenarios. A validated mathematical model reflecting the actual membrane behaviour is crucial for understanding the process accurately and designing it effectively. This study investigated a prototype spiral wound 4040 module for OARO in a pilot plant, using NaCl solutions at various concentrations as feed and sweep solutions. Experiments were carried out at feed concentrations from 17 g/L to 226 g/L and sweep solution concentrations equal to or less than the feed. Steady-state water flux data were collected applying pressures from 8 to 28 bar. In parallel, a predictive mathematical model based on material balances was developed and validated to describe water flux variation within the membrane module, providing insights that are useful for process optimization. Positive water fluxes (1–2 LMH) were obtained even for highly concentrated solutions (226 g/L), indicating the system's capability to handle high salinity feeds. It has been observed that deformation of the membrane under high pressures can adversely affect its performance in a significant way. This is because deformation reduces the cross-sectional area of the membrane and increases the pressure drop on the sweep side. In conclusion, the results demonstrate promising membrane capability in managing high solute concentrations, and the validity of the developed predictive model.

Effect of pore size and temperature on the behaviour of alpha-lactalbumin and the A and B genetic variants of beta-lactoglobulin during protein fractionation microfiltration

The aim of this study was to investigate the influence of membrane pore size and filtration temperature on six individual milk protein fractions (αS-CN, β- CN, κ-CN, α-LA, β-LG A, β-LG A) during the protein fractionation microfiltration process. Pasteurised skimmed milk was microfiltrated using two different pore sizes of spiral-wound membranes, with pore sizes of 0.2 μm and 0.5 μm, at temperatures of 15 °C and 45 °C respectively. The microfiltration process was carried out with a final volume reduction of 66% and a diafiltration volume of 120% (300 L) of the original feed (250 L). It was observed that neither the pore size nor the filtration temperature significantly (p < 0.05) affected the permeation of the α-LA fraction. However, the permeation of the β-LG A and β-LG B fractions can be influenced by membrane pore size and filtration temperature, and the behaviour of the three whey protein fractions, A and B genetic variants of the β-LG and α-LA fractions differs significantly during the microfiltration process. The results of this study could form the basis for the development of new, unique tailor-made milk protein ingredients.

Efficient separation of HEPES and CO2-derived fructose by nanofiltration: Optimizing pH for improved separation and proposing a potential mechanism

Utilization of an in vitro multi-enzyme catalytic system for the synthesis of fructose from carbon dioxide is a promising approach towards achieving carbon neutrality. However, the lack of effective separation methods for the buffer HEPES (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid) and the product fructose within the system has hindered the industrialization of in vitro multi-enzyme catalytic synthesis systems. This study aimed to separate and recover HEPES and fructose using nanofiltration technology. We investigated the influence of various parameters, including total solution concentration, solute concentration ratio, pH, and temperature, on the nanofiltration separation performance. Experimental results revealed that increasing the pH to 9.0 significantly decreased the fructose retention rate while maintaining a nearly complete HEPES retention rate. The HEPES-fructose mixed solution was further subjected to diafiltration using a spiral-wound membrane, ultimately yielding fructose and HEPES solutions with purities of 90.22 % and 92.93 %, respectively. Combining separation test results with models such as DSPM-DE, and using characterization methods such as ATR-FTIR and pore size distribution analysis, we observed pore swelling during nanofiltration of the HEPES-fructose solution at pH 9.0. A mechanism for this pore swelling, induced by the dissociation of HEPES under the influence of pH, was proposed: Dissociated HEPES in the solution interacts with the membrane surface at the liquid-membrane interface, causing reversible swelling of the membrane pores at the membrane surface, thereby reducing the retention rate of fructose. The nanofiltration process developed in this study effectively separates HEPES and fructose, enabling resource recycling and cost reduction. Furthermore, this study provides theoretical foundations and practical guidance for the design of nanofiltration separation strategies for similar systems using HEPES as a buffer, holding significant scientific and practical value.

Energy comparison and cost estimation of pressure-retarded osmosis using spiral wound membrane

Advancements in Pressure Retarded Osmosis (PRO) technology are enhancing the feasibility of evaluating its economic viability against other renewable energy production methods. This is done using the Levelized Cost of Energy (LCOE) as a metric. The study focuses on three PRO scenarios designed to minimize environmental impact and promote sustainable energy. These scenarios utilize a spiral-wound membrane module combined with hyper-saline solutions from Reverse Osmosis (RO) and wastewater from demineralization processes. Experimental results using a commercial spiral-wound membrane in the PRO system yielded LCOE values of USD 0.0702/kWh for a draw solution (DS) concentration of 36.2 g/l, USD 0.0563/kWh for 44.2 g/l, and USD 0.0721/kWh for 51.8 g/l. The study also evaluated environmental viability by considering the cost of CO2 emissions. This comprehensive comparison highlighted PRO's competitiveness with fossil fuels, showing it to be a reasonable alternative to coal and oil but less practical than natural gas. Specifically, the environmental analysis revealed that PRO is approximately 25.2 % more competitive than coal and 9.76 % more competitive than oil but 27.16 % less competitive compared to natural gas in terms of CO2 emission costs. This underscores the importance of considering carbon emission mitigation in energy generation.

Direct numerical simulation of flow in a membrane channel under oscillating inlet conditions

Effects of inflow oscillation in feed channels of spiral wound membranes are investigated. Pulsation has previously been used as a membrane cleaning method in Reverse Osmosis (RO) and other membrane desalination processes. However, there is still a gap in the fundamental fluid dynamics study of pulsation and fouling mitigation. Three-dimensional, transient, high-fidelity Computational Fluid Dynamics investigation using Direct Numerical Simulation has been performed on a geometry of 9 × 3 feed square space elements at Reynolds number of 350 based on inlet velocity. Sinusoidal-wave and step function pulsations are simulated at three frequencies (1, 4, 8 Hz). Five levels of permeate velocity are investigated, from 0.2 % to 0 % (impermeable). Pulsating inflow produces a fully-unstable flow regime. Flow streamlines show no large recirculation regions, unlike for the steady inflow, and flow structures show higher levels of instabilities with a larger range of scales, resulting in smaller stagnation regions near the surfaces. Consequently, the area of low shear decreases and its distribution is limited to the spacer filament crossings instead of the permeate walls. These findings show that inflow oscillation for a membrane channel creates flow conditions that could be beneficial for reducing fouling propensity in RO and other membrane processes with similar feed channel geometry.

Long-Term Performance Evaluation and Fouling Characterization of a Full-Scale Brackish Water Reverse Osmosis Desalination Plant

Water scarcity in Tunisia’s semi-arid regions necessitates advanced brackish water desalination solutions. This study evaluates the long-term performance and fouling characteristics of the largest brackish water reverse osmosis desalination plant in southern Tunisia over a period of 5026 days. The plant employs two-stage spiral-wound membrane elements to treat groundwater with a salinity of 3.2 g L−1. The pre-treatment process includes oxidation, sand filtration, and cartridge filtration, along with polyphosphonate antiscalant dosing. Membrane performance was assessed through the analysis of operational data, standardization of permeate flow (Qps) and salt passage (SPs), and the calculation of water (A), solute (B), and ionic (Bj) permeability coefficients. Over the operational period, there was an increase in operating pressure, pressure drop, and permeate conductivity, accompanied by a gradual increase in SPs as well as in the solute B and ionic Bj permeability coefficients. The average B increased by 82%, reflecting a decrease in solute rejection over time. Additionally, the ionic permeability coefficients for both SO42− and Cl− ions increased, with Cl− showing an 88% increase and SO42− showing an 87% increase. The produced water’s salinity increased by 67%, indicating a significant loss of membrane performance. To identify the cause of these problems, membrane characterization was analyzed using visual inspection, X-ray fluorescence (XRF), and Fourier transform infrared spectroscopy (FTIR). The characterization revealed the complex nature of the foulants, with a predominant presence of calcium sulfate, along with minor quantities of calcite, dolomite, and silica. The extent of CaSO4 deposition suggests poor antiscaling efficiency, highlighting the critical importance of selecting an effective antiscalant to mitigate membrane fouling.

Ethanol mass transfer model of spiral-wound membrane module with PDMS membrane for pervaporation considering module structure parameters

Pervaporation mass transfer model of spiral-wound membrane module with polydimethylsiloxane (PDMS) membrane considering module structure parameters has been developed for ethanol separation. Membrane intrinsic parameters involved mass transfer including limiting diffusivity of ethanol, plasticization coefficient of ethanol and partition coefficient were firstly determined, and then the model was verified by the experimental results with a correlation coefficient of 0.998. It has been calculated that bulk ethanol concentration (xe) would be decreased from 9 v/v% to 7.26 v/v% along the flow direction, under the ethanol feeding concentration of 9 v/v%, feeding velocity of 0.008 ms−1, membrane length of 1 m, membrane width of 1.5 m, channel height of 1.2 mm, if polydimethylsiloxane/polyamide (PDMS/PA) membrane was applied. Owing to the concentration-dependence of the membrane mass transfer coefficient (km), km and local ethanol flux (Je) was also decreased from 7.20 × 10-6 m·s-1to 7.07 × 10-6 m·s−1, and 386 g·m−2·h−1 to 306 g·m−2·h−1, respectively. For polydimethylsiloxane/polyvinylidene difluoride/Polyethylene terephthalate (PDMS/PVDF/PET) membrane, km and Je were decreased from 7.72 × 10-7 m·s-1to 7.65 × 10-7 m·s−1, and 137 g·m−2·h-1to 128 g·m−2·h−1, respectively, under the same condition. Higher ethanol feeding concentration and longer module would lead to more obvious change in xe, km and Je. While higher feeding velocity would lead to weaker change in xe, km and Je.

Numerical study of energy consumption in spacer-filled feed channels through 3D inverse modeling and computational fluid dynamics

This project employs advanced Computational Fluid Dynamics (CFD) simulations to investigate the complex flow field dynamics within the channel of membrane module featuring a commercially available feed spacer. Utilizing Micro-CT scanning, the intricate three-dimensional (3D) structure of the spacer is accurately captured, enhancing the precision of the simulation models. The project focuses on the effects of varying Reynolds number (Re) and Aspect Ratio (AR) on the energy consumption within the feed channel of membrane module, analyzing streamline patterns, vorticity, and flow separation angles in detail. Findings indicate that the total enstrophy identification method effectively pinpoints areas of high energy consumption, especially at lower Re levels where flow separation significantly contributes to hydraulic losses. As Re increases, the separation vortex shifts rearward, resulting in a marked decrease in the energy consumption coefficient. Furthermore, the flow separation angle consistently declines with increasing Re, stabilizing at higher levels. Significantly, a reduction in AR from 1.015 to 0.725 more than doubles the decrease in flow separation angle, highlighting substantial potential energy savings through spacer design optimization. These insights are crucial for improving the design and efficiency of spiral wound membrane modules and for refining feed spacer configurations to enhance performance.

Advancing electrodialysis: Harnessing the potential of spiral-wound membrane stacks for improved desalination-efficiency and cost-efficiency

Membrane separation technology encompasses a variety of processes, of which electrodialysis (ED) has become one of the irreplaceable technologies due to its high concentration factor and energy saving. Currently, the main membrane stacks of ED technology on the market are plate-and-frame membrane (PFM) stacks, while there are almost no spiral-wound membrane (SWM) stacks. The SWM stacks have many advantages, such as higher mass transfer efficiency, higher packing density, etc. Inspired by its advantages, we have designed and assembled a SWM for ED. In this study, the PFM and SWM stacks in the efficacy of the two processes were compared using the Finite Element Method to simulate the distribution of fluid and electric fields within the stacks. The desalination efficiency of SWM has been improved compared with that of PFM. In particular, when the voltage is 36 V, the single path desalination rate is 98.7 %. The effective area of the membrane stack has been increased from 63.6 % to 88.9 % since the components of the SWM stack are more efficient and easy to assemble. Due to its low cost, excellent performance and partial fluid simulation, it is believed that this work can provide an inspiration for the assembly of membrane stacks.

Power feasibility of single-staged full-scale PRO systems with hypersaline draw solutions

Pressure retarded osmosis (PRO) is a process that allow to generate energy from osmotic gradient. This process uses selective membranes in order to produce electrical energy through a hydraulic turbine. PRO can be used as a renewable energy technology where water resources are inexhaustible. PRO has the advantage of knowing when and how much energy will be produced. Unfortunately at the moment there are certain limiting factors concerning membrane and module characteristics that have prevented PRO to be fully exploited at full-scale. This study aims to assess the impact of hypersaline draw solutions (60–180 g L−1), membrane characteristics such as structural parameter, module membrane surface and permeability coefficients on the net energy generated by single-staged full-scale PRO system with up to 8 spiral wound membrane modules (SWMMs) in series in a pressure vessel. To carry out this study, characteristics of existing PRO membranes at lab-scale were scaled up to 8 inches SWMM. The results showed the change in the optimal operating parameters with the change of membrane characteristics and draw solution concentration. This study concluded that single-staged full-scale PRO process would be viable from an energy point of view if membranes were manufactured on an industrial scale and with the characteristics of existing membranes on a laboratory scale.

A reduced model for pilot-scale vacuum-enhanced air gap membrane distillation (V-AGMD) modules: Experimental validation and paths for process improvement

A fast and robust computational model of a spiral-wound vacuum-enhanced air gap membrane distillation (V-AGMD) module at the pilot-scale is proposed and implemented. In contrast with data-driven models available in the literature, a physics-based approach is adopted for more reliable generalization beyond the validation dataset. A total of 86 experimental results, of which 41 are described in this work and 45 come from independent sources available in the literature, are used in the validation effort with quite favorable results. With the confidence on the robustness of the methodology due to the wide range of operational parameters and the use of spiral-wound modules of four different sizes included in the validation comparisons, a physical analysis is conducted varying the air gap pressure, the number of feedwater channels, the feedwater flow rate, and the membrane area. Improvements of up to 60% in both water productivity and energy efficiency can be achieved by intensifying the vacuum in the air gap or decreasing the number of feedwater channels. These parameters achieve performance gains due to less resistance in the air gap for vapor to migrate through it, in the former case, and a reduced temperature polarization effect, in the latter case. Smaller flow rates favor energy efficiency at the expense of water productivity by simultaneously decreasing transport-phenomena-related irreversibility and the partial pressure difference across the membrane and the air gap. In addition, this tradeoff between energy efficiency and driving force is shown to lead to an optimum value for the membrane area beyond which the permeate flow rate through the membrane starts to fall due to the small driving force. An illustrative case is predicted to achieve energy efficiency metrics, such as a gain-output ratio of 12.7, competitive with multi-effect distillation.

A spiral-windable, free-standing, durable membrane constructed with ultralong hydrogel@MnO2 nanowires for oil/water separation under harsh environment

An ideal membrane for oil/water separation at industrial scale is expected to possess the combined merits of excellent separation performance, sound mechanical flexibility, and high durability under harsh environments. In response to these challenging requirements, we came up with a new concept to design the membrane constructed with ultralong hydrogel-functionalized MnO2 nanowires. The super-oleophobic nanowires form highly open and tight pore structures within the membrane, which endows its high permeation flux (2800 L h−1 m−2 bar−1), high oil/water separation efficiency (>99 %) and low fouling tendency for separating emulsified oil from water. Furthermore, the brittleness problem of MnO2 materials is collectively resolved due to the high aspect ratio and surface functionalization of the hydrogel-functionalized MnO2 nanowires. This results in the new membrane with extraordinary mechanical flexibility and potential for spiral-wound membrane modules, which are highly desired in industrial applications due to a lower footprint and lower capital cost. The new membrane also demonstrates high durability under harsh environments with non-neutral pH values or high salinities. Given its facile synthesis process and inexpensive materials, this spiral-windable and durable membrane with high separation performance has the great potential to be applied at industrial scale for oily wastewater treatment under harsh environments.

CFD for the optimization of spiral wound film assembly

In this paper, a conventional mesh shim for a spiral wound membrane assembly is structurally optimized by adding jet holes to achieve the jet function, and the effect of curvature on fluid flow is investigated. The three different gaskets are compared with each other and the performance of the optimized gaskets is investigated by using computational fluid dynamics (CFD) techniques and analyzed parametrically. This knowledge can be supplemented by the use of CFD techniques for spacers, whereby the geometry of the spacer can be optimized and the corresponding performance of the spiral wound film assembly can be improved.

Integrated membrane process for pretreating and desolventizing hexane-soybean oil miscella – A pilot plant study

The study aimed to develop a membrane desolventizing technology for solvent recovery in vegetable oil extraction. Pretreatment of crude miscella is a prerequisite for an organic solvent nanofiltration (OSN) based desolventizing process. Solvent-resistant ultrafiltration (SRUF) membrane employed in micelle-enhanced ultrafiltration (MEUF) of hexane-crude soybean oil miscella displayed high phospholipids (PL) rejection (98.5 %) and productivity (∼28 L/m2/h), accompanied with a moderate oil rejection (∼22 %). The PL-rich retentate fraction was alkali-treated to recover the oil in the stream (8.8 %). This complementary pretreatment approach met the quality requirements and maximized the yield of treated oil (>98 %) while reducing the chemicals in the process. A subsequent two-stage desolventizing of MEUF-treated miscella with solvent-resistant nanofiltration (SRNF) membrane reduced the oil-in-permeate to 1.37 %, achieving the set recycling criteria (<2 %). The results obtained from the pilot scale study (batch size 40 kg of crude miscella) revealed that the MEUF met the pretreatment requirements, and the subsequent OSN process recovered ∼63 % of hexane through a non-thermal route for recycling in the extraction process. The pilot-scale evaluation demonstrated the technical feasibility of the proposed membrane desolventizing process employing indigenous spiral-wound SRUF and SRNF membrane modules.

A review of spiral wound membrane modules and processes for groundwater treatment

The demand for freshwater keeps increasing on a global scale, and on the other hand, the availability of freshwater keeps diminishing. Groundwater has been identified as the largest source of freshwater that is readily accessible. Although the water is available for abstraction, it must be treated to meet application standards. Membrane processes are the options that industry and researchers are turning to for the purification of groundwater. This review provides an insight into the use of pressure-driven membrane processes for groundwater treatment, with focus on the spiral wound membrane module. A brief description of what a spiral wound module is and the plant set-up in which it is used is given. The various applications of the spiral wound module with regards to groundwater treatment have been reviewed. The shortcomings and challenges limiting the application of spiral wound modules and by extension, the treatment plant itself have been highlighted. To cap it all, the opportunities that can be exploited to overcome these challenges and position pressure-driven membrane processes for groundwater treatment as the go-to purification method have been discussed.

Large-Area Ultrathin Metal-Organic Framework Membranes Fabricated on Flexible Polymer Supports for Gas Separations.

Ultrathin continuous metal-organic framework (MOF) membranes have the potential to achieve high gas permeance and selectivity simultaneously for otherwise difficult gas separations, but with few exceptions for zeolitic-imidazolate frameworks (ZIF) membranes, current methods cannot conveniently realize practical large-area fabrication. Here, we propose a ligand back diffusion-assisted bipolymer-directed metal ion distribution strategy for preparing large-area ultrathin MOF membranes on flexible polymeric support layers. The bipolymer directs metal ions to form a cross-linked two-dimensional (2D) network with a uniform distribution of metal ions on support layers. Ligand back diffusion controls the feed of ligand molecules available for nuclei formation, resulting in the continuous growth of large-area ultrathin MOF membranes. We report the practical fabrication of three representative defect-free MOF membranes with areas larger than 2,400 cm2 and ultrathin selective layers (50-130 nm), including ZIFs and carboxylate-linker MOFs. Among these, the ZIF-8 membrane displays high gas permeance of 3,979 GPU for C3H6, with good mixed gas selectivity (43.88 for C3H6/C3H8). To illustrate its scale-up practicality, MOF membranes were prepared and incorporated into spiral-wound membrane modules with an active area of 4,800 cm2. The ZIF-8 membrane module presents high gas permeance (3,930 GPU for C3H6) with acceptable ideal gas selectivity (37.45 for C3H6/C3H8).

Scalable nanofiltration membranes with sharpened pore distribution and enhanced negativity for mono/divalent anion separation

The petrochemical industry is an important producer of high salinity wastewater, necessitating the efficient separation of salts in zero discharge processes. This study reports the development of an industrially scalable thin film composite nanofiltration membranes that facilitate the effective separation of NaCl/Na2SO4. Employing a one-step functionalization process, the membrane pore distribution is sharpened, and the surface negativity is intensified. Branched polyethyleneimine with abundant reactive amine groups is employed as an aqueous co-monomer, leading to the generation of high density grafting active sites. Nucleophilic substitution reaction is employed to functionalize the membrane surface with negatively charged sulfonic acid groups. Simultaneously, large voids within the free volume are filled and the pore size distribution is effectively narrowed. The resultant membranes demonstrate an impressive rejection of 99.5 % for Na2SO4, a selectivity of 163.4 for NaCl/Na2SO4 and a selectivity of 488 for Cl−/SO42−, with a water flux of 45 LMH under 0.5 MPa. The corresponding 8″ × 40″ sized spiral wound membrane modules exhibit a NaCl/Na2SO4 selectivity of 100.4 and a Cl−/SO42− selectivity of 258.3, demonstrating high practical applicability. A pilot trial is planned to integrate these novel membrane products into zero discharge processes within the internal chemical enterprises of Sinopec.