Water Transport Model Research Articles

A brief history of the cortical thick ascending limb: a systems-biology perspective.

Here, we review key events in the accrual of knowledge about the cortical thick ascending limb (CTAL) of the kidney, starting with its initial characterization by Maurice Burg in 1973. Burg's work showed that the CTAL actively reabsorbs NaCl and that, because its water permeability is virtually zero, it can lower the luminal NaCl concentration to a "static head" level well below blood levels. This process is central to the kidney's ability to excrete dilute urine in states of high water intake. Following Burg's original observations, Greger and Schlatter, working in the 1980s, identified the membrane transport processes responsible for transepithelial NaCl transport in the CTAL. In the 1990s, several investigators identified the key transporter genes and proteins at a molecular level by cDNA cloning. The successful completion of human and mouse genome sequencing projects at the turn of the century led to the development of transcriptomic and proteomic methodologies that allowed the identification of complete transcriptomes and proteomes of CTAL cells. Knowledge accrual was enhanced by the development of differential equation-based models of transport in the CTAL in the 2010s. Here, we used a simplified mathematical model of NaCl ("salt"), urea, and water transport in the CTAL to address three key questions about CTAL function: 1) What is the mechanism of Burg's "static head" phenomenon? 2) How does the kidney compensate for the very short length of the CTALs of juxtamedullary nephrons? 3) Which of the three isoforms of the apical Na-K-2Cl cotransporter (NKCC2) dominates functionally in the CTAL?NEW & NOTEWORTHY Here, we review key events in the accrual of knowledge about the cortical thick ascending limb (CTAL) of the kidney, starting with its initial characterization by Maurice Burg in 1973, and culminating with the application of systems biology techniques including mathematical modeling.

Studying rainfall characteristics affecting low-impact development runoff control measures via numerical simulation

ABSTRACT To gain a comprehensive understanding of the intricate interplay between rainfall characteristics and the effectiveness of runoff control, this study focuses on a representative urban district equipped with low-impact development (LID) features within the Xi'an New Area, China. By utilizing a diverse range of rainfall profiles and employing the GPU-Accelerated Surface Water Flow and Transport Model (GAST), a sophisticated two-dimensional hydrodynamic model was developed to simulate surface runoff dynamics. Our findings highlighted the substantial influence of rainfall intensity, duration, and peak coefficients on the efficiency of runoff control. Specifically, we observed that a rainfall event with a duration of 2 h and a peak coefficient of 0.2 resulted in a runoff control rate varying from 86.17 to 45.44%, depending on the specific rainfall conditions. Furthermore, when rainfall intensity was varied from 19.20 to 87.22 mm, while maintaining a peak coefficient of 0.5, the runoff control rate fluctuated between 82.70 and 44.97%. This investigation reveals a quantifiable framework that elucidates the intricate relationship between rainfall attributes and runoff control effectiveness, providing crucial insights into the development of informed urban flood management strategies.

Evaluation of combined open ditch and subsurface drainage: Experimental data and optimization of specifications in arid Northwest China

Open ditches and subsurface drainage are effective measures for improving saline soils. Installations of subsurface drainage are now complementing surface drainage in Northwest China, but their optimisation has not been attempted. Therefore, the drainage and desalination performance of a combined subsurface drainage-open ditch system was analysed using two years of field experiments. The data were then utilised to calibrate and validate a water and salt transport model. The drainage volume in surface drains were 9-fold those in subsurface pipes. Additionally, 25 sets of orthogonal numerical experiments were designed with the subsurface pipe length, depth, and open ditch depth as variables. The results revealed that these three factors significantly affected the desalination efficiency of salinealkaline farmland (P <0.05). The ditch depth, pipe length, and pipe depth F values were 9.954, 50.286, and 6.557, respectively, and no interactions were observed among these factors. When a single open ditch was used for drainage, the desalination rate initially increased and then decreased as the distance from the open ditch increased. The inflection point varied with the open ditch depth and occurred within a range of 32–43 m when the ditch depth was 180–300 cm. The combination of an open ditch and a subsurface pipe produced a larger desalination area, and its efficiency was 170 % that of a single open ditch. Within the inflection point range, the desalination rate increased with increasing ditch depth. Beyond the inflection point, subsurface drainage played a primary role, and the desalination rate increased as the subsurface drainage depth increased but remained relatively stable along the drainage direction. The optimal installation depth for subsurface pipes was estimated to be 90–110 cm, and the depth of ditches was 180–210 cm in a combined system. The maximum length for full flow in long-distance subsurface drainage was 750–850 m. This study provides references for the optimal application of combined subsurface drainage–open ditch systems in arid Northwest China.

Numerical Modeling of Water Transport in a Microporous Layer-Coated Porous Transport Layer for a Polymer Electrolyte Membrane Water Electrolyzer with an Interdigitated Flow Field for Internal Gas-Liquid Separation

We have developed a novel interdigitated flow field for polymer electrolyte membrane electrolyzers (proton exchange membrane water electrolysis cells) for ground and space applications1),2), which are supposed to work in a hybrid system with a low temperature Sabatier reactor for effective use of heat3),4). This design separates the oxygen and liquid water inside the anode of the cell. It dispenses with water circulators and external separators that use natural or centrifugal buoyancy. To date, we have developed a numerical model for optimizing cell structures. Finite element modeling (COMSOL Multiphysics) of water transport is three-dimensionally conducted for the anode porous transport layer coated with a hydrophobic microporous layer (MPL) (SIGRACET 29BC, SGL Carbon Inc.) assembled with the interdigitated flow field. The MPL can separate the evolved oxygen gas and pressurized liquid water owing to capillary pressure5). The electrochemical kinetic parameters for the model are determined using electrochemical impedance spectra. We model the current densities and the current ratio between the reactant liquid water and water vapor at the interface between the MPL and catalyst layer (CL)6). The model involves the fractional bubble coverage of the produced oxygen gas at the CL, as well as liquid water saturation and liquid water permeability in the MPL7). The vapor evaporating from the liquid water in the MPL is assumed to be mixed with the evolved oxygen for diffusive water transport. The volumetric evaporation rate was estimated from experimental data8). Acknowledgement This study is based on results obtained from a project, JPNP21014, commissioned by the New Energy and Industrial Technology Development (NEDO).References1) Y. SONE, O.S. HERNANDEZ-MENDOZA, A. SHIMA, M. SATO, H. NAKAJIMA, and H. MATSUMOTO, Water Electrolysis by the Direct Water Supply to the Solid Polymer Electrolyte through the Interdigitated Structure of the Electrode, Electrochemistry, 89 (2021) 138–140. https://doi.org/10.5796/electrochemistry.20-00145.2) H. NAKAJIMA, V. VEDIYAPPAN, H. MATSUMOTO, M. SATO, O.S. MENDOZA-HERNANDEZ, A. SHIMA, and Y. SONE, Water Transport Analysis in a Polymer Electrolyte Electrolysis Cell Comprised of Gas/Liquid Separating Interdigitated Flow Fields, Electrochemistry, 90 (2022) 017002. https://doi.org/10.5796/electrochemistry.21-000973) H. NAKAJIMA, A. SHIMA, M. INOUE, T. ABE, H. MATSUMOTO, O.S. MENDOZA-HERNANDEZ, and Y. SONE, Three-Dimensional Numerical Modeling of a Low-Temperature Sabatier Reactor for a Tandem System of CO2 Methanation and Polymer Electrolyte Membrane Water Electrolysis, Electrochemistry, 90 (2022) 22–00035. https://doi.org/10.5796/electrochemistry.22-000354) A. Shima, M. Sakurai, Y. Sone, H. Nakajima, M. Inoue, and T. Abe, Development of CO2 Reduction-Water Electrolysis Tandem Device as a Full-Scale Model, in: 52nd Int. Conf. Environ. Syst., 2023: ICES-2023-196. https://hdl.handle.net/2346/896225) H. Nakajima, S. Iwasaki, and T. Kitahara, Pore network modeling of a microporous layer for polymer electrolyte fuel cells under wet conditions, J. Power Sources, 560 (2023) 232677. https://doi.org/10.1016/j.jpowsour.2023.2326776) H. Nakajima, H. Ekström, A. Shima, Y. Sone, and G. Lindbergh, Water Transport Modeling in a Microporous Layer for a Polymer Electrolyte Membrane Water Electrolyzer Having a Gas-Liquid Separating Interdigitated Flow Field, ECS Transactions, 112 (4) (2023) 273–281. https://doi.org/10.1149/11204.0273ecst7) S. Kubota, H. Nakajima, M. Sato, A. Shima, M. Sakurai, and Y. Sone, Liquid Water Permeability in a Hydrophobic Microporous Layer for the Anode Interdigitated Flow Field of a Gas-Liquid Separating Polymer Electrolyte Membrane Water Electrolyzer, ECS Transactions, 112 (4) (2023) 207-214. https://doi.org/10.1149/11204.0207ecst8) P. Wang, H. Nakajima, and T. Kitahara, Effect of Hydrophilic Layer in Double Microporous Layer Coated Gas Diffusion Layer on Performance of a Polymer Electrolyte Fuel Cell, J. Electrochem. Soc., 170 (2023) 124514. https://doi.org/10.1149/1945-7111/ad13da

Test Study on Water and Salt Transport in Soil Transition Layer under Water Storage Irrigation Based on Big Data Technology and its Mechanism

At present, it is necessary to vigorously transform saline-alkali wasteland, dry land and coastal tidal flat to realize the balance of cultivated land occupation and compensation. In this paper, the experiment and mechanism of water and salt transport in soil transition layer under water storage irrigation are studied by combining big data technology. Moreover, based on the basic principle of water and salt balance, the numerical model of water and salt transport in vadose zone of study area under brackish water irrigation is constructed on the basis of existing data. The model is a set of numerical models for simulating water transport, heat transport, solute transport and root water uptake in one-dimensional variable saturated media. The model analysis shows that soil water and salt transport is a complex natural phenomenon under the joint action of a large number of natural factors and human factors. In addition, this paper uses normal test analysis to find out whether the salt content of each soil layer conforms to the normal distribution, and combines with big data technology to perform mechanism analysis and verify the effectiveness of this method.

Modeling nitrogen recovery and water transport in gas-permeable membranes

This study presents a new modeling approach for nitrogen recovery in gas-permeable membrane (GPM) contactors, including both ammonia and water transport dynamics. A distinct feature of the model is its capacity to model water transport across the membrane, which has been overlooked in most publications. Osmotic pressure differences are used to predict the behavior of ammonia and water transport in the GPM contactor. Experiments carried out to develop, test and calibrate the model examined the dynamics of ammonia and water transport through the GPM contactor at various nitrogen concentrations. Specifically, the GPM contactor was tested for nitrogen recovery from high-strength synthetic wastewaters (2.4–10.6 g N/L) at 35 °C and at pH 9. The initial volume of the trapping solution (diluted H2SO4) was 10 times lower than that of the synthetic wastewater, aiming to concentrate the recovered nitrogen. The estimated ammonia transport constant (Km) ranged between (1.2 - 2.1)·10–6 m/s and water transport constant Kw between (2.8 - 8.2)·10–10 m/(s bar). Numerical determination of the model parameters revealed high R² values, demonstrating strong agreement with experimental data.

An impedance spectroscopy study to unravel the effect of water on proton and oxygen transport in PEM fuel cells

A recent physics-based model for liquid and gaseous water transport in the cathode catalyst layer (CCL) is incorporated into our 1d ＋ 1d model for the PEM fuel cell impedance. The model includes parametric dependencies of the CCL oxygen diffusivity and proton conductivity on the liquid saturation. Fitting of the 1d ＋ 1d model to experimental impedance spectra of a PEM fuel cell reveals two intriguing effects. Contrary to common belief, the liquid water saturation in the CCL is nearly independent of cell current density due to the growing liquid pressure gradient that drives liquid water removal from the CCL. Further, the “dry” oxygen diffusivity of the catalyst layer increases with cell current density. Apparently, at small current density, electrochemical conversion proceeds primarily in narrow pores, where the Knudsen oxygen diffusivity is low. With growing current density, larger and better connected pores with higher oxygen diffusivity dominate in the current conversion, leading to increase in effective oxygen diffusivity observed in impedance spectroscopy data.

Numerical Modeling of Water Transport in a Microporous Layer-Coated Porous Transport Layer for a Polymer Electrolyte Membrane Water Electrolyzer with an Interdigitated Flow Field for Internal Gas-Liquid Separation

A novel design for interdigitated flow fields in polymer electrolyte membrane electrolyzers has been developed for both ground and space applications. This design separates oxygen and liquid water internally, eliminating the need for water circulators to remove bubbles and external gas-liquid separators with buoyancy. The capillary pressure in the hydrophobic microporous layer (MPL) of the anode porous transport layer facilitates internal separation of oxygen gas and pressurized liquid water. A finite element model (COMSOL Multiphysics) simulates water transport in the MPL, while electrochemical impedance spectra determine the electrochemical kinetic parameters for the model. The model takes into account the oxygen bubble coverage of the cathode, liquid water saturation in the MPL, and the current ratio between liquid water and water vapor at the MPL-cathode layer interface. The vapor from liquid water in the MPL is modeled to mix with oxygen for diffusion. A volumetric water evaporation rate as a linear function of liquid water saturation in the MPL is assumed, where the rate constant is estimated from vapor permeation tests.

Numerical Modeling of Water Transport in a Microporous Layer-Coated Porous Transport Layer for a Polymer Electrolyte Membrane Water Electrolyzer with an Interdigitated Flow Field for Internal Gas-Liquid Separation

A novel design for interdigitated flow fields in polymer electrolyte membrane electrolyzers has been developed for both ground and space applications. This design separates oxygen and liquid water internally, eliminating the need for water circulators to remove bubbles and external gas-liquid separators with buoyancy. The capillary pressure in the hydrophobic microporous layer (MPL) of the anode porous transport layer facilitates internal separation of oxygen gas and pressurized liquid water. A finite element model (COMSOL Multiphysics) simulates water transport in the MPL, while electrochemical impedance spectra determine the electrochemical kinetic parameters for the model. The model takes into account the oxygen bubble coverage of the cathode, liquid water saturation in the MPL, and the current ratio between liquid water and water vapor at the MPL-cathode layer interface. The vapor from liquid water in the MPL is modeled to mix with oxygen for diffusion. A volumetric water evaporation rate as a linear function of liquid water saturation in the MPL is assumed, where the rate constant is estimated from vapor permeation tests.

Modeling Water Transport in Polymer Electrolyte Membrane Electrolyzers Using a One-Dimensional Transport Model

In this work, we present a water transport model to quantify the movement of water across Nafion® membranes in a proton exchange membrane electrolyzer as a function of varying operating conditions and membrane parameters. This physics-based model is based on the three main water transport mechanisms: diffusion, electro-osmotic drag, and pressure-driven flow. Three sets of equations are obtained to model the movement of water on the cathode side – I. Material balances for hydrogen and water in the flow channel (z-direction), II. Water movement across the membrane in the x-direction, and III. Expressions for variable membrane properties to serve as model inputs. The condensation of water at the cathode is also modeled to understand the respective transport contributions from the vapor and liquid phases. The coupled equation sets are solved numerically with appropriate boundary conditions. An analytical solution is also obtained for the governing differential equation for the mole fraction of water in the vapor phase. This study is perhaps the first effort for a detailed physics-based transport model to predict the water transport in the electrolyzer in one dimension using the actual measured values for the physical parameters of the system. The model results are compared with the experimental data available for water transport, and a good agreement is observed over the wide range of current, temperature and pressure differentials. Further, with the help of this simple transport model, the numerical analysis is performed to delineate the effect of electrolyzer operating conditions on the net water transport across the membrane, water condensation at the cathode, individual contribution of the transport fluxes, and electrolyzer design. Finally, the model is exercised to simulate the dependence of water transport as a function of membrane thickness. This confirms the validity of the current approach of using thin reinforced membranes by electrolyzer fabricators. Figure 1

On the transferability of residence time distributions in two 10-km long river sections with similar hydromorphic units

Quantifying hydrologic exchange fluxes (HEFs) at the stream-groundwater interface and their residence time distributions (RTDs) in the subsurface are important for managing the water quality and ecosystem health in dynamic river corridors. However, field measurements and directly simulating high-spatial resolution HEFs and RTDs can be time-consuming, particularly at watershed-scale. Recent research has proposed the potential application of using hydromorphic units (HUs), which cluster the bathymetry and surface water hydrodynamics attributes, to aid in RTD estimation. However, more pioneering studies have demonstrated that underground structure and large-scale river channel geomorphology are the primary factors controlling the HEFs and RTDs. To address this contradiction, this work evaluates the HEFs and resulting HU-RTD relationships for two 10-km long river sections along the Columbia River, leveraging a one-way coupled three-dimensional transient surface–subsurface water transport modeling framework. Applying such a framework at the two river sections with similar HUs allows for quantitative comparisons of HEFs and RTDs using both statistical tests and machine learning classification models. The comparison reveals that the similarity and transferability of the HU-RTD relationship is very low for the two investigated river sections. This suggests that, creating a general algorithm to estimate RTDs in large-scale river reaches based solely on surface water hydrodynamics and short-distance bathymetry topography data may be nearly impossible.

Three-dimensional mass transfer modeling and phenolic chemistry exploration for ultrasound-assisted and microwave drying of goji berry

Herein, goji berries were pretreated with sodium carbonate (Na2CO3) and then dried via ultrasound-assisted air drying or microwave drying. Water migration and phenolic chemistry of goji berries were studied under drying. A three-dimensional ellipsoid water transport model, accounting for porosity and temperature fluctuations, was established to explore the intricacies of the drying mechanism. Generally, microwave drying promoted interior water transport compared to ultrasound drying. Among all the drying methods, microwave drying at 240 W (MW-240 W) exhibited the highest De (from 7.34 × 10−9 to 9.61 × 10−9 m2/s) and kc (6.78 × 10−4 m/s) values. The goji berries received a considerably high water content gradient between its surface and center within the first 2 s of all the drying treatments. Microwave drying diminished the water content gradient earlier than air drying and ultrasound-assisted air drying treatments. Furthermore, most correlations observed among phenolics, oxidase activity, and cell wall pectin did not align with the established theories, highlighting the highly nonlinear nature of phenolic chemistry during goji berry drying. This study provides a three-dimensional model to study the mass transfer mechanism of goji berries and analyzes the evolution of polyphenols during the drying process.

Water Crossover in Proton Exchange Membrane Water Electrolysis

Water management is critical for high performance of polymer electrolyte membrane water electrolysis (PEMWE). In this work, we investigated the water crossover for 5 cm2 PEMWE single cell by varying the temperature (40–80 °C), current density (0–2 A cm−2 geo), cathode pressure (ambient, 310 kPagauge,inlet), and nitrogen purge rate (50, 100 nccm). Using an advanced gravimetric method, the water crossover to the cathode could be established very accurately and also corrected by the water vapor fraction. Here, we pointed out that the cathode exhaust gas is saturated with water vapor, either from diffusion or by proton drag at low or high current densities, respectively. Very importantly, the water crossover at high current density is controlled by the proton drag and are used to extract the temperature-dependent proton drag coefficient at 1 A cm−2 geo. Our results reveal that the proton drag coefficient increases from 2.5 ± 0.2 at 40 °C to 3.2 ± 0.2 at 80 °C (+28%). Altogether, we have developed a sophisticated gravimetric method to accurately determine the water crossover under PEMWE operating conditions and proposed a model of the temperature-dependent proton drag coefficient. Unravelling the proton drag and diffusion is very important for modeling of water transport in PEMWE.

Renal calcium and magnesium handling during pregnancy: modeling and analysis.

Pregnancy is associated with elevated demand of most nutrients, with many trace elements and minerals critical for the development of fetus. In particular, calcium (Ca2+) and magnesium (Mg2+) are essential for cellular function, and their deficiency can lead to impaired fetal growth. A key contributor to the homeostasis of these ions is the kidney, which in a pregnant rat undergoes major changes in morphology, hemodynamics, and molecular structure. The goal of this study is to unravel the functional implications of these pregnancy-induced changes in renal handling of Ca2+ and Mg2+, two cations that are essential in a healthy pregnancy. To achieve that goal, we developed computational models of electrolyte and water transport along the nephrons of a rat in mid and late pregnancy. Model simulations reveal a substantial increase in the reabsorption of Mg2+ along the proximal tubules and thick ascending limbs. In contrast, the reabsorption of Ca2+ is increased in the proximal tubules but decreased in the thick ascending limbs, due to the lower transepithelial concentration gradient of Ca2+ along the latter. Despite the enhanced transport capacity, the marked increase in glomerular filtration rate results in elevated urinary excretions of Ca2+ and Mg2+ in pregnancy. Furthermore, we conducted simulations of hypocalcemia and hypomagnesemia. We found that hypocalcemia lowers Ca2+ excretion substantially more than Mg2+ excretion, with this effect being more pronounced in virgin rats than in pregnant ones. Conversely, hypomagnesemia reduces the excretion of Mg2+ and Ca2+ to more similar degrees. These differences can be explained by the greater sensitivity of the calcium-sensing receptor (CaSR) to Ca2+ compared with Mg2+.NEW & NOTEWORTHY A growing fetus' demands of minerals, notably calcium and magnesium, necessitate adaptations in pregnancy. In particular, the kidney undergoes major changes in morphology, hemodynamics, and molecular structure. This computational modeling study provides insights into how these pregnancy-induced renal adaptation impact calcium and magnesium transport along different nephron segments. Model simulations indicate that, despite the enhanced transport capacity, the marked increase in glomerular filtration rate results in elevated urinary excretions of calcium and magnesium in pregnancy.

Water, Salt, and Ion Transport and Its Response to Water-Saving Irrigation in the Hetao Irrigation District Based on the SWAT-Salt Model

Soil salinization is one of the main hazards affecting the sustainable development of agriculture in the Hetao Irrigation District (HID) of Inner Mongolia. To grasp the water and salt transport patterns and spatial–temporal distribution characteristics of the HID at the regional scale, the improved Soil and Water Assessment Tool with a salinity module (SWAT-Salt) model was used to establish the distributed water and salt transport model for the watershed in this study. The results demonstrated that the modified model could more accurately represent the process of water and salt changes in the HID. The coefficient of determination (R2) in the simulation of streamflow and discharge salt loading was 0.83 and 0.86, respectively, and the Nash–Sutcliffe efficiency (NSE) was 0.80 and 0.74, respectively. Based on this, different hydrological processes (surface runoff, lateral flow, groundwater, soil seepage) as well as spatial–temporal distribution characteristics of water salinity in groundwater and soil were analyzed in the HID. Differences in groundwater and soil salinity in different land uses and soil types were also compared. Of these, surface runoff and lateral flow salt discharge loading are concentrated in the southwestern portion of the basin, while groundwater salt discharge loading is concentrated in the eastern as well as southwestern portions of the basin. The salt discharge loading from groundwater accounts for about 98.7% of the total salt discharge loading from all hydrological pathways and is the major contributing part of salt discharge from the irrigation area. Soil salinity increases gradually from west to east. Groundwater salinity (2946 mg/L) and soil water electrical conductivity (0.309 dS/m) were minimized in the cropland. Meanwhile, rational allocation of irrigation water can appropriately increase the amount of salt discharge loading. In conclusion, the model could provide a reference for the investigation of soil salinization and water–salt management measures in irrigation areas.

Predicting the impact of water transport on carbonation-induced corrosion in variably saturated reinforced concrete

A modelling framework for predicting carbonation-induced corrosion in reinforced concrete is presented. The framework constituents include a new model for water transport in cracked concrete, a link between corrosion current density and water saturation, and a theory for characterising concrete carbonation. The theoretical framework is numerically implemented using the finite element method and model predictions are extensively benchmarked against experimental data. The results show that the model is capable of accurately predicting carbonation progress, as well as wetting and drying of cracked and uncracked concrete, revealing a very good agreement with independent experiments from a set of consistent parameters. In addition, insight is gained into the evolution of carbonation penetration and corrosion current density under periodic wetting and drying conditions. Among others, we find that cyclic wetting periods significantly speed up the carbonation progress and that the induced corrosion current density is very sensitive to concrete saturation.

A preliminary model of water and salt transport in a laboratory scale pressure-retarded osmosis (PRO) module

Nowadays, more and more attention is being paid to the production of green energy. Recently, energy from salinity gradients has also attracted interest. One such process that can generate useful work is the pressure-retarded osmosis (PRO), which uses a semi-permeable membrane to separate the feed and pressurized draw solutions. The semi-permeable membrane allows the transport of solvent (water) from the feed solution (diluted low pressure) side to the draw solution (concentrated high pressure) side, and thus, the excess of pressurized water on the draw side can be used to generate power, i.e., by expansion in the turbine. This work presents a preliminary numerical model developed to study the water and NaCl salt transport through the semi-preamble membrane and in the PRO module designed to perform experimental studies. The model was first verified for simple 2D module geometry. It was then used to study the flow through a simplified 3D module, mimicking the real one used in laboratory-scale experiments. The influence of the hydrodynamic pressure and the NaCl draw solution’s mass flow rate in the module on the energy generation efficiency was examined. The maximum power density obtained for half the osmotic pressure of the NaCl draw solution (i.e., for 28 bar) was found to be equal to approximately 4 W/m2. An increase in the flow rate of the draw solution causes a decrease in the thickness of the boundary layer at the membrane, which reduces the effect of the external concentration polarization. This results in an increase in the concentration difference on either side of the membrane, contributing to a non-linear increase in power density depending on this mass flow rate. Increasing the average velocity from 0.02 m/s to 0.1 m/s increases the power density by up to 80%, from approximately 2.6 to 4.7 W/m2.

A hard sphere model for single-file water transport across biological membranes

We use Gürsey’s statistical mechanics of a one-dimensional fluid to find a formula for the Pf/Pd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{f}/P_\ extrm{d}$$\\end{document} ratio in the transport of hard spheres across a membrane through a narrow channel that can accommodate molecular movement only in single file. Pf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{f}$$\\end{document} is the membrane permeability for osmotic flow and Pd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{d}$$\\end{document} the permeability for exchange across the membrane in the absence of osmotic flow. The deviation of the ratio from unity indicates the degree of cooperative transport relative to ordinary diffusion of independent molecules. In contrast to an early idea that Pf/Pd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{f}/P_\ extrm{d}$$\\end{document} must be equal to the number of molecules in the channel, regardless of the physical nature of the interactions among the molecules, we find a functional dependence on the fractional occupancy of the length of the channel by the hard spheres. We also attempt a random walk calculation for Pd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{d}$$\\end{document} individually, which gives a result for Pf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{f}$$\\end{document} as well when combined with the ratio.Graphical The convection/diffusion ratio for hard spheres in single-file transport

The solution-diffusion model for water transport in reverse osmosis: What went wrong?

Reverse osmosis (RO) stands as the state-of-the-art desalination technology, owing to its high energy efficiency and low cost. Further improvements in the performance of this technology require a fundamental understanding of transport mechanisms in RO membranes. For decades, the solution-diffusion model has been the prevalent approach to describe water transport mechanism in RO membranes. In this model, water first partitions into the membrane and then diffuses down a concentration gradient of water within the RO membrane. However, recent experimental and theoretical findings pose serious challenges to the fundamental assumptions of this theory. In this perspective, we discuss seven critical flaws in the solution-diffusion model and explain why the model fails to describe water transport in RO membranes. Instead, through our careful analyses, we determine that the pore-flow model, in which a pressure gradient drives water flow through membrane pores or interconnected free volumes, represents the true mechanism for water transport. We conclude by highlighting the need for research efforts to better understand the frictional interactions between water, salt, and membrane and their impact on water transport. Overall, a fundamental understanding of the water transport mechanism will inform the development of next-generation RO desalination membranes.

Modeling water transport in polymer electrolyte membrane electrolyzers using a one-dimensional transport model

In this paper, we present a one-dimensional transport model for water transport across Nafion® membranes in a proton exchange membrane electrolyzer. This physics-based model is based on the three main water transport mechanisms: diffusion, electro-osmotic drag, and pressure-driven flow. A good agreement is obtained between the model predictions using the measured values of the physical parameters as inputs and the previously reported experimental data. Further, with the help of this simple transport model, the numerical analysis is performed to delineate the effect of electrolyzer operating conditions on the net water transport across the membrane, water condensation at the cathode, individual contribution of the transport fluxes, and electrolyzer design. Finally, the model is exercised to simulate the dependence of water transport as a function of membrane thickness. This confirms the validity of the current approach of using thin reinforced membranes by electrolyzer fabricators.