Perfluoroalkyl and polyfluoroalkyl substances (PFAS) are persistent fluorinated micropollutants. In recent years, stringent limits have been proposed by regulatory agencies, creating significant challenges for many water utilities. Although activated carbon is widely used for the adsorption and removal of PFAS, its rapid breakthrough, particularly with short-chain PFAS, requires frequent regeneration. This study presents a novel electroregeneration technology for the potential on-site regeneration of activated carbon. PFAS are initially adsorbed onto activated carbon, which is then regenerated in an electrochemical cell with a countercarbon electrode separated by a cation-exchange membrane. The experiments were conducted using a solution with an ionic strength comparable to that of surface water, implying a high concentration of competing ions. For PFPeA, a short-chain PFAS, we achieved effluent concentrations during electroregeneration 130 times higher than initial levels, with most PFPeA successfully desorbed. The method was effective for all short-chain PFAS examined (PFPeA, PFBS, and GenX), which are particularly concerning due to their rapid breakthrough in activated carbon filters. We studied the effect of electronic charge in the electrodes on PFAS adsorption as well as the impact of electrode surface modifications on PFAS electroregeneration performance. Surface modifications increased the presence of positively charged chemical groups, which, in turn, influenced the efficiency of PFAS electroregeneration.

Water vapor transport between saline solutions is commonly investigated in membrane distillation systems operating under temperature differences between 20 and 40 °C. Such studies, conducted under significant temperature differences, do not address equilibrium or the approach toward equilibrium of two solutions in contact via the gas phase. Here, we study water transport through the gas phase between salt solutions of different temperatures and salinities separated by a hydrophobic membrane. By measuring small water fluxes over extended times, we follow the approach toward equilibrium and compare the measurements with theoretical predictions. The observed fluxes are quantitatively described by the difference in water vapor pressure between the solutions, with no need for additional driving forces, for example, an additional dependence on the difference in temperature. These findings contribute to the thermodynamic description of vapor-phase water transport between saline solutions near equilibrium.

We investigate a continuous electrochemical pH-swing method to capture CO2 from a gas phase. The electrochemical cell consists of a single cation-exchange membrane (CEM) and a recirculation of a mixture of salt and phenazine-based redox-active molecules. In the absorption compartment, this solution is saturated by CO2 from a mixed gas phase at high pH. In the electrochemical cell, pH is reduced, and CO2 is selectively released in a desorption step. We investigate the influence of redox molecule concentration on the charge storage capacity of the solution, as well as the impact of current density and solution recirculation rate on process performance. A theoretical framework, based on a minimal set of assumptions, is established. This framework describes the data very accurately and can be used for system design and optimization. We evaluate the trade-off between energy consumption and CO2 capture rate and compare with published reports. We report a low energy consumption of 32 kJ/mol of CO2 at a capture rate of 39 mmol/m2/min.

Developing a detailed two-dimensional (2D) theoretical framework for mass transport in a spiral wound reverse osmosis (RO) module is crucial to better understand membrane processes. In this study, we developed a 2D mass transport model for a monovalent binary symmetric salt (1:1) using the solution friction theory. Mass and volume balances were used to define cross-flow velocity and salt concentration along the module length. The numerical simulations analyzed local RO module performance, such as fluxes, pressures, axial velocity, mass transfer coefficient, water recovery, and salt rejection. The simulation results demonstrated that hydraulic pressure loss along the module length has a minor effect on a single module's local and overall performance. Conversely, the effect becomes significant when several modules are stacked in a pressure vessel (PV). The performance optimization for brackish water and seawater desalination membranes was conducted using low-salinity feed water (50 mM NaCl). This involved a detailed parametric study on the operational conditions, membrane geometry, and number of module elements in a PV.

In recent decades, increasing global population and industrialization have driven interest in the sustainable extraction of valuable resources from water, as well as in water reuse applications. This includes selectively removing undesired ions, such as sodium, or extracting valuable ions, such as lithium, from water. These separations are difficult to achieve due to the high concentrations of competing ions with similar properties, such as charge and size. As a result, separating similar ions, e.g., sodium, potassium, and lithium, is often regarded as the ‘holy grail’ of ion separation. Although selective separation can be achieved with electrochemical desalination technologies, the limited selectivity for ions with the same charge is insufficient for many applications. In this manuscript, we introduce a novel approach for achieving exceptionally high selectivity between two very similar ions, sodium and potassium, by adapting switching times of ion collection. We demonstrate that our method, termed Concentration Dependent Switching (CDS), is effective for sodium and potassium, achieving high removal of one ion while leaving the other in solution. The high removal can be achieved to either of the ions in solution. We highlight its applicability to other challenging separations, including lithium and sodium. The CDS method can be integrated into any cyclically operated deionization technology that exhibits differences in the dynamics of adsorption and desorption of ions.

Reverse osmosis and nanofiltration are membrane-based methods that remove solutes from solvent, for instance they remove salts from water (desalination). In these methods, an applied pressure is the driving force for solvent to pass the membrane, while most of the solutes are blocked. Very important in the theory of mass transport is the concentration polarization layer (CP layer), which develops on the upstream side of the membrane. Because of the CP layer, the solvent flux through the membrane is reduced while leakage of solutes through the membrane increases, and both these effects must be minimized. So it is very important to understand and describe the nature of the CP layer accurately, especially to find a good estimate of the CP layer mass transfer coefficient, $k$. This is also important for the accurate characterization of membranes in a test cell geometry. We theoretically analyze the structure of the CP layer using three levels of mathematical models. First, we present a modification of an equation for $k$ by Sherwood et al. (1965) and show that it works very well in a zero dimensional model. Second, we evaluate a one-dimensional model that is more accurate, which can incorporate any equation for the flow of solvent and solutes through the membrane, and which also makes use of the new modified Sherwood equation. Finally, we fully resolve the complete channel in a two-dimensional geometry, to validate the lower-order models and to illustrate the structure of the CP layer. The overall conclusion is that for typical test cell conditions, the modified Sherwood equation can be used to characterize the CP layer, also when solvent flux through the membrane changes between inlet and outlet of the test cell. Furthermore, the one-dimensional model accurately describes solute removal (for instance water desalination) not just in a short test cell but also in a longer module.

Mineral scaling in water desalination is caused by the precipitation of salts, which is affected by various factors such as the presence of specific ions, solution pH, and temperature. While extensively researched in technologies like reverse osmosis (RO), understanding mineral scaling in membrane capacitive deionization (MCDI) remains limited. During MCDI operation, the pH of the effluent fluctuates, potentially triggering mineral scaling. The present study investigates how the adsorption and desorption of HCO3− ions and the distribution of dissolved inorganic carbon (DIC) species (H2CO3, HCO3−, and CO32−) drive pH changes. We examine mineral scaling formation at various water recoveries during MCDI operation using different thicknesses of the anion exchange membrane (AEM). Our findings indicate that pH changes increase with higher water recoveries and that increasing the AEM thickness provides a pathway to enhance MCDI stability, consequently lowering the need for anti-scaling agents.

Reverse osmosis (RO) is one of the most successful membrane technologies for desalination and contaminant removal from water. RO is applied globally, and can be used for both small- and large-scale applications. To characterize membrane performance, standard testing uses membrane coupons and a NaCl solution in a labscale setup under controlled conditions. Ideally, experiments are done for a range of applied hydrostatic pressures and salt concentrations, with water flux and salt rejection measured in each experiment. This full dataset can then be checked for internal consistency, and all these data must then be described by a comprehensive theoretical framework, i.e., we need an appropriate set of equations to parametrize these data. Parameters derived from this procedure, such as water and salt permeability, can then be compared to those obtained in other studies, for other membranes, salts, or temperatures. If this theory indeed correctly describes data for water flux and salt flux, it can also be applied in larger scale models for RO modules and combinations of modules, which are the basis of engineering design and economic optimization. Herein, we present a novel equation for salt flux that we derive from the full solution-friction (SF) theory. This equation interpolates between an equation for neutral membranes on the one hand, and an equation for highly-charged membranes on the other hand, and thus it is more generally applicable. We apply this new equation to several datasets of seawater RO membranes, and we propose an accurate method to compare the salt permeability of different membranes.

Bipolar membranes (BPMs), a special class of ion exchange membranes with the unique ability to electrochemically induce either water dissociation or recombination, are of growing interest for environmental applications including eliminating chemical dosage for pH adjustment, resource recovery, valorization of brines, and carbon capture. However, ion transport within BPMs, and particularly at its junction, has remained poorly understood. This work aims to theoretically and experimentally investigate ion transport in BPMs under both reverse and forward bias operation modes, taking into account the production or recombination of H+ and OH-, as well as the transport of salt ions (e.g., Na+, Cl-) inside the membrane. We adopt a model based on the Nernst-Planck theory, that requires only three input parameters─membrane thickness, its charge density, and pK of proton adsorption─to predict the concentration profiles of four ions (H+, OH-, Na+, and Cl-) inside the membrane and the resulting current-voltage curve. The model can predict most of the experimental results measured with a commercial BPM, including the observation of limiting and overlimiting currents, which emerge due to particular concentration profiles that develop inside the BPM. This work provides new insights into the physical phenomena in BPMs and helps identify optimal operating conditions for future environmental applications.

Reverse osmosis (RO) is a method to desalinate water with membranes and an applied pressure. Very important in the theory of mass transport in RO is the concentration polarization (CP) layer, which develops on the upstream side of the membrane because of a combination of salt convection and diffusion. Because of the CP-effect, the salt concentration at the membrane surface is higher than in the channel, and this increases the osmotic pressure there, and thus transmembrane water flux is reduced (the osmotic pressure acts against water flux), while salt leakage through the membrane increases. So it is very important to understand and describe the CP-layer accurately. We analyze a one-dimensional geometry, which is of relevance for a typical lab-scale RO setup using small membrane coupons where the solution on the feed side of the membrane is stirred. For this geometry, the standard film layer approach is often used that assumes a stagnant film layer of a defined thickness, which however does not exist in reality. We set up a model without that assumption but including refreshment of solution because of the flow of water along the membrane due to stirring. We show that the `exponential law' for the CP-layer that is predicted by the the film model, also applies for this more accurate model. We further improve the model by including the activity coefficient of salt ions, as described by the Bjerrum theory that is based on ion-ion Coulombic interactions. We evaluate the original linearized Bjerrum theory as well as an extended Bjerrum equation that is valid up to 1.5 M salt concentration. We show how including this activity correction leads to a reduction of the diffusional driving force at high concentration, and thus the salt concentration at the membrane further increases. However, the effect can be easily included by reducing the CP-layer mass transfer coefficient by a fixed percentage.

We analyze selective removal of anions in electrodialysis (ED) from a multicomponent ion mixture where all ions are monovalent, both experimentally, and by a modified theory. The theory makes use of the Nernst-Planck equation to describe transport of ions across ion-exchange membranes in combination with the ion affinity, which is a parameter that accounts for the preference of membrane materials to adsorb one ion more than another. For a mixture of NO-3 and Cl- anions, ion affinity was measured in an adsorption experiment, and it was found that NO-3 adsorbs more in anion-exchange membranes (AEMs) than Cl-. Faster transport of NO-3 relative to Cl- in batch-mode ED experiments is well described by the transport theory, for three types of AEMs that we tested. From analysis of the model, we can derive that membrane selectivity in ED between different anions can be increased further by: i) an increase in the difference in ion affinity of the anions, ii) an increase in the AEM thickness, and iii) a decrease in the charge density of the AEM. The last two strategies go against the general understanding that thin highly charged membranes are in general better for ED. Our proposed strategies follow rigorously from our combined theoretical-experimental study.

Modeling mass transport of ions across the polyamide active layer of a reverse osmosis (RO) membrane requires a comprehensive understanding of membrane structure and chemistry. For instance, membrane charge ionization and thus salt transport greatly depend on feedwater pH and composition, but these relations are not yet well understood. To address this gap in understanding, a one dimensional model is developed that couples transport of all ions using the extended Donnan steric partitioning pore model. The model includes membrane charge ionization as well as interaction with H+ and OH- -ions. The dependence of ion rejection and permeate pH is described as function of feedwater pH. Finally, model predictions are quantitatively compared with experimental data by adjusting a few fitting parameters using the Nelder-Mead algorithm. Contrary to other RO studies, we show that the polyamide is only weakly charged, but this small charge still plays a key role to determine membrane performance. These findings reveal the key role of local pH in the ionization of membrane functional groups, and how local charge affects overall membrane rejection of ions as well as permeate pH.

Reverse osmosis (RO) is the most important membrane technology for the desalination of water. Measured water and salt fluxes are traditionally analyzed in the context of the solution-diffusion (SD) model which leads to a water permeability, A, and a salt permeability, B. However, this parametrization of the salt flux is not correct for water desalination by RO membranes, because these membranes show markedly different retentions for different feed salt concentrations, a classical observation in the literature, and this effect is not captured by the SD model. Thus, the traditional salt permeability B is not an intrinsic property of these membranes. We present a new analysis for desalination of a 1:1 salt, which follows from a transport theory that is based on the assumption that coions are strongly excluded from the membrane, and we demonstrate that it accurately describes a large dataset of salt retention by an RO membrane as function of pressure and feed salt concentration. This analysis leads to unique values of the water and salt permeabilities, A and B″, not dependent on salt concentration or permeate water flux. Because we now have an improved parametrization, we can more accurately compare different membranes or study in more detail how membrane performance depends on conditions such as salt type and temperature. The new equation can provide guidance for the design of high-performance desalination membranes and for process modeling of desalination systems.

Reverse osmosis (RO) and electrodialysis (ED) are the two most important membrane technologies for water desalination and treatment. Their desalination and transport mechanisms are very different, but on a closer look also have many similarities. In this tutorial review, we describe state-of-the-art theory for both processes, focusing on simple examples that are helpful for the non-specialist and for classroom teaching. We describe relevant theory for ion and water transport and the coupling with theory for chemical and mechanical equilibrium on membrane/solution interfaces. For RO of neutral solutes, we explain the solution-friction (SF) model which is closely related to the classical sieving or pore flow model. The SF model includes advection, diffusion, and solute partitioning, and leads to simple relationships for the coupled fluxes of water and solutes (and thus for solute retention as well), also when a diffusion boundary (or concentration polarization) layer is included in the model. Subsequently this theory is extended to describe RO for symmetric salt solutions with charged membranes. For the desalination of salt solutions, both for RO and ED we present two-dimensional module-scale calculations which lead to a characteristic curve that determines optimum operational conditions based on a simple cost calculation that offsets energy and material costs. We discuss the two-fluid model (TFM) that comprehensively describes ion and water flow both in RO and ED, and we explain how this theory also accurately describes osmosis experiments where water and ions are transported in opposite directions through a membrane. Finally, we present results of optimization studies of the combination of multiple modules for RO and ED, and we evaluate the relevance of concentration polarization by using a 3D model for cross-current flow in an ED module.

For a thorough mechanistic understanding of reverse osmosis (RO), data on ion retention obtained by desalination of multi-ionic solutions are needed. In this paper, we show how to obtain such data under controlled laboratory conditions at any nonextreme pH. For that, we propose a simple method where we use N2 and CO2 gas control to set the composition of a gas phase in equilibrium with the feedwater solution. By increasing the CO2 partial pressure, the pH of the solution will decrease and vice versa. We applied this method of CO2 gas control to extend and validate an existing data set on ion retention of multi-ionic brackish water with 10 different ionic species, whereas conditions in the prior data set were slightly uncontrolled; in our new analysis, we performed experiments at precisely controlled pH and temperature. We run experiments at pH 6.73 and pH 7.11 and in a temperature range of T = 15–31 °C. Our results show that when pH is decreased, or temperature increased, the ion retention of most ions decreases. We also tested the influence of the Na+ to Ca2+ concentration ratio in this multi-ionic solution on ion retention at pH 6.73 and T ∼ 31 °C. We noticed that this ratio has a larger effect on ion retention for cations than for anions. We compare our data with the earlier reported data and describe similarities and differences. The improved data set will be an important tool for future development of accurate and validated RO ion transport models. Such RO models that describe desalination performance in detail are important for successful commercial application of the RO technology. We also discuss a relevant preparation method for water slightly oversaturated with barely soluble CaCO3 by solution preparation at high CO2 pressure, after which the solution is brought to the required pH by the N2 and CO2 gas control method.

Understanding the salt-water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solution-diffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane. In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst-Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.

Membrane capacitive deionization (MCDI) is a water desalination technology employing porous electrodes and ion-exchange membranes. The electrodes are cyclically charged to adsorb ions and discharged to desorb ions. During MCDI operation, a difference in pH between feed and effluent water is observed, changing over time, which can cause the precipitation of hardness ions and consequently affect the long-term stability of electrodes and membranes. These changes can be attributed to different phenomena, which can be divided into two distinct categories: Faradaic and non-Faradaic. In the present work, we show that during long-term operation, as the electrodes age over time, the magnitude and direction of pH changes shift. We studied these changes for two different feed water solutions: a NaCl solution and a tap water solution. Whereas we observe a pH decrease during the regeneration with a NaCl solution, we observe an increase during regeneration with tap water, potentially resulting in the precipitation of hardness ions. We compare our experimental findings with theory and conclude that with aged electrodes, non-Faradaic processes are the prominent cause of pH changes. Furthermore, we find that for desalination with tap water, the adsorption and desorption of HCO3-and CO32- ions affect the pH changes.

Selective ion removal has been a point of focus in capacitive deionization because of its industrial applications such as water purification, water softening, heavy metal separation and resource recovery. Conventionally, carbon is used as electrode material for selectivity. However, recent developments focus on intercalation materials such as Prussian Blue Analogues, due to their size-based preference towards cations. Selectivity of nickel hexacyanoferrate electrodes from a mixture of Na+, Mg2+, and Ca2+ ions was studied in this work. Here, a CDI cell with two identical NiHCF electrodes was operated in two desalination modes: (a) cyclic, in which ions are removed from and released into the same water reservoir and thus, the ion concentration remains the same after one cycle, and (b) continuous, in which ions are removed from one water reservoir and released back in a different reservoir. An average separation factor of ≈15 and 25, reflecting the selectivity of the electrodes, was obtained for Na+ over Ca2+ and Mg2+ from an equimolar solution of Na+, Ca2+ and Mg2+ in both, cyclic and continuous desalination. It was concluded that NiHCF, used in a symmetric CDI cell, is a promising material for highly selective removal of Na+ from a multivalent ion mixture.

Membrane capacitive deionization (MCDI) is a technique for water desalination by adsorbing ions in charged porous electrodes. In the present experimental and theoretical study, we analyze the performance, in terms of energy consumption, salt rejection and water recovery, of MCDI operated in intermittent flow mode. With this mode, the water recovery of MCDI is increased by reducing the water flow ratio during regeneration. Both experimental and theoretical results show that high values for water recovery and salt rejection can be achieved with a lab-scale MCDI system for feed water with a salinity of 40 mM. Importantly, we find that the energy requirement of MCDI is a factor of 2.0–2.5 higher than of RO. For RO, the energy requirements were calculated with a system-scale model developed by Qin et al. [1]. Furthermore, we show that, based on our theoretical predictions, improved MCDI can reach high salt rejection and water recovery, without an additional energy penalty. In these conditions, the energy consumption of MCDI is lower than of RO. In the present work, we present new insights for a fair performance comparison of MCDI and RO.

The novel liquid-infused membranes have been shown to mitigate membrane biofouling. Here, the long-term stability of these membrane have been tested and analyzed using bacterial growth curve models.