Polyelectrolyte-based nanofiltration membranes are obtained through a layer-by-layer sequential deposition of oppositely charged polyelectrolytes (PEs) onto a porous support structure. The resulting polyelectrolyte membrane offers tailored salt rejections for nanofiltration applications. However, little is known about the exact location of the deposited PEs on top or inside a membrane pore. Also, scarce information is available on the contribution of the different potential PE locations that affect the salt rejection of the overall membrane. Hence, research challenges, such as the influence of (a) an adsorbed PE layer inside the support membrane or (b) the bridging of the original pores and the position of the bridging layer, can only be unraveled through rigorous simulations. We present a significant extension of our previously published model into a two-dimensional layers PEn, and the support structure S) capable of addressing the selective layer additionally formed on the walls of the support capillary structure. The model solves a set of two-dimensional nonlinear Extended Nernst-PlanckPoisson and Navier-Stokes-Brinkman equations, enabling the prediction of ionic rejections from the top coating, wall coating, and a PE bridging forming inside the capillary. The proposed model framework systematically identifies and quantifies the influence of the capillary coating beneath the top layer on NaCl rejection and addresses the challenge of improving rejection rates. The model reveals that PEs deposited inside the support structure contribute significantly to NaCl rejection. It enables the predictions of differences in the rejection rates depending on the location of the PE coating, the diameter of the support capillary, and the transmembrane pressure. The model gives insight into PE bridging forming inside the support capillary and explains how its position and fixed charge density change ion rejection rates. As such, the model unravels insightful details on the rejection characteristics of coated capillaries, making it a powerful tool for designing polyelectrolyte membranes.

Polyelectrolyte multilayer nanofiltration membranes (PEMMs) achieve tailor-made rejection and selectivity of ions for water treatment applications through a layer-by-layer coating procedure, in which a charged support membrane surface is sequentially contacted with positively and negatively charged polyelectrolytes. This results in the adsorption and formation of such selective multilayer membrane skins with defined molecular compositions. The selective properties of the PEMM depend on the intrinsic properties of the respective layers. Today's research efforts aim to correlate the membrane's selective characteristics, its structural parameters, and the operating conditions to a model representation of the membrane's properties. We use our previously published pEnPEn model, which solves the pressure (p) driven transport of ions through n electrolyte layers (En) and n polyelectrolyte layers (PEn). Here, we expand the model to predict the multi-ionic pressure-induced transport through PEMMs solving one-dimensional Nernst–Planck–Poisson equations. The simulations quantify the influence of asymmetric charge distributions and individual PE layers on the ion selectivity for multi-ion solutions. These asymmetric layer properties represent the nanometer-scale membrane properties emerging from the ionic crosslinking, fixed charge compensation, and overcompensation. The model gives insight into each ion's concentration profile for n layers of electrolyte and n layers of polyelectrolytes. Now, multi-ion compositions inside and outside of the membrane are simulated, and it is shown that the membrane charge distribution even influences the onset of scaling at the fluid membrane interface. As pEnPEn provides a detailed understanding of the rejection and selectivity characteristics as a function of membrane flux and feed concentration including feed side concentration polarization, it can now predict flux-scaling boundaries for the different membrane charge distributions, making it a powerful tool for choosing process parameters and even for designing tailored PEMMs for specific separation tasks.

Overlimiting current regimes are of practical interest for electrodialysis with ion-exchange membranes (IEMs) operating at current densities significantly higher than the limiting current density. Such high ion currents across the membranes allows reducing the investments into expensive IEMs and stacks. Electroconvection (EC) is the major contributor to the overlimiting current and concepts to utilize EC are highly desired. Most of the known theoretical works describing EC in electrodialysis channels are performed when only a single cation exchange membrane is considered. The presence of a neighboring anion-exchange membrane has not been considered so far. We report the results of direct numerical simulations of ion and water transport involving EC in an electrodialysis channel formed by a cation- and an anion-exchange membrane. A 2D "basic" model involving the Nernst-Planck-Poisson-Navier-Stokes equations is introduced. Details of spatio-temporal changes in the distribution of concentrations and space charge patterns as well as the interactions of EC vortices are analyzed. The presence of the anion-exchange membrane in the transition to a close-to-chaotic regime at high potential difference is examined. For the first time, we discover the phenomenon of space-charge breakdown where the space charges of opposite sign formed at the two membranes are short-circuited throughout the desalination channel. The details of the mechanism of this phenomenon are analyzed using the 2D model and a simplified 1D model. Simulations show that the space-charge breakdown leads to a decrease in the size and number of EC vortices in the region of breakdown, which results in a reduction of the local current density. This phenomenon, apparently, determines the upper limit of the possible increase in the mass transfer rate by electroconvection.

Active layers of ion separation membranes often consist of charged layers that retain ions based on electrostatic repulsion. Conventional fabrication of these layers, such as polyelectrolyte deposition, can in some cases lead to excess coating to prevent defects in the active layer. This excess deposition increases the overall membrane transport resistance. The study at hand presents a manufacturing procedure for controlled polyelectrolyte complexation in and on porous supports by support wetting control. Pre-wetting of the microfiltration membrane support, or even supports with larger pore sizes, leads to ternary phase boundaries of the support, the coating solution, and the pre-wetting agent. At these phase boundaries, polyelectrolytes can be complexated to form partially freestanding selective structures bridging the pores. This polyelectrolyte complex formation control allows the production of membranes with evenly distributed polyelectrolyte layers, providing (1) fewer coating steps needed for defect-free active layers, (2) larger support diameters that can be bridged, and (3) a precise position control of the formed polyelectrolyte multilayers. We further analyze the formed structures regarding their position, composition, and diffusion dialysis performance.

In electromembrane desalination systems, ion transport near ion exchange membranes induces inevitable concentration polarization, which complicates mass transport. To mitigate the effect of concentration polarization and increase mass transport, spacers which promote mixing and change the flow velocity distribution in the channel. The authors investigated the effect of several spacers (from one to three) on the electromembrane system and varied the size and shape of the spacers, distance to the membranes and flow rate. It has been shown that the presence of spacers actually makes it possible to redistribute the speed and direction of the flow in the system and to increase the current efficiency. The article analyzes the impact of the spacers in the distant exorbitant conditions on mass transport and electroconvective vortices. In the article, we calculated and compared the current-voltage characteristics in the ohmic region, the “plateau” region and overlimiting region for channels with and without spacers. The work investigates fundamental laws depending on the location, size and number of spacers. This paper investigates the effect of non-conductive spacers. It has been shown that, for example, the presence of several spacers (three) near the center of the channel, slightly shifted towards the anion-exchange membrane, increases the mass transport by about 24% -25%. In addition, the influence of spacers on the emergence and development of electroconvective vortices has been studied.

Innovative membrane technologies optimally integrated into large separation process plants are essential for economical water treatment and disposal. However, the mass transport through membranes is commonly described by nonlinear differential-algebraic mechanistic models at the nano-scale, while the process and its economics range up to large-scale. Thus, the optimal design of membranes in process plants requires decision making across multiple scales, which is not tractable using standard tools. In this work, we embed artificial neural networks (ANNs) as surrogate models in the deterministic global optimization to bridge the gap of scales. This methodology allows for deterministic global optimization of membrane processes with accurate transport models – avoiding the utilization of inaccurate approximations through heuristics or short-cut models. The ANNs are trained based on data generated by a one-dimensional extended Nernst-Planck ion transport model and extended to a more accurate two-dimensional distribution of the membrane module, that captures the filtration-related decreasing retention of salt. We simultaneously design the membrane and plant layout yielding optimal membrane module synthesis properties along with the optimal plant design for multiple objectives, feed concentrations, filtration stages, and salt mixtures. The developed process models and the optimization solver are available open-source, enabling computational resource-efficient multi-scale optimization in membrane science.

Polyelectrolyte (PE) multilayer nanofiltration membranes are composite membranes obtained by layer-by-layer (LbL) adsorption/advection of oppositely charged polyelectrolytes. The mass transport properties of such polyelectrolyte multilayer membranes (PEMMs) strongly depend on membrane structural parameters related to the synthetic preparation conditions as well as on the operating conditions. Understanding the relationship between such structural features and transport properties remains a difficult question to answer. We propose a one-dimensional numerical simulation framework solving the Nernst-Planck-Poisson equations for the transport of ions through n electrolyte layers En and n polyelectrolyte layers PEn - coining this pressure (p) driven transport model as pEnPEn. We utilize different EnPEn-architectures of this model to interpret experimental data of new LbL-membranes. The proposed model framework systematically evaluates the impact of the effect of polycation/polyanion architecture with respect to the rejection of symmetric and asymmetric salts. pEnPEn can be tuned to reveal and explain the influence of the ionic crosslinking, charge compensation, and overcompensation. The model enables to formulate an effective charge distribution for different polyelectrolyte multilayer (PEM) structures. As such, the model framework gives insightful details on ion rejection phenomena, yet it will be a prerequisite and will become even more valuable when combined with neural network modeling based on a hybrid data set combining pEnPEn simulations with experimental input parameter.

Monovalent ion selective membranes are permeable for monovalent ions while rejecting divalent ions to some extent. Different processes and applications like electrodialysis, microbial fuel cells, and flow batteries utilize such selective properties. Industrial membranes have a specific coating of equal charge to reject the bivalent counter ions. It has been suggested in the past that the current density regime at which such composite ion exchange membranes are operated can strongly influence their ion selectivity towards monovalent ions. Here, we now confirm this observation for a commercial CMS membrane as well as for a novel microgel modified membrane. The higher the applied current density is, the more acute the drop in selectivity becomes as opposed to the unmodified reference membrane where bivalent ions are transported preferentially. This work focuses on the relationship between selectivity and current density regime using (1) a conventional commercial membrane, (2) a commercial monovalent ion selective membranes as well as (3) a tailor-made selective membrane, the latter being surface-modified with quaternized Poly (2-vinylpyridine) (qP2VP) microgels. Experimental electrodialysis results in combination with (a) direct numerical simulations of mixed ion transport through the composite architecture and (b) a swelling analysis of the microgels by ellipsometry reveal that layer responsiveness and structural change of the modification layer is responsible for the decrease in permselectictivity upon an increased current density. The swelling reduces the charge density of the modification and therewith the rejection of divalent ions. It would be highly desirable to synthesize modification layers that have a low ion transport resistance while maintaining its volumetric charge density independent of the current density applied.

Organic acids are highly valuable platform chemicals that can be obtained from bioresources and subsequently transformed into a wide spectrum of profitable consumer goods. After their synthesis, organic acids need to be separated from other by-products and conveniently upconcentrated. Based on the ionic nature of organic acids, electromembrane processes are viable technologies for their recovery. Transport of weak acids through ion-exchange membranes is a complex process influenced by multiple phenomena, i.e. concentration polarization, water dissociation and counterion-membrane interactions. In the present study, the transport of two different organic acids (citric and oxalic acid) through anion-exchange membranes is investigated by means of using linear sweep voltammetry, chronopotentiometry and electrochemical impedance spectroscopy (EIS). Results have shown that, at pH values where multivalent acid anions predominate in solution, a first limiting current density is registered in the current-voltage curves, followed by an increase in membrane resistance. A further increase in current leads to a second limiting current density and a steeper increase in membrane resistance associated with an intensified ion depletion. A strong correlation between polarization curves and electrochemical impedance measurements reveals that such increase in resistance is prompted by generation of H+ and OH− ions and the concomitant onset of homogeneous reactions in very thin solution layers. The generation of H+ and OH− ions is tracked by a Gerischer arc in the impedance spectra. As the polarization level increases, the subsequent reaction of multivalent anions into lower-charge acid anions involves the evolution of additional Gerischer arcs. Furthermore, the lower conductivity of the reaction products correlates with the increased system resistance. The characteristic times of these reactions are in the order of milliseconds, thus being only directly accessible with the use of frequency response analysis techniques, such as EIS.

Bipolar ion-exchange membranes (BPM) have a long history and many uses. Still, the number of applications continues to grow every year, as does the interest in a better understanding of the mechanisms of ion transport and water splitting. We reconsider the existing theoretical background for the BPMs and propose a one-dimensional stationary model. For the first time, the Nernst-Planck-Poisson equations are coupled with the equations, which locally describe the water splitting kinetics. The catalytic effects exerted by the functional groups and the catalyst (if present), the protonation-deprotonation reactions of these groups as well as the effect of strong electric field (the second Wien effect) are taken into account when describing the reverse-bias mode. The effective rate constant of water splitting occurring in the absence of electric field is determined from the acid dissociation constants (Ka). The concentration profiles, the thickness of the reaction zone and space charge region (SCR) are simulated and analyzed. The results of numerical computation are compared with the known analytical estimations. Thus, the basic assumptions of the theory of BPMs are examined, and the conditions under which these assumptions are valid or not are found. Current-voltage curves and partial currents are calculated and compared with experimental data. The occurrence of two limiting currents at pKa close to 7 is predicted due to current-induced membrane discharge. According to simulations, any increase in the SCR thickness leads to a decrease of the water spitting rate at a fixed voltage due to a decrease in the second Wien effect. A very thin (about 4 nm) catalytic layer within the bipolar junction is sufficient to obtain 100 mA cm−2 current density at 1 V even when the anion-exchange and cation-exchange membrane layers do not contain catalytically active functional groups.

Concentration polarization is a diffusion‐limited phenomenon for ion transport in electrodialysis based desalination processes. Once a so‐called limiting current is reached, the resistance of the system rises notably manifested as a plateau region in the current–voltage curves. For long it is hypothesized that altering the surface properties of the membrane can overcome the diffusional transport limitation by the induction of electroconvective vortices mixing the laminar boundary layer. To systematically investigate the influence of geometrical and chemical membrane surface topology on the evolution of electroconvection, circular patterns of polystyrene, poly(2‐vinylpyridine) (P2VP), and P2VP microgels are inkjet printed on cation‐exchange membranes. All types of patterns cause an insignificant increase in membrane resistance but they reduce the plateau lengths indicating the desired accelerated onset of electroconvection. In case of polystyrene (PS) patterns, the drop in plateau length results in a small reduction in transport resistance for overlimiting currents. However, membranes modified with linear P2VP and P2VP microgel patterns do exhibit a significantly decreased resistance in this region at a simultaneous increase of the limiting current density. Direct numerical simulations support the interpretation that the surface charge of the printed patterns influences the direction of the vortices being advantageous during ion transport toward the membrane.