Nanofiltration performance of conical and hourglass nanopores

Multiscale modelling of transport in polymer-based reverse-osmosis/nanofiltration membranes: present and future

Nanofiltration (NF) and reverse osmosis (RO) processes are physical separation technologies used to remove contaminants from liquid streams by employing dense polymer-based membranes with nanometric voids that confine fluids at the nanoscale. At this level, physical properties such as solvent and solute permeabilities are intricately linked to molecular interactions. Initially, numerous studies focused on developing macroscopic transport models to gain insights into separation properties at the nanometer scale. However, continuum-based models have limitations in nanoconfined situations that can be overcome by force field molecular simulations. Continuum-based models heavily rely on bulk properties, often neglecting critical factors like liquid structuring, pore geometry, and molecular/chemical specifics. Molecular/mesoscale simulations, while encompassing these details, often face limitations in time and spatial scales. Therefore, achieving a comprehensive understanding of transport requires a synergistic integration of both approaches through a multiscale approach that effectively combines and merges both scales. This review aims to provide a comprehensive overview of the state-of-the-art in multiscale modeling of transport through NF/RO membranes, spanning from the nanoscale to continuum media.

Desalination Performance in Janus Graphene Oxide Channels: Geometric Asymmetry vs Charge Polarity

Improving the desalination performance of membranes is always in the spotlight of scientific research; however, Janus channels with polarized surface charge as nanofiltration membranes are still unexplored. In this work, using molecular dynamics simulations, we demonstrate that Janus graphene oxide (GO) channels with appropriate geometry and surface charge can serve as highly efficient nanofiltration membranes. We observe that the water permeability of symmetric Janus GO channels is significantly superior to that of asymmetric channels without sacrificing much ion rejection, owing to weakened ion blockage and electrostatic effects. Furthermore, in symmetric Janus GO channels, the transport of water and ions is sensitive to the charge polarity of the channel inner surface, which is realized by tuning the ratio of cationic and anionic functionalization. Specifically, with the increase in cationic functionalization, the water flux decreases monotonously, while ion rejection displays an interesting maximum behavior that indicates desalination optimization. Moreover, the trade-off between water permeability and ion rejection suggests that the Janus GO channels have an excellent desalination potential and are highly tunable according to the specific water treatment requirements. Our work sheds light on the key role of channel geometry and charge polarity in the desalination performance of Janus GO channels, which paves the way for the design of novel desalination devices.

Smart nanochannels: tailoring ion transport properties through variation in nanochannel geometry

This research explores ion transport behavior and functionality in a hybrid nanochannel that consists of two conical and cylindrical parts. The numerical investigation focuses on analyzing the length of each part in the nanochannel. The nanochannels are hybrid cavities embedded in a membrane, where the size of the conical part varies as equal to, larger than, or smaller than the cylindrical part. The nanochannel is coated with a polyelectrolyte layer that exhibits a dense charge density distribution. The charge density of the soft layer is described using the soft step distribution function. We study the electroosmotic flow, ionic current, rectification, and selectivity of the nanochannel versus bulk electrolyte concentration, the charge density of the polyelectrolyte layer, and decay length, while considering the effect of ionic partitioning. The steady-state Poisson-Nernst-Planck and Navier-Stokes equations are solved using the finite element method. The findings reveal that the nanochannel with a more extensive conical section demonstrates increased rectification, with the rectification factor rising from 1.4 to 2 at a bulk concentration of 100 mM. Additionally, the nanochannel with a longer cylindrical part exhibits improved selectivity under negative voltage conditions, while positive voltage introduces a different situation. The nanochannel with equal cylindrical and conical parts significantly affects conductivity by modifying the charge density in the soft layer, resulting in a 3.125-fold increase in conductivity under positive voltage when the charge density in the polyelectrolyte layer is raised from 25 to 100 mol m-3. This research focuses on creating intelligent nanochannels by controlling mass concentration, charge density, and collapse length, improving system performance, and optimizing properties. It also offers valuable insights into ion transport mechanisms in nanochannel systems, advancing our understanding in this field.

Quantifying uncertainty in nanofiltration transport models for enhanced metals recovery

To decarbonize our global energy system, sustainably harvesting metals from diverse sourcewaters is essential. Membrane-based processes have recently shown great promise in meeting these needs by achieving high metal ion selectivities with relatively low water and energy use. An example is nanofiltration, which harnesses steric, dielectric, and Donnan exclusion mechanisms to perform size- and charge-based fractionation of metal ions. To further optimize nanofiltration systems, multicomponent models are needed; however, conventional methods necessitate large amounts of data for model calibration, introduce substantial uncertainty into the characterization process, and often yield poor results when extrapolated. In this work, we develop a new computational architecture to alleviate these concerns. Specifically, we develop a framework that: (1) reduces the data requirement for model calibration to only charged species measurements; (2) eliminates uncertainty propagation problems present in conventional characterization processes; (3) enables exploration of pH optimization for enhancing metal ion selectivities; and (4) enables uncertainty quantification to assess the sensitivity of partition coefficients and ion driving forces to learned pore size distributions. Our framework captures eight independent datasets comprising over 500 measurements to within ±15%. Our studies also suggest that the expectation-maximization algorithm can effectively learn pore size distributions and that optimizing pH can improve metal ion selectivities by a factor of 3-10×. Our findings also reveal that image charges appear to play a less pronounced role in dielectric exclusion under the studied conditions and that ion driving forces are more sensitive to pore size distributions than partition coefficients.

Cation pumping against a concentration gradient in conical nanopores characterized by load capacitors

We study the cation transport against an external concentration gradient (cation pumping) that occurs in conical nanopores when zero-average oscillatory and white noise potentials are externally applied. This pumping, based on the electrically asymmetric nanostructure, is characterized here by a load capacitor arrangement. In the case of white noise signals, the conical nanopore acts as an electrical valve that allows extraction of order from chaos. No molecular carriers, specific ion pumps, and competitive ion-binding phenomena are required. The nanopore conductance on/off states mimic those of the voltage-gated ion channels in the cell membrane. These channels allow modulating membrane potentials and ionic concentration gradients along oscillatory pulses in circadian rhythms and the cell cycle. We show that the combination of asymmetric nanostructures with load capacitors can be useful for the understanding of nanofluidic processes based on bioelectrochemical gradients.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Ion and Water Transport in Ion-Exchange Membranes for Power Generation Systems: Guidelines for Modeling

Artificial ion-exchange and other charged membranes, such as biomembranes, are self-organizing nanomaterials built from macromolecules. The interactions of fragments of macromolecules results in phase separation and the formation of ion-conducting channels. The properties conditioned by the structure of charged membranes determine their application in separation processes (water treatment, electrolyte concentration, food industry and others), energy (reverse electrodialysis, fuel cells and others), and chlore-alkali production and others. The purpose of this review is to provide guidelines for modeling the transport of ions and water in charged membranes, as well as to describe the latest advances in this field with a focus on power generation systems. We briefly describe the main structural elements of charged membranes which determine their ion and water transport characteristics. The main governing equations and the most commonly used theories and assumptions are presented and analyzed. The known models are classified and then described based on the information about the equations and the assumptions they are based on. Most attention is paid to the models which have the greatest impact and are most frequently used in the literature. Among them, we focus on recent models developed for proton-exchange membranes used in fuel cells and for membranes applied in reverse electrodialysis.

Numerical Investigation of Diffusioosmotic Flow in a Tapered Nanochannel

Diffusioosmosis concerns ionic flow driven by a concentration difference in a charged nano-confinement and has significant applications in micro/nano-fluidics because of its nonlinear current-voltage response, thereby acting as an active electric gating. We carry out a comprehensive computation fluid dynamics simulation to investigate diffusioosmotic flow in a charged nanochannel of linearly varying height under an electrolyte concentration gradient. We analyze the effects of cone angle (α), nanochannel length (l) and tip diameter (dt), concentration difference (Δc = 0–1 mM), and external flow on the diffusioosmotic velocity in a tapered nanochannel with a constant surface charge density (σ). External flow velocity (varied over five orders of magnitude) shows a negligible influence on the diffusioosmotic flow inside the tapered nanochannel. We observed that a cone angle causes diffusioosmotic flow to move towards the direction of increasing gap thickness because of stronger local electric field caused by the overlapping of electric double layers near the smaller orifice. Moreover, the magnitude of average nanoflow velocity increases with increasing |α|. Flow velocity at the nanochannel tip increases when dt is smaller or when l is greater. In addition, the magnitude of diffusioosmotic velocity increases with increasing Δc. Our numerical results demonstrate the nonlinear dependence of tapered, diffusioosmotic flow on various crucial control parameters, e.g., concentration difference, cone angle, tip diameter, and nanochannel length, whereas an insignificant relationship on flow rate in the low Peclet number regime is observed.

Asymmetric transport and desalination in graphene channels

An asymmetric desalination phenomenon occurs in graphene channels with different geometries.

Pressure-driven power generation and ion separation using a non-uniformly charged nanopore

Due to its versatile potential applications, nanofluidic devices have drawn much attention of researches in various fields. Among these, pressure-driven power generation is considered as a candidate for the next generation alternative green energy source, and pressure-driven ion separation (nanofiltration) for desalination. Aiming to achieve a better performance in these two representative cases, a cylindrical nanopore having different types of non-uniform surface charge profile is adopted, and its performance under various conditions assessed. We show that lower the surface charge density near the nanopore inlet region can suppress the effect of ion concentration polarization (ICP) and improve the selectivity, thereby enhancing appreciably its power generation performance. For a fixed averaged surface charge density, if the bulk salt concentration is low, the higher the surface charge density near the nanopore openings, the better its performance. The degree of ICP can be alleviated by applying a sufficiently large pressure difference. Although previous studies showed that salt rejection is influenced significantly by the profile of the electric field inside a nanopore, we find that the electric field at nanopore openings also plays a role. Through choosing appropriately the surface charge profile, it is possible to solve the trade-off between rejection and flow rate.

Nanopore-based desalination subject to simultaneously applied pressure gradient and gating potential

The performance of a dielectric membrane in desalting is assessed by considering a cylindrical nanopore, surface modified by a dielectric layer, subject to simultaneously applied pressure gradient and gating potential. The charged conditions of the nanopore can be tuned by modulating the applied gating potential so that it can be used for rejecting different types of salt. In general, the thinner the dielectric layer and/or the larger its dielectric constant the better the salt rejection performance. For example, if the thickness of the dielectric layer is 10 nm with a relative dielectric constant of 25, applying a pressure difference of 5 MPa and gating potential of 1 V yields 49% rejection. However, it declines to 9% if the relative dielectric constant is lowered to 5 with other parameters fixed, and 23% if that thickness is 50 nm with other parameters fixed. The results of numerical simulation based on various types of single salt and mixture salts with ions of different valences reveal that the type of ions which need be filtrated can be selected effectively through regulating the gating potential.

Investigation of dielectric constants of water in a nano-confined pore

We report the dielectric properties of pure water confined in a silica hydrophilic nanopore determined from the computation of the density of liquid in the confined phase by the grand canonical Monte Carlo (GCMC) simulations. The silica cylindrical nanopore is divided into n concentric radial shells to get a better insight into the dielectric properties of nanoconfined water. We find that the average values of the dielectric constants are very close and almost independent of the number of concentric radial shells. The decrease in the dielectric constant of confined pure water is due to the strong orientation of water dipoles in the vicinity of the surface while water dipoles do not exhibit any preferential orientation in bulk phase.

Investigation of dielectric properties in a silica hydrophilic pore with two water reservoirs.

Physico-chemical processes

The review scans research articles published in 2018 on physico-chemical processes for water and wastewater treatment. The paper includes eight sections, that is, membrane technology, granular filtration, flotation, adsorption, coagulation/flocculation, capacitive deionization, ion exchange, and oxidation. The membrane technology section further divides into six parts, including microfiltration, ultrafiltration, nanofiltration, reverse osmosis/forward osmosis, and membrane distillation. PRACTITIONER POINTS: Totally 266 articles on water and wastewater treatment have been scanned; The review is sectioned into 8 major parts;  Membrane technology has drawn the widest attention from the research community.

Ionic transport characteristics of negatively and positively charged conical nanopores in 1:1, 2:1, 3:1, 2:2, 1:2, and 1:3 electrolytes

We study experimentally the current (I)-voltage (V) curves of 1:1, 2:1, 3:1, 2:2, 1:2, and 1:3 electrolytes in positively and negatively charged conically-shaped pores of nanoscale dimensions. The positive charges are poly(allylamine hydrochloride) chains functionalized on the pore surface by electrostatic interactions while the negative charges are carboxylic acid groups. Under physiological conditions, these fixed-charge groups are ionized and strongly interact with the different monovalent, divalent, and trivalent ions in the pore solution. The current rectification of the I-V curves and the membrane potentials provide fundamental information on the interaction of the pore charge groups with the mobile ions present at electrochemically and biologically relevant concentrations. The different pores and electrolytes studied, together with the abundant experimental data provided, can be useful to develop new theoretical simulations of transport phenomena in nanoscale solutions that are confined within charged surfaces.

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

Artificial charged membranes, similar to the biological membranes, are self-assembled nanostructured materials constructed from macromolecules. The mutual interactions of parts of macromolecules leads to phase separation and appearance of microheterogeneities within the membrane bulk. On the other hand, these interactions also cause spontaneous microheterogeneity on the membrane surface, to which macroheterogeneous structures can be added at the stage of membrane fabrication. Membrane bulk and surface heterogeneity affect essentially the properties and membrane performance in the applications in the field of separation (water desalination, salt concentration, food processing and other), energy production (fuel cells, reverse electrodialysis), chlorine-alkaline electrolysis, medicine and other. We review the models describing ion transport in ion-exchange membranes and electromembrane systems with an emphasis on the role of micro- and macroheterogeneities in and on the membranes. Irreversible thermodynamics approach, “solution-diffusion” and “pore-flow” models, the multiphase models built within the effective-medium approach are examined as the tools for describing ion transport in the membranes. 2D and 3D models involving or not convective transport in electrodialysis cells are presented and analysed. Some examples are given when specially designed surface heterogeneity on the membrane surface results in enhancement of ion transport in intensive current electrodialysis.