High energy conversion efficiency in nanofluidic channels

Energy harvesting from water streaming at charged surface

Water flowing at a charged surface may produce electricity, known as streaming current/potentials, which may be traced back to the 19th century. However, due to the low gained power and efficiencies, the energy conversion from streaming current was far from usable. The emergence of micro/nanofluidic technology and nanomaterials significantly increases the power (density) and energy conversion efficiency. In this review, we conclude the fundamentals and recent progress in electrical double layers at the charged surface. We estimate the generated power by hydrodynamic energy dissipation in multi-scaling flows considering the viscous systems with slipping boundary and inertia systems. Then, we review the coupling of volume flow and current flow by the Onsager relation, as well as the figure of merits and efficiency. We summarize the state-of-the-art of electrokinetic energy conversions, including critical performance metrics such as efficiencies, power densities, and generated voltages in various systems. We discuss the advantages and possible constraints by the figure of merits, including single-phase flow and flying droplets.

Nature of Overcharging and Charge Inversion in Electrical Double Layers

Understanding overcharging and charge inversion is one of the long-standing challenges in soft matter and biophysics. To study these phenomena, we employ the modified Gaussian renormalized fluctuation theory, which allows for the self-consistent accounting of spatially varying ionic strength as well as the spatial variations in dielectric permittivity and excluded volume effects. The underlying dependence of overcharging on the electrostatic coupling is elucidated by varying the surface charge, counterion valency, and dielectric contrast. Consistent with simulations, three characteristic regimes corresponding to weak, moderate, and strong coupling are identified. Important features like the inversion of zeta potential, crowding, and ionic layering at the surface are successfully captured. For weak coupling, there is no overcharging. In the moderate coupling regime, overcharging increases with the surface charge. Finally, in the strong coupling regime, ionic crowding and saturation in overcharging are observed. Our theory predicts a nonmonotonic dependence of charge inversion on multivalent salt concentration as well as the addition of monovalent salt, in quantitative agreement with experiments.

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.

Electrostatic correlations in electrolytes: Contribution of screening ion interactions to the excess chemical potential

A new theory for the electrostatic component of the chemical potential for homogeneous electrolytes modeled with the primitive model is developed. This Mean Countershell Approximation (MCSA) is an analytic theory derived by including the interactions between the ions' screening clouds. At molar concentrations, these contribute substantially to the excess chemical potential but are absent in classical Debye-Hückel and Mean Spherical Approximation (MSA) theories. Simulations show that the MCSA is highly accurate, including at the low dielectric constants of ionic liquids. While sharing a mathematical framework with the MSA, the MCSA has simpler formulas and is qualitatively more accurate when there is ion size asymmetry.

Wood Ionic Cable

The combination of good stability, biocompatibility, and high mechanical strength is attractive for bio-related material applications, but it remains challenging to simultaneously achieve these properties in a single, ionically conductive material. Here a "wood" ionic cable, made of aligned wood nanofibrils, demonstrating a combination of biocompatibility, high mechanical strength, high ionic conductivity, and excellent stability is reported. The wood ionic cable possesses excellent flexibility and exhibits high tensile strength up to 260 MPa (in the dry state) and ≈80 MPa (in the wet state). The nanochannels within the highly aligned cellulose nanofibrils and the presence of negative charges on the surfaces of these nanochannels, originating from the cellulose hydroxyl groups, provide new opportunities for ion regulation at low salt concentrations. Ion regulation in turn enables the wood ionic cable to have unique nanofluidic ionic behaviors. The Na⁺ ion conductivity of the wood ionic cable can reach up to ≈1.5 × 10^-4 S cm^-1 at low Na⁺ ion concentration (1.0 × 10^-5 mol L^-1 ), which is an order of magnitude higher than that of bulk NaCl solution at the same concentration. The scalable, biocompatible wood ionic cable enables novel ionic device designs for potential ion-regulation applications.

Vertically-Oriented Ti3C2Tx MXene Membranes for High Performance of Electrokinetic Energy Conversion

The electrokinetic effect to convert the mechanical energy from ambient has gained sustained research attention because it is free of moving parts and easy to be miniaturized for microscale applications. The practical application is constrained by the limited electrokinetic energy conversion performance. Herein, we report vertically oriented MXene membranes (VMMs) with ultrafast permeation as well as high ion selectivity, in which the permeation is several thousand higher than the largely researched horizontally stacked MXene membranes (HMMs). The VMMs can achieve a high streaming current of 8.17 A m^-2 driven by the hydraulic pressure, largely outperforming all existing materials. The theoretical analysis and numerical calculation reveal the underlying mechanism of the ultrafast transport in VMMs originates from the evident short migration paths, the low energy loss during the ionic migration, and the large effective inlet area on the membrane surface. The orientation of the 2D lamella in membranes, the long-overlooked element in the existing literatures, is identified to be an essential determinant in the performance of 2D porous membranes. These understandings can largely promote the development of electrokinetic energy conversion devices and bring advanced design strategy for high-performance 2D materials.

Nanofluidic Charge Transport under Strong Electrostatic Coupling Conditions

The comprehensive depiction of the many-body effects governing nanoconfined electrolytes is an essential step for the conception of nanofluidic devices with optimized performance. By incorporating self-consistently multivalent charges into the Poisson-Boltzmann equation dressed by a background monovalent salt, we investigate the impact of strong-coupling electrostatics on the nanofluidic transport of electrolyte mixtures. We find that the experimentally observed negative streaming currents in anionic nanochannels originate from the collective effect of Cl^- attraction by the interfacially adsorbed multivalent cations and the no-slip layer reducing the hydrodynamic contribution of these cations to the net current. The like-charge current condition emerging from this collective mechanism is shown to be the reversal of the average potential within the no-slip zone. Applying the formalism to surface-coated membrane nanoslits located in the giant dielectric permittivity regime, we reveal a new type of streaming current activated by attractive polarization forces. Under the effect of these forces, multivalent ions added to the KCl solution set a charge separation and generate a counterion current between the neutral slit walls where the pure KCl conductivity vanishes. The adjustability of the current characteristics solely via the valency and amount of the added multivalent ions identifies the underlying process as a promising mechanism for nanofluidic ion separation purposes.

Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models

Biological ion channels and synthetic nanopores are responsible for passive transport of ions through a membrane between two compartments. Modeling these ionic currents is especially amenable to reduced models because the device functions of these pores, the relation of input parameters (e.g., applied voltage, bath concentrations) and output parameters (e.g., current, rectification, selectivity), are well defined. Reduced models focus on the physics that produces the device functions (i.e., the physics of how inputs become outputs) rather than the atomic/molecular-scale physics inside the pore. Here, we propose four rules of thumb for constructing good reduced models of ion channels and nanopores. They are about (1) the importance of the axial concentration profiles, (2) the importance of the pore charges, (3) choosing the right explicit degrees of freedom, and (4) creating the proper response functions. We provide examples for how each rule of thumb helps in creating a reduced model of device behavior.

Transport behavior of pressure-driven electrolyte solution through a surface-charged nanochannel

The transport behavior of a pressure-driven electrolyte solution through a surface-charged nanochannel is investigated using molecular dynamics (MD) simulations. Similar to pure water, the relationship between the applied pressure (P) and the average transport velocity ([Formula: see text]) of the electrolyte solution is roughly linear, which matches with the theoretical solution very well. The friction coefficient λ is used to describe the transport behavior (a higher λ leads to a lower [Formula: see text]), which scales with the slope of the P- [Formula: see text] relationship and increases with the increases of both the charge density of the channel wall σ and the electrolyte concentration n. The physical mechanism is found as follows: the solid-liquid interaction energy between the channel wall and the liquid inside the channel decreases with both σ and n (being more negative), which makes it more difficult for the liquid boundary layer to slide against the channel wall, leading to a higher λ. In addition, the increase of σ also causes a significant decrease of the liquid-liquid interaction energy but the opposite effect is found with the increase of n. However, λ increases with the increase of both σ and n, suggesting that the relationship between λ and the liquid-liquid interaction energy is more complicated for an electrolyte solution, different from the corresponding result of pure water.

Coupling effects in electromechanical ion transport in graphene nanochannels

In this work, we use molecular dynamics simulations to study the transport of ions in electromechanical flows in slit-like graphene nanochannels. The variation of ionic currents indicates a nonlinear coupling between pressure-driven and electroosmotic flows, which enhances the ionic currents for electromechanical flows compared with the linear superposition of pressure-driven and electroosmotic flows. The nonlinear coupling is attributed to the reduction of the total potential energy barrier due to the density variations of ions and water molecules in the channel. The numerical results may offer molecular insights into the design of nanofluidic devices for energy conversion.

Nanochannels regulating ionic transport for boosting electrochemical energy storage and conversion: a review

Electrochemical power sources, as one of the most promising energy storage and conversion technologies, provide great opportunities for developing high energy density electrochemical devices and portable electronics. However, uncontrolled ionic transport in electrochemical energy conversion, typically undesired anion transfer, usually causes some issues degrading the performance of energy storage devices. Nanochannels offer an effective strategy to solve the ionic transport problems for boosting electrochemical energy storage and conversion. In this review, the advantages of nanochannels for electrochemical energy storage and conversion and the construction principle of nanochannels are introduced, including ion selectivity and ultrafast ion transmission of nanochannels, which are considered as two critical factors to achieve highly efficient energy conversion. Recent advances in applications of nanochannels in lithium secondary batteries (LSBs), electrokinetic energy conversion systems and concentration cells are summarized in detail. Nanochannels exist in the above systems in two typical forms: functional separator and electrode protective layer. Current research on nanochannel-based LSBs is still at the early stage, and deeper and broader applications are expected in the future. Finally, the remaining challenges of nanochannel fabrication, performance improvement, and intelligent construction are presented. It is envisioned that this paper will provide new insights for developing high-performance and versatile energy storage electronics based on nanochannels.

Electric Double Layers with Surface Charge Regulation Using Density Functional Theory

Surprisingly, the local structure of electrolyte solutions in electric double layers is primarily determined by the solvent. This is initially unexpected as the solvent is usually a neutral species and not a subject to dominant Coulombic interactions. Part of the solvent dominance in determining the local structure is simply due to the much larger number of solvent molecules in a typical electrolyte solution.The dominant local packing of solvent then creates a space left for the charged species. Our classical density functional theory work demonstrates that the solvent structural effect strongly couples to the surface chemistry, which governs the charge and potential. In this article we address some outstanding questions relating double layer modeling. Firstly, we address the role of ion-ion correlations that go beyond mean field correlations. Secondly we consider the effects of a density dependent dielectric constant which is crucial in the description of a electrolyte-vapor interface.

A hybrid theoretical method for predicting electrokinetic energy conversion in nanochannels

The traditional methods to predict electrokinetic energy conversion (EKEC) in nanochannels are mostly based on the Navier-Stokes (NS) equation for ionic flow and the Poisson-Boltzmann (PB) equation for charge distributions, which is questionable for ion transport through highly charged nanochannels. In this work, the classical density functional theory (cDFT) is used together with molecular dynamics (MD) simulation and the Navier-Stokes (NS) equation to predict the electrical current and the thermodynamic efficiency of electrokinetic energy conversion in nanochannels. By introducing numerical results for the slip length calculated from MD simulation, a significant increase of the electrokinetic current is predicted in comparison to that obtained from the traditional electrokinetic equations with the non-slip boundary condition, leading to the theoretical predictions of the thermodynamic efficiency for electrokinetic energy conversion in nanochannels in good agreement with recent experiments. The hybrid method predicts that maximum electrokinetic efficiency can be achieved by tuning the channel height and solution conditions including electrolyte concentrations, ion valences, and surface energies. The theoretical results provide new insights into pressure-driven electrical energy generation processes and helpful guidelines for engineering design and optimization of electrokinetic energy conversion.

Electrical Power Generation from Wet Textile Mediated by Spontaneous Nanoscale Evaporation

Developing low-weight, frugal, and sustainable power sources for resource-limited settings appears to be a challenging proposition for the advancement of next-generation sensing devices and beyond. Here, we report the use of centimeter-sized simple wet fabric pieces for electrical power generation by deploying the interplay of a spontaneously induced ionic motion across fabric nanopores due to capillary action and simultaneous water evaporation by drawing thermal energy from the ambient. Unlike other reported devices with similar functionalities, our arrangement does not necessitate any input mechanical energy or complex topographical structures to be embedded in the substrate. A single device is capable of generating a sustainable open circuit potential up to ∼700 mV, which is further scaled up to ∼12 V with small-scale multiplexing (i.e., deploying around 40 numbers of fabric channels simultaneously). The device is able to charge a commercial supercapacitor of ∼0.1 F which can power a white light-emitting diode for more than 1 h. This suffices in establishing an inherent capability of functionalizing self-powered electronic devices and also to be potentially harnessed for enhanced power generation with feasible up-scaling.

Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration

In charged colloidal dispersion systems the interest is in finding their stability conditions, phase transitions, and transport properties, either in bulk or confinement, among other physicochemical quantities, for which the knowledge of the dispersions' molecular structure and the associated macroion-macroion forces is crucial. To investigate these phenomena simple models have been proposed. Most of the theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence, these studies have been focused on the electrolyte structure around one or two isolated central particle(s), where phenomena as charge reversal, charge inversion and surface charge amplification have been shown to be relevant. However, experimental studies at finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. A simple, yet useful, model is the Colloidal Primitive Model, in which the colloidal dispersion is modeled as a mixture of size (and charge) asymmetrical hard spheres, at finite volume fraction. In this paper we review recent integral equations solutions for this model, where very long-range attractive-repulsive forces, as well as new long-range, giant charge inversions are reported. The calculated macroions radial distribution functions, charge distributions, and macroion-macroion forces are qualitatively consistent with existing experimental results, and Monte Carlo and molecular dynamics simulations.

Non-Negligible Roles of Pore Size Distribution on Electroosmotic Flow in Nanoporous Materials

Electroosmotic flow in nanoporous materials is of fundamental importance for the design and development of filtration membranes and electrochemical devices such as supercapacitors and batteries. Recent experiments suggest that ion transport in a porous network is substantially different from that in individual nanochannels due to the pore size distribution and pore connectivity. Herein, we report a theoretical framework for ion transport in nanoporous materials by combing the classical density functional theory to describe the electrical double layer (EDL) structure, the Navier-Stokes equation for the fluid flow, and the effective medium approximation to bridge the gap between individual nanopores and the network connectivity. We find that ion conductivity in nanoporous materials is extremely sensitive to the pore size distribution when the average size of micropores is comparable to the EDL thickness. The theoretical predictions provide an explanation of the giant gap between the conductivity of a single pore and that of a porous network and highlight the mechanism of ion transport through nanoporous materials important for numerous practical applications.

Enhancement of oil flow in shale nanopores by manipulating friction and viscosity

Understanding the viscosity and friction of a fluid under nanoconfinement is the key to nanofluidics research. Existing work on nanochannel flow enhancement has been focused on simple systems with only one to two fluids considered such as water flow in carbon nanotubes, and large slip lengths have been found to be the main factor for the massive flow enhancement. In this study, we use molecular dynamics simulations to study the fluid flow of a ternary mixture of octane-carbon dioxide-water confined within two muscovite and kerogen surfaces. The results indicate that, in a muscovite slit, supercritical CO₂ (scCO₂) and H₂O both enhance the flow of octane due to (i) a decrease in the friction of octane with the muscovite wall because of the formation of thin layers of H₂O and scCO₂ near the surfaces; and (ii) a reduction in the viscosity of octane in nanoconfinement. Water reduces octane viscosity by weakening the interaction of octane with the muscovite surface, while scCO₂ reduces octane viscosity by weakening both octane-octane and octane-surface interactions. In a kerogen slit, water does not play any significant role in changing the friction or viscosity of octane. In contrast, scCO₂ reduces both the friction and the viscosity of octane, and the enhancement of octane flow is mainly caused by the reduction of viscosity. Our results highlight the importance of multicomponent interactions in nanoscale fluid transport. The results presented here also have a direct implication in enhanced oil recovery in unconventional reservoirs.

Multiscale analysis of the effect of surface charge pattern on a nanopore's rectification and selectivity properties: From all-atom model to Poisson-Nernst-Planck

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics, and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns, that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit- and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore but are relatively transferable to different voltages and charge patterns with the same total charge.

Steady State and Dynamic Response of Voltage-Operated Membrane Gates

An electrochemical flow cell with Nafion 212, aqueous LiI/I2 redox solution, and carbon paper electrode was operated as an electro-osmotic gate based on the Electrokinetic Energy Conversion (EKEC) principle. The gate was operated in different modes. (i) In normal DC pump operation it is shown to follow the predictions from the phenomenological transport equations. (ii) Furthermore, it was also demonstrated to operate as a normally open, voltage-gated valve for microfluidic purposes. For both pump and valve operations low energy requirements (mW range) were estimated for precise control of small flows (μL range). (iii) Finally, the dynamic response of the pump was investigated by using alternating currents at a range of different frequencies.

Emerging hydrovoltaic technology

Water contains tremendous energy in a variety of forms, but very little of this energy has yet been harnessed. Nanostructured materials can generate electricity on interaction with water, a phenomenon that we term the hydrovoltaic effect, which potentially extends the technical capability of water energy harvesting and enables the creation of self-powered devices. In this Review, starting by describing fundamental properties of water and of water-solid interfaces, we discuss key aspects pertaining to water-carbon interactions and basic mechanisms of harvesting water energy with nanostructured materials. Experimental advances in generating electricity from water flows, waves, natural evaporation and moisture are then reviewed to show the correlations in their basic mechanisms and the potential for their integration towards harvesting energy from the water cycle. We further discuss potential device applications of hydrovoltaic technologies, analyse main challenges in improving the energy conversion efficiency and scaling up the output power, and suggest prospects for developments of the emerging technology.

Supercritical CO2-induced atomistic lubrication for water flow in a rough hydrophilic nanochannel

A fluid flow in a nanochannel highly depends on the wettability of the channel surface to the fluid. The permeability of the nanochannel is usually very low, largely due to the adhesion of fluid at the solid interfaces. Using molecular dynamics (MD) simulations, we demonstrate that the flow of water in a nanochannel with rough hydrophilic surfaces can be significantly enhanced by the presence of a thin layer of supercritical carbon dioxide (scCO2) at the water-solid interfaces. The thin scCO2 layer acts like an atomistic lubricant that transforms a hydrophilic interface into a super-hydrophobic one and triggers a transition from a stick- to- a slip boundary condition for a nanoscale flow. This work provides an atomistic insight into multicomponent interactions in nanochannels and illustrates that such interactions can be manipulated, if needed, to increase the throughput and energy efficiency of nanofluidic systems.

Assessing the accuracy of three classical density functional theories of the electrical double layer

Classical density functional theory (DFT) is a useful tool to compute the structure of the electrical double layer because it includes ion-ion correlations due to excluded-volume effects (i.e., steric correlations) and ion screening effects (i.e., electrostatic correlations beyond the electrostatic mean-field potential). This paper systematically analyzes the accuracies of three different electrostatic excess free-energy functionals, as compared to Monte Carlo (MC) simulations of the planar electrical double layer, over a large parameter space. Specifically, we tested the reference fluid density (RFD) [Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)10.1088/0953-8984/14/46/317], functionalized mean spherical approximation (fMSA) [Roth and Gillespie, J. Phys.: Condens. Matter 28, 244006 (2016)10.1088/0953-8984/28/24/244006], and bulk fluid (BF) [Kierlik and Rosinberg, Phys. Rev. A 44, 5025 (1991)10.1103/PhysRevA.44.5025; Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)10.1063/1.464569] functionals. Previous work compared these DFT methods to MC simulations only for a small set of parameters. Here, a total of twelve different cations were studied, with valences of +1, +2, and +3 and ion diameters of 0.15, 0.30, 0.60, and 0.90 nm at bulk concentrations between 1 μM and 1 M. The anion always had valence -1 and diameter 0.30 nm. The structure of the double layer of these charged, hard-sphere ions was computed for surface charges ranging from 0 to -0.50C/m^{2}. All the DFTs were compared against each other for all the parameters, as well as to 378 MC simulations. Overall, RFD was the best of the three functionals, while BF was the least accurate. fMSA performed significantly better than BF, making it a reasonable choice that is less computationally expensive than RFD. For monovalent cations, all three functionals worked reasonably well, except BF was qualitatively different from MC at very low surface charges. For multivalent cations, BF underestimated charge inversion while fMSA overestimated it. All DFTs performed poorly for small multivalent ions.

Hydroelectric power plant on a paper strip

We exploit the combinatorial advantage of electrokinetics and tortuosity of a cellulose-based paper network on laboratory grade filter paper for the development of a simple, inexpensive, yet extremely robust (shows constant performance for 12 days) 'paper-and-pencil'-based device for energy harvesting applications. We successfully achieve harvesting of a maximum output power of ∼640 pW in a single channel, while the same is significantly improved (by ∼100 times) with the use of a multichannel microfluidic array (maximum of up to 20 channels). Furthermore, we also provide theoretical insights into the observed phenomenon and show that the experimentally predicted trends agree well with our theoretical calculations. Thus, we envisage that such ultra-low cost devices may turn out to be extremely useful in energizing analytical microdevices in resource limited settings, for instance, in extreme point of care diagnostic applications.

Selectivity and polarization in water channel membranes: lessons learned from polymeric membranes and CNTs

The aspects of ion exclusion and concentration polarization are highlighted as critical for achieving high selectivity in an artificial water channel.

Mimicking wettability alterations using temperature gradients for water nanodroplets

A sessile droplet or a film usually moves from hotter regions to colder regions, due to variations in interfacial tension. This, known as the so-called Marangoni effect, is true for most pure liquids like water for which the surface tension decreases with an increase in temperature. In stark contrast to this existing understanding, we bring forth the coupled effect of wettability and temperature gradients on the dynamics of the three-phase contact line. By simultaneously tracking the dynamic evolution of the three-phase contact line due to the evaporation and diffusion of molecules through molecular dynamics simulations, we explore the coterminous effects of the change of surface tension coefficients and wetting parameters with temperature on sessile droplets residing on surfaces with different wettabilities. We demonstrate, for the very first time, that the inverse Marangoni effect, which is believed to be exclusively observed in mixtures and self-rewetting fluids, is feasible in pure water at scales where inertial effects are negligible. The results of the study find application in electronic chip cooling where by the combined tuning of surface characteristics and Marangoni forces, droplets can be passively transported to warmer regions for efficient thermal management.

Multiscale Model for Electrokinetic Transport in Networks of Pores, Part II: Computational Algorithms and Applications

The first part of this two-article series presented a robust mathematical model for the fast and accurate prediction of electrokinetic phenomena in porous networks with complex topologies. In the second part of this series, we first present a numerical algorithm that can efficiently solve the model equations. We then demonstrate that the resulting framework is capable of capturing a wide range of transport phenomena in microstructures by considering a hierarchy of canonical problems with increasing complexity. The developed framework is validated against direct numerical simulations of deionization shocks in micropore-membrane junctions and concentration polarization in micro- and nanochannel systems. We demonstrate that for thin pores subject to concentration gradients our model consistently captures correct induced osmotic pressure, which is a macroscopic phenomena originally derived from thermodynamic principles but here is naturally predicted through microscopic electrostatic interactions. Moreover, we show that the developed model captures current rectification phenomena in a conical nanopore subject to an axial external electric field. Finally, we provide discussions on examples involving stationary and moving deionization shocks in micropore nanopore T-junctions as well as induced-flow loops when pores of varying sizes are connected in parallel.

Multiscale Model for Electrokinetic Transport in Networks of Pores, Part I: Model Derivation

We present an efficient and robust numerical model for the simulation of electrokinetic phenomena in porous media and microstructure networks considering a wide range of applications including energy conversion, deionization, and microfluidic-based lab-on-a-chip systems. Coupling between fluid flow and ion transport in these networks is governed by the Poisson-Nernst-Planck-Stokes equations. These equations describe a wide range of phenomena that can interact in a complex fashion when coupled in networks involving multiple pores with variable properties. Capturing these phenomena by direct simulation of the governing equations in multidimensions is prohibitively expensive. We present here a reduced-order model that treats a network of many pores via solutions to 1D equations. Assuming that each pore in the network is long and thin, we derive a 1D model describing the transport in the pore's longitudinal direction. We take into account the cross-sectional nonuniformity of potential and ion concentration fields in the form of area-averaged coefficients in different flux terms representing fluid flow, electric current, and ion fluxes. These coefficients are obtained from the solutions to the Poisson-Boltzmann equation and are tabulated against dimensionless surface charge and dimensionless thickness of the electric double layer (EDL). Although similar models have been attempted in the past, distinct advantages of the present framework include a fully conservative discretization with zero numerical leakage, fully bounded area-averaged coefficients without any singularity in the limit of infinitely thick EDLs, a flux discretization that exactly preserves equilibrium conditions, and extension to a general network of pores with multiple intersections. In part II of this two-article series, we present a numerical implementation of this model and demonstrate its applications in predicting a wide range of electrokinetic phenomena in microstructures.

Two-Dimensional Electric Double Layer Structure with Heterogeneous Surface Charge

In this work we present a systematic study of the lateral (parallel to the wall) and normal (perpendicular to the wall) nanostructure of the electric double layer at a heterogeneous interface between two regions of different surface charges, often found in nanoscale electrochemical devices. Specifically, classical density functional theory (DFT) is used to probe a cation concentration range of 10 mM to 1 M, for valences of +1, + 2, and +3, and a diameter range of 0.15-0.9 nm over widely varying surface charges (between -0.15 and +0.15 C/m²). The DFT results predict significant lateral and normal nanostructure in the form of ion concentration oscillations. These results are directly compared with those from Poisson-Boltzmann theory, showing significant deviation between the two theories, not only in the concentration profiles, but also in the sign of the electrostatic potential.

Nanofluidics in two-dimensional layered materials: inspirations from nature

This review highlights the recent progress, current challenges, and future perspectives in the design and application of 2D layered materials for nanofluidic research, with emphasis on the thought of bio-inspiration.

Non-scaling behavior of electroosmotic flow in voltage-gated nanopores

Ionic size effects and electrostatic correlations result in the non-monotonic dependence of the electrical conductivity on the pore size. For ion transport at a high gating voltage, the conductivity oscillates with the pore size due to a significant overlap of the electric double layers.

Electrokinetics in polyelectrolyte grafted nanofluidic channels modulated by the ion partitioning effect

The effects of ion partitioning on the electrokinetics in a polyelectrolyte grafted nanochannel, which is the representative of a soft nanochannel, are analyzed. Earlier studies in this regard have considered low polyelectrolyte layer (PEL) grafting density at the rigid nanochannel wall and, hence, an equal permittivity inside and outside the grafted layer. In order to overcome this shortcoming, the concept of Born energy is revisited. The coupled system of the modified Poisson-Boltzmann and Navier-Stokes equation is solved numerically, going beyond the widely employed Debye-Hückel linearization and low PEL densities. The complex interplay between the hydrodynamics and charge distribution, modulated by the ion partitioning effect, along with their consequent effects on the streaming potential and electrokinetic energy conversion efficiency (EKEC) have been systemically investigated. It has been observed that the ion partitioning effect reduces the EKEC in comparison to the case with equal permittivity up to a certain electrical double layer thickness after which it increases the EKEC. For a high concentration of mobile charges within the PEL, the net gain in the maximum EKEC due to the ion partitioning effect is about 10 fold that of the case when the ion partitioning effect is not considered. We delve into the various scaling regimes in the streaming potential and intriguingly point out the exact location of peaks in efficiency. The present study also reveals the possibility of improvement in streaming potential mediated energy conversion by the use of polyelectrolyte materials, which possess substantially lower dielectric permittivity than the bulk electrolyte.

Slippery to Sticky Transition of Hydrophobic Nanochannels

Contrary to common intuition that hydrophobic surfaces trivially cause water to slip, we discover a slippery-to-sticky transition in tunable hydrophobic nanochannels. We demonstrate this remarkable phenomenon by bringing out hitherto unveiled interplay between ion inclusions in the water and the interfacial lattice configuration over molecular scales. The consequent alterations in frictional characteristics illustrate that so-called hydrophobic nanochannels can be switchable to manifest features that are otherwise typically associated with hydrophilicity, causing water to stick. Our proposition may bear immense consequences toward fluidically functionalizing a hydrophobic interface without necessitating elaborate surface treatment techniques, bringing in far-ranging implications in diverse applications ranging from nature to energy.

A novel fluidic control method for nanofluidics by solvent-solvent interaction in a hybrid chip

The fluidic control method is a fundamental technology for the development of nanofluidics. In this report, an organic phase was driven to flow inside the nanochannel because of its dissolution into an aqueous phase. With selective modification, a stable organic/aqueous interface was generated at the junction of the micro/nanochannels in a hybrid chip. The aqueous phase was kept flowing in the microchannel, and the organic phase in the nanochannel dissolved into the aqueous phase through the interface and produced a flow inside the nanochannel. This method is simple, easy to control and requires no specific equipment. Importantly, the flow is driven by the surface tension in a controllable manner, which will not be affected by the depth of the nanochannel. This method can be a useful alternative to the present fluidic control methods in nanofluidics.

High electrokinetic energy conversion efficiency in charged nanoporous nitrocellulose/sulfonated polystyrene membranes

The synthesis, characterization, and electrokinetic energy conversion performance have been investigated experimentally in a charged polymeric membrane based on a blend of nitrocellulose and sulfonated polystyrene. The membrane is characterized by a moderate ion exchange capacity and a relatively porous structure with average pore diameter of 11 nm. With electrokinetic energy conversion, pressure can be converted directly into electric energy and vice versa. From the electrokinetic transport properties, a remarkably large intrinsic maximum efficiency of 46% is found. It is anticipated that the results are an experimental verification of theoretical models that predict high electrokinetic energy conversion efficiency in pores with high permselectivity and hydrodynamic slip flow. Furthermore, the result is a promising step for obtaining efficient low-cost electrokinetic generators and pumps for small or microscale applications.