Liquid-Solid Slip on Charged Walls: The Dramatic Impact of Charge Distribution

On Diffusiophoresis of a Soft Particle with a Hydrophobic Inner Core: A Semianalytical Study

The current study deals with a theoretical analysis of diffusiophoresis of a soft particle, consisting of a hydrophobic charged rigid core coated with an ion- and fluid-penetrable charged polymer layer suspending in an electrolyte medium in reaction to an applied concentration gradient. The inner core's hydrophobicity is assumed to be characterized by a surface-charge-dependent slip length parameter. Based on a weak particle charge consideration, the governing equations describing the flow phenomena are solved theoretically to deduce a semianalytic general diffusiophoretic mobility expression applied to an arbitrary Debye layer thickness. A closed-form analytic solution is also obtained, which applies to a thin Debye length and low permeable porous layer. The impact of the charge-dependent wettability of the rigid core on the particle's diffusiophoretic motion is analyzed. We found that the inner core's hydrophobicity profoundly influences the particle mobility at a thicker Debye layer with a constant surface charge density when the chemiphoresis and electrophoresis components assist each other. At a fixed ζ-potential, the effect of the hydrophobic core is substantial for a thinner Debye length. In addition, with a critical selection of core and polymer layer charges, mobility reversal is demonstrated by modulating the salt concentration and slip length parameters.

Hydrodynamic slip in nanoconfined flows: a review of experimental, computational, and theoretical progress

Nanofluidics has made significant impacts and advancements in various fields, including ultrafiltration, water desalination, biomedical applications, and energy conversion. These advancements are driven by the distinct behavior of fluids at the nanoscale, where the solid-fluid interaction characteristic lengthscale is in the same order of magnitude as the flow conduits. A key challenge in nanofluidics is understanding hydrodynamic slip, a phenomenon in which fluids flow past solid boundaries with a non-zero surface velocity, deviating from the classical no-slip boundary condition. This review consolidates experimental, computational, and theoretical efforts to elucidate the mechanisms behind hydrodynamic slip in nanoconfined flows. Key experimental methods, such as the surface force apparatus, atomic force microscopy, and micro-particle image velocimetry are evaluated alongside emerging techniques like suspended microchannel resonators, dynamic quartz crystal microbalance, and hybrid graphene/silica nanochannels, which have advanced hydrodynamic slip characterization at the nanoscale. In addition to direct slip measurement techniques, methods like sum frequency generation spectroscopy, X-ray reflectometry, and ellipsometry are discussed for their roles in probing solid-liquid interfacial interactions, shedding light on the origins of hydrodynamic slip. The review also highlights the contributions of molecular dynamics simulations, including both non-equilibrium (NEMD) and equilibrium (EMD) approaches, in modeling interfacial phenomena and slip behavior. Additionally, it explores the influence of factors such as surface wettability, shear rate, and confinement on slip, emphasizing the interaction between liquid structuring and solid-liquid interactions. Advancements made so far have uncovered more complexities in nanoconfined flows which have not been considered in the past, inviting more investigation to fully understand and control fluid behavior at the molecular level.

The influence of water polarization on slip friction at charged interfaces

The present study employs equilibrium molecular dynamics simulations to explore the potential mechanism for controlling friction by applying electrostatic fields in nanoconfined aqueous electrolytes. The slip friction coefficient demonstrates a gradual increase corresponding to the surface charge density for pure water and aqueous electrolytes, exhibiting a similar trend across both nanochannel walls. An expression is formulated to rationalize the observed slip friction behavior, describing the effect of the electric field on the slip friction coefficient. According to this formulation, the slip friction coefficient increases proportionally to the square of the uniform electric field emanating from the charged electrode. This increase in slip friction results from the energy change due to the orientation polarization of interfacial water dipoles. The minimal variations in the empirically determined proportionality constant for pure water and aqueous electrolytes indicate that water polarization primarily governs slip friction at charged interfaces. These findings offer insights into the electrical effects on nanoscale lubrication of aqueous electrolytes, highlighting the significant role of water polarization in determining slip.

Existence of a maximum flow rate in electro-osmotic systems

In this work, we investigate the effect of the hydrodynamic wall-fluid friction in electro-osmotic flows. First, we present the solution to the electro-hydrodynamic equation for the electro-osmotic velocity profile, which is derived for an ionic system composed of cations immersed in uncharged solvent particles. The system (solution and walls) is kept electrically neutral using negatively charged walls and will here be referred to as a "counterion-only" system. The theory predicts the existence of a counterion concentration that results in maximum electro-osmotic flow rate, but only if the wall-fluid friction, or equivalently the slip length, is correlated with the system electrostatic screening length. Through equilibrium molecular dynamics simulations, we precisely determine the hydrodynamic slip from the wall-fluid friction, and then, this is used as input to the theoretical predictions. Comparison between the theory and independent non-equilibrium molecular dynamics simulation data confirms the existence of the maximum. In addition, we find that standard hydrodynamic theory quantitatively agrees with the simulation results for charged nanoscale systems for sufficiently small charge densities and ion charges, if the correct slip boundaries are applied.

Nanofluidic Thermoelectric Transducer with Ultrahigh and Tunable Sensitivity

Thermosensitive transient receptor potential (thermoTRP) ion channels can transduce external thermal stimuli to neural electrical signals, allowing organisms to detect and respond to changes in environmental temperature. Reproducing such ionic machinery holds promise for advancing the design of highly efficient low-grade thermal energy harvesters and ultrasensitive thermal sensors. However, there still exist challenges for artificial nanofluidic architectures to achieve comparable thermoelectric performance. Here, we report nanofluidic thermoelectric transducers with ultrahigh and tunable sensitivities controlled by electrostatic gating in graphene nanochannels. The equivalent Seebeck coefficient can be significantly boosted and reaches 1 order of magnitude higher than the current state of the art, even beyond thermoTRP ion channels. The improvement is attributed to substantial slippage on the highly charged graphene surface, leading to enhanced electrokinetic ion transport inside the graphene channel, which is confirmed by a scaling theory for thermoelectric coupling as well as molecular dynamic simulations. The dependence of the nanofluidic thermoelectric on the concentration, channel size, and cation types is also investigated to further clarify the underlying mechanism.

Counterion Blockade in a Heterogeneously Charged Single-File Water Channel

The Possion-Nernst-Planck theories fail to describe the ionic transport in Angstrom channels, where conduction deviates from Ohm's law, which is attributed to the dehydration/self-energy barrier and dissociation of Bjerrum ion pairs in previous work. Here, we find that the cations can be strongly bound to the surface charge, which blocks the ionic transport in a single-file water channel, causing nonlinear current-voltage curves. The presence of free ions significantly increases the probability of bound ions being released, resulting in an ionic current. We find that ionic conduction gradually becomes Ohmic as the surface charge density increases, but the conduction amplitude decreases due to the increased friction from the bound ions. We rationalize the ionic transport using 1D Kramers' escape theory framework, which describes nonlinear ionic current and the impact of surface charge density on the I-V curves. Our results show that the strong Coulomb interaction between the counterion and surface charge may cause ionic blockade in Angstrom channels.

Non-monotonic variation in the streaming potential in polyelectrolyte grafted nanochannels mediated by ion partitioning effects

BACKGROUND

Polyelectrolyte grafted 'soft' nanochannels are known to enhance electrokinetic energy conversion efficiency, paving the way for a sustainable energy harvesting mechanism. However, the true potential of their efficacy remains to be tapped, as attributed to a deficit in accounting for the interplay between solution pH and ion partitioning effect arising due to permittivity contrast between the coated layer and the bulk media, leading to predictions of an erroneous ionic distribution and a wrongly estimated electrokinetic response.

RESULTS

We unravel the electrokinetic behavior of a pH-regulated zwitterionic polyelectrolyte layer grafted nanofluidic system. To this end, we derive a detailed theoretical formulation that considers the nuanced interplay between solution pH and the ion partitioning effect through a thermodynamically consistent ionic distribution. Here, for the first time, we demonstrate a non-monotonic trend in the streaming potential with an increase in the ion partitioning effect, in contrast to a monotonic increase as reported previously. Additionally, we identify a critical permittivity ratio specific to the solution pH at which maximum streaming potential can be obtained.

SIGNIFICANCE

We shed light on the counterintuitive effect borne from the increased ion partitioning effect, unveiling a hitherto hidden facet of electrokinetics. By elucidating the delicate balance between solution pH, ion partitioning effect, and polyelectrolyte charge, our findings offer a comprehensive understanding of the multifaceted interplay shaping soft-electrokinetic systems, thereby paving the way for transformative advancements in energy conversion technologies.

Donnan equilibrium in charged slit-pores from a hybrid nonequilibrium molecular dynamics/Monte Carlo method with ions and solvent exchange

Ion partitioning between different compartments (e.g., a porous material and a bulk solution reservoir), known as Donnan equilibrium, plays a fundamental role in various contexts such as energy, environment, or water treatment. The linearized Poisson-Boltzmann (PB) equation, capturing the thermal motion of the ions with mean-field electrostatic interactions, is practically useful to understand and predict ion partitioning, despite its limited applicability to conditions of low salt concentrations and surface charge densities. Here, we investigate the Donnan equilibrium of coarse-grained dilute electrolytes confined in charged slit-pores in equilibrium with a reservoir of ions and solvent. We introduce and use an extension to confined systems of a recently developed hybrid nonequilibrium molecular dynamics/grand canonical Monte Carlo simulation method ("H4D"), which enhances the efficiency of solvent and ion-pair exchange via a fourth spatial dimension. We show that the validity range of linearized PB theory to predict the Donnan equilibrium of dilute electrolytes can be extended to highly charged pores by simply considering renormalized surface charge densities. We compare with simulations of implicit solvent models of electrolytes and show that in the low salt concentrations and thin electric double layer limit considered here, an explicit solvent has a limited effect on the Donnan equilibrium and that the main limitations of the analytical predictions are not due to the breakdown of the mean-field description but rather to the charge renormalization approximation, because it only focuses on the behavior far from the surfaces.

Elucidating the transport of water and ions in the nanochannel of covalent organic frameworks by molecular dynamics

Inspired by biological channels, achieving precise separation of ion/water and ion/ion requires finely tuned pore sizes at molecular dimensions and deliberate exposure of charged groups. Covalent organic frameworks (COFs), a class of porous crystalline materials, offer well-defined nanoscale pores and diverse structures, making them excellent candidates for nanofluidic channels that facilitate ion and water transport. In this study, we perform molecular simulations to investigate the structure and kinetics of water and ions confined within the typical COFs with varied exposure of charged groups. The COFs exhibit vertically arrayed nanochannels, enabling diffusion coefficients of water molecules within COFs to remain within the same order of magnitude as in the bulk. The motion of water molecules manifests in two distinct modes, creating a mobile hydration layer around acid groups. The ion diffusion within COFs displays a notable disparity between monovalent (M+) and divalent (M2+) cations. As a result, the selectivity of M+/M2+ can exceed 100, while differentiation among M+ is less pronounced. In addition, our simulations indicate a high rejection (R > 98%) in COFs, indicating their potential as ideal materials for desalination. The chemical flexibility of COFs indicates that would hold significant promise as candidates for advanced artificial ion channels and separation membranes.

Impart of Heterogeneous Charge Polarization and Distribution on Friction at Water-Graphene Interfaces: a Density-Functional-Theory based Machine Learning Study

Accurately characterizing friction behaviors at water-solid interfaces remains a challenge because of the dynamic nature of water molecules and temporal variations in solid surface charges. By using a density-functional-theory (DFT) based machine learning (ML) technique and long-time ML-parametrized molecular dynamics simulations, we have systematically investigated water-induced charge polarization and redistribution on graphene, as well as its impact on friction at water-graphene interfaces. Heterogeneous charge polarization and distribution are observed for water-covered graphene accompanied by the formation of electric double layers (EDLs). The introduction of defects into graphene significantly enhances the heterogeneity in charge polarization and distribution. Compared to pristine graphene, defected graphene exhibits reduced friction at water-graphene interfaces due to stronger charge heterogeneity, resulting in lower surface charge density and the inverse relationship between slip length and surface charge density for EDLs. Our results highlight the pivotal roles of defects and charge heterogeneity in reducing friction at water-graphene interfaces.

Interlink between Abnormal Water Imbibition in Hydrophilic and Rapid Flow in Hydrophobic Nanochannels

Nanoscale extension and refinement of the Lucas-Washburn model is presented with a detailed analysis of recent experimental data and extensive molecular dynamics simulations to investigate rapid water flow and water imbibition within nanocapillaries. Through a comparative analysis of capillary rise in hydrophilic nanochannels, an unexpected reversal of the anticipated trend, with an abnormal peak, of imbibition length below the size of 3 nm was discovered in hydrophilic nanochannels, surprisingly sharing the same physical origin as the well-known peak observed in flow rate within hydrophobic nanochannels. The extended imbibition model is applicable across diverse spatiotemporal scales and validated against simulation results and existing experimental data for both hydrophilic and hydrophobic nanochannels.

Experimental and Theoretical Insights into Interfacial Properties of 2D Materials for Selective Water Transport Membranes: A Critical Review

Interfacial properties, such as wettability and friction, play critical roles in nanofluidics and desalination. Understanding the interfacial properties of two-dimensional (2D) materials is crucial in these applications due to the close interaction between liquids and the solid surface. The most important interfacial properties of a solid surface include the water contact angle, which quantifies the extent of interactions between the surface and water, and the water slip length, which determines how much faster water can flow on the surface beyond the predictions of continuum fluid mechanics. This Review seeks to elucidate the mechanism that governs the interfacial properties of diverse 2D materials, including transition metal dichalcogenides (e.g., MoS2), graphene, and hexagonal boron nitride (hBN). Our work consolidates existing experimental and computational insights into 2D material synthesis and modeling and explores their interfacial properties for desalination. We investigated the capabilities of density functional theory and molecular dynamics simulations in analyzing the interfacial properties of 2D materials. Specifically, we highlight how MD simulations have revolutionized our understanding of these properties, paving the way for their effective application in desalination. This Review of the synthesis and interfacial properties of 2D materials unlocks opportunities for further advancement and optimization in desalination.

Effect of the Surface Charge-Dependent Boundary Slip on the Electrophoresis of a Hydrophobic Polarizable Rigid Colloid

The electrophoresis of a hydrophobic charged rigid colloid is studied by considering the lateral movement of the adsorbed surface charge. The slip velocity condition at the hydrophobic surface is modified to take into account the impact of the frictional and electric forces created by the adsorbed laterally mobile surface charge. Though the dependency of the surface charge on the slip velocity in the context of electrophoresis has been addressed before, the effect of the laterally mobile adsorbed surface charge on the electrophoresis of hydrophobic colloids has not been studied. The dielectric colloid is considered to polarize and create an induced immobile surface charge when subjected to an imposed electric field. The impact of the mobile surface charge along with the immobile induced surface charge on electrophoresis of a hydrophobic colloid is elucidated by numerically solving the governing electrokinetic equations in their full form. We have also developed a simplified model under a weak applied field consideration, which can be further reduced to a closed-form analytic expression for the mobility under the Debye-Hückel approximation. This analytic model for mobility is in excellent agreement with the exact numerical solution for an entire range of the Debye length when the ζ-potential is in the order of the thermal potential. One of the notable features of this closed-form mobility expression is that it accounts for the mobile adsorbed surface charge on the hydrodynamic slip condition and the dielectric polarization of the particle. We find that the mobility of the surface charge decreases the electrophoretic mobility of the hydrophobic dielectric colloid. However, the mobile surface charge enhances the mobility of a conducting hydrophobic colloid.

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.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Enhanced Heat Flow between Charged Nanoparticles and an Aqueous Electrolyte

Heat transfer through the interface between a metallic nanoparticle and an electrolyte solution has great importance in a number of applications, ranging from nanoparticle-based cancer treatments to nanofluids and solar energy conversion devices. However, the impact of the surface charge and dissolved ions on heat transfer has been scarcely explored so far. In this study, we compute the interface thermal conductance between hydrophilic and hydrophobic charged gold nanoparticles immersed in an electrolyte using equilibrium molecular dynamics simulations. Compared with an uncharged nanoparticle, we report a 3-fold increase of the Kapitza conductance for a nanoparticle surface charge of +320 mC/m2. This enhancement is shown to be approximately independent of the surface wettability, charge spatial distribution, and salt concentration. This allows us to express the Kapitza conductance enhancement in terms of the surface charge density on a master curve. Finally, we interpret the increase of the Kapitza conductance as a combined result of the shift of the water density distribution toward the charged nanoparticle and an accumulation of the counterions around the nanoparticle surface which increase the Coulombic interaction between the liquid and the charged nanoparticle. These considerations help us to apprehend the role of ions in heat transfer close to electrified surfaces.

Complex coupling between surface charge and thermo-osmotic phenomena

Thermo-osmotic flows, generated at liquid-solid interfaces by thermal gradients, can be used to produce electric currents from waste heat on charged surfaces. The two key parameters controlling the thermo-osmotic current are the surface charge and the interfacial enthalpy excess due to liquid-solid interactions. While it has been shown that the contribution from water to the enthalpy excess can be crucial, how this contribution is affected by surface charge remained to be understood. Here, we start by discussing how thermo-osmotic flows and induced electric currents are related to the interfacial enthalpy excess. We then use molecular dynamics simulations to investigate the impact of surface charge on the interfacial enthalpy excess, for different distributions of the surface charge, and two different wetting conditions. We observe that surface charge has a strong impact on enthalpy excess, and that the dependence of enthalpy excess on surface charge depends largely on its spatial distribution. In contrast, wetting has a very small impact on the charge-enthalpy coupling. We rationalize the results with simple analytical models, and explore their consequences for thermo-osmotic phenomena. Overall, this work provides guidelines to search for systems providing optimal waste heat recovery performance.

Thermo-Osmosis in Charged Nanochannels: Effects of Surface Charge and Ionic Strength

Thermo-osmosis refers to fluid migration due to the temperature gradient. The mechanistic understanding of thermo-osmosis in charged nano-porous media is still incomplete, while it is important for several environmental and energy applications, such as low-grade waste heat recovery, wastewater recovery, fuel cells, and nuclear waste storage. This paper presents results from a series of molecular dynamics simulations of thermo-osmosis in charged silica nanochannels that advance the understanding of the phenomenon. Simulations with pure water and water with dissolved NaCl are considered. First, the effect of surface charge on the sign and magnitude of the thermo-osmotic coefficient is quantified. This effect was found to be mainly linked to the structural modifications of an aqueous electrical double layer (EDL) caused by the nanoconfinement and surface charges. In addition, the results illustrate that the surface charges reduce the self-diffusivity and thermo-osmosis of interfacial liquid. The thermo-osmosis was found to change direction when the surface charge density exceeds -0.03C · m^-2. It was found that the thermo-osmotic flow and self-diffusivity increase with the concentration of NaCl. The fluxes of solvent and solute are decoupled by considering the Ludwig-Soret effect of NaCl ions to identify the main mechanisms controlling the behavior. In addition to the advance in microscopic quantification and mechanistic understanding of thermo-osmosis, the work provides approaches to investigate a broader category of coupled heat and mass transfer problems in nanoscale space.

Surface-charge governed ionic blockade in angstrom-scale latent-track channels

When channels are scaled down to the size of hydrated ions, Coulomb interactions are enhanced in confinement, resulting in new phenomena. Herein, we found blockade of ionic transport in latent-track angstrom-scale channels governed by surface charge, fundamentally different from Coulomb blockade or Wien effects. The channels are non-conductive at low voltage, blocked by cations bound at the surface in confinement; however, they change to conductive with increasing voltage due to the release of bound ions. The increase in surface charge density gradually causes the conduction to be ohmic. Using Kramers' escape framework, we rationalized an analytical equation to describe the experimental results, uncovering new fundamental insights into ion transport in the smallest channels.

Hierarchical triphase diffusion photoelectrodes for photoelectrochemical gas/liquid flow conversion

Photoelectrochemical device is a versatile platform for achieving various chemical transformations with solar energy. However, a grand challenge, originating from mass and electron transfer of triphase-reagents/products in gas phase, water/electrolyte/products in liquid phase and catalyst/photoelectrode in solid phase, largely limits its practical application. Here, we report the simulation-guided development of hierarchical triphase diffusion photoelectrodes, to improve mass transfer and ensure electron transfer for photoelectrochemical gas/liquid flow conversion. Semiconductor nanocrystals are controllably integrated within electrospun nanofiber-derived mat, overcoming inherent brittleness of semiconductors. The mechanically strong skeleton of free-standing mat, together with satisfactory photon absorption, electrical conductivity and hierarchical pores, enables the design of triphase diffusion photoelectrodes. Such a design allows photoelectrochemical gas/liquid conversion to be performed continuously in a flow cell. As a proof of concept, 16.6- and 4.0-fold enhancements are achieved for the production rate and product selectivity of methane conversion, respectively, with remarkable durability.

Temperature-dependent slip length for water and electrolyte solution

HYPOTHESIS

The temperature dependence of boundary slip at liquid-solid interface is critical both for the fundamental theory and applications of fluid mechanics on micro and nanoscale, such as sustainable cooling of electronic devices. However, there is a controversy on the temperature dependence of boundary slip which lacks experimental evidence, we aim to resolve it by hypothesizing that the temperature dependent slip length depends on the variation in the interfacial energy barrier.

EXPERIMENTS

Here, we measured l_s - T relation of water and NaCl solution on self-assembled FDTS (Perfluorodecyltrichlorosilane) surface using colloidal probe AFM. The transition of l_s - T monotonicity is found. For water and 0.1 M NaCl solution, l_s is negatively correlated with T, while for 1 M NaCl solution, l_s is positively correlated with T.

FINDINGS

Together with molecular dynamics simulations, such observation is quantitatively explained with an analytical model based on rate theory, where the l_s - T monotonicity depends on the difference between liquid-solid interfacial energy barrier and liquid internal energy barrier. Our results provide not only solid experimental evidence for the boundary slip being a rate process, but also a basis for the thermal-hydrodynamic design of microfluidic and nanofluidic devices.

Liquid-Liquid Flow at Nanoscale: Slip and Hydrodynamic Boundary Conditions

Nonequilibrium molecular dynamics (NEMD) simulations have been performed to describe the flow of a fluid nanolayer confined by another fluid. The results show that the behavior of liquids can still be described by the Navier-Stokes equation at the nanoscale, i.e., when only few molecular layers are involved. NEMD furthermore gives additional knowledge on flow. Indeed, while a very small slip is evidenced for a solid-liquid interface as, e.g., in lubrication, the slip lengths are significantly larger at the liquid-liquid interface, as encountered, e.g., in droplet coalescence. The slip lengths of the two fluids are linked. The increase in hydrodynamic slip for liquid-liquid interfaces is attributed to the enhancement of fluid diffusion, which reduces friction.

Accurate estimation of dynamical quantities for nonequilibrium nanoscale systems

Fluctuations of dynamical quantities are fundamental and inevitable. For the booming research in nanotechnology, huge relative fluctuation comes with the reduction of system size, leading to large uncertainty for the estimates of dynamical quantities. Thus, increasing statistical efficiency, i.e., reducing the number of samples required to achieve a given accuracy, is of great significance for accurate estimation. Here we propose a theory as a fundamental solution for such problem by constructing auxiliary path for each real path. The states on auxiliary paths constitute canonical ensemble and share the same macroscopic properties (NVT) with the initial states of the real path. By implementing the theory in molecular dynamics simulations, we obtain a nanoscale Couette flow field with an accuracy of 0.2μm/s with relative standard error <0.1. The required number of samples is reduced by 12 orders compared to conventional method. The predicted thermolubric behavior of water sliding on a self-assembled surface is directly validated by experiment under the same velocity. This theory only assumes the system is initially in thermal equilibrium, then driven from that equilibrium by an external perturbation. It could serve as a general approach for extracting the accurate estimate of dynamical quantities from large fluctuations to provide insights on atomic level under experimental conditions, and benefit the studies on mass transport through (biological) nanochannels and fluid film lubrication of nanometer thickness.

Electrical Conductance of Charged Nanopores

A nanopore's response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.

Translucency and negative temperature-dependence for the slip length of water on graphene

Carbonous materials, such as graphene and carbon nanotubes, have attracted tremendous attention in the fields of nanofluidics due to the slip at the interface between solid and liquid. The dependence of slip length for water on the types of supporting substrates and thickness of the carbonous layer, which is critical for applications such as sustainable cooling of electronic devices, remains unknown. In this paper, using colloidal probe atomic force microscopy, we measured the slip length l_s of water on graphene supported by hydrophilic and hydrophobic substrates, i.e., SiO₂ and octadecyltrimethoxysilane (OTS). The l_s on single-layer graphene supported by SiO₂ is found to be 1.6 ± 1.9 nm, and that of OTS is 8.5 ± 0.9 nm. When the thickness of few-layer graphene increases to 3-4 layers, both l_s values gradually converge to the value of graphite (4.3 ± 3.5 nm). Such a thickness dependence is termed slip length translucency. Further, l_s is found to decrease by about 70% when temperature increases from 300 K to 350 K for 2-layer graphene supported by SiO₂. These observations are explained by analysis based on the Green-Kubo relation and McLachlan theory. Our results provide the first set of reference values for the slip length of water on supported few-layer graphene. They can not only serve as a direct experimental reference for solid-liquid interaction, but also provide a guideline for the design of nanofluidics-based devices, for example thermo-mechanical nanofluidic devices.

Electrophoresis of Dielectric and Hydrophobic Spherical Fluid Droplets Possessing Uniform Surface Charge Density

The present article deals with the theoretical study on electrophoresis of hydrophobic and dielectric spherical fluid droplets possessing uniform surface charge density. Unlike the ideally polarizable liquid droplet bearing constant surface ζ-potential, the tangential component of the Maxwell stress is nonzero for dielectric fluid droplets with uniform surface charge density. We consider the continuity of the tangential component of total stress (sum of the hydrodynamic and Maxwell stresses) and jump in dielectric displacement along the droplet-to-electrolyte interface. The typical situation is considered here for which the interfacial tension of the fluid droplet is sufficiently high so that the droplet retains its spherical shape during its motion. The present theory can be applied to nanoemulsions, hydrophobic oil droplets, gas bubbles, droplets of immiscible liquid suspended in aqueous medium, etc. Based on weak field and low charge assumptions and neglecting the Marangoni effect, the resultant electrokinetic equations are solved using linear perturbation analysis to derive the closed form expression for electrophoretic mobility applicable for the entire range of Debye-Hückel parameter. We further deduced an alternate approximate expression for electrophoretic mobility without involving exponential integrals. Besides, we have derived analytical results for mobility pertaining to various limiting cases. The results are further illustrated to show the impact of pertinent parameters on the overall electrophoretic mobility.

Surface Roughness Explains the Observed Water Contact Angle and Slip Length on 2D Hexagonal Boron Nitride

Hexagonal boron nitride (hBN) is a two-dimensional (2D) material that is currently being explored in a number of applications, such as atomically thin coatings, water desalination, and biological sensors. In many of these applications, the hBN surface comes into intimate contact with water. In this work, we investigate the wetting and frictional behavior of realistic 2D hBN surfaces with atomic-scale defects and roughness. We combine density functional theory calculations of the charge distribution inside hBN with free energy calculations using molecular dynamics simulations of the hBN-water interface. We find that the presence of surface roughness, but not that of vacancy defects, leads to remarkable agreement with the experimentally observed water contact angle of 66° on freshly synthesized, uncontaminated hBN. Not only that, the inclusion of surface roughness predicts with exceptional accuracy the experimental water slip length of ∼1 nm on hBN. Our results underscore the importance of considering realistic models of 2D materials with surface roughness while modeling nanomaterial-water interfaces in molecular simulations.

Enhanced nanofluidic transport in activated carbon nanoconduits

Carbon has emerged as a unique material in nanofluidics, with reports of fast water transport, molecular ion separation and efficient osmotic energy conversion. Many of these phenomena still await proper rationalization due to the lack of fundamental understanding of nanoscale ionic transport, which can only be achieved in controlled environments. Here we develop the fabrication of 'activated' two-dimensional carbon nanochannels. Compared with nanoconduits with 'pristine' graphite walls, this enables the investigation of nanoscale ionic transport in great detail. We show that activated carbon nanochannels outperform pristine channels by orders of magnitude in terms of surface electrification, ionic conductance, streaming current and (epi-)osmotic currents. A detailed theoretical framework enables us to attribute the enhanced ionic transport across activated carbon nanochannels to an optimal combination of high surface charge and low friction. Furthermore, this demonstrates the unique potential of activated carbon for energy harvesting from salinity gradients with single-pore power density across activated carbon nanochannels, reaching hundreds of kilowatts per square metre, surpassing alternative nanomaterials.

Liquid-Solid Interfaces under Dynamic Shear Flow: Recent Insights into the Interfacial Slip

The development of micro/nanofluidic techniques has recently revived interest in dynamic shear flow at liquid-solid interfaces. When the nature of the liquid-solid boundaries was revisited, the slip of the fluids relative to the solid wall was predicted theoretically and confirmed experimentally. This indicates that the molecular-level structures of the liquid-solid interfaces will be influenced by the liquid flow over certain temporal and spatial criteria. However, the fluid flow at the boundary layer still cannot be precisely predicted and effectively controlled, somehow limiting its practical applications. Here, we summarize the recent advances for the microscopic structures at the liquid-solid interfaces upon shear flow. Special attention was given to a second-order nonlinear optical technique, sum frequency generation vibrational spectroscopy, which is a powerful tool for exploring the molecular-level structures and structural dynamics at the liquid-solid interfaces and offering new insights into the molecular mechanisms of the fluid slip at the interfaces. Moreover, we discuss the possible approaches for controlling the interfacial slip at the molecular level and highlight the current challenges and opportunities. Although the theoretical framework of the slip at the liquid-solid interfaces is still incomplete, we hope that this Perspective will complement and enhance our understanding of various interfacial properties and phenomena with respect to practical non-equilibrium dynamic processes happening at the interfaces.

Fluctuation-induced quantum friction in nanoscale water flows

The flow of water in carbon nanochannels has defied understanding thus far¹, with accumulating experimental evidence for ultra-low friction, exceptionally high water flow rates and curvature-dependent hydrodynamic slippage^2-5. In particular, the mechanism of water-carbon friction remains unknown⁶, with neither current theories⁷ nor classical^8,9 or ab initio molecular dynamics simulations¹⁰ providing satisfactory rationalization for its singular behaviour. Here we develop a quantum theory of the solid-liquid interface, which reveals a new contribution to friction, due to the coupling of charge fluctuations in the liquid to electronic excitations in the solid. We expect that this quantum friction, which is absent in Born-Oppenheimer molecular dynamics, is the dominant friction mechanism for water on carbon-based materials. As a key result, we demonstrate a marked difference in quantum friction between the water-graphene and water-graphite interface, due to the coupling of water Debye collective modes with a thermally excited plasmon specific to graphite. This suggests an explanation for the radius-dependent slippage of water in carbon nanotubes⁴, in terms of the electronic excitations of the nanotubes. Our findings open the way for quantum engineering of hydrodynamic flows through the electronic properties of the confining wall.

Fast and versatile thermo-osmotic flows with a pinch of salt

Thermo-osmotic flows - flows generated in micro and nanofluidic systems by thermal gradients - could provide an alternative approach to harvest waste heat. However, such use would require massive thermo-osmotic flows, which are up to now only predicted for special and expensive materials. Thus, there is an urgent need to design affordable nanofluidic systems displaying large thermo-osmotic coefficients. In this paper, we propose a general model for thermo-osmosis of aqueous electrolytes in charged nanofluidic channels, taking into account hydrodynamic slip, together with the different solvent and solute contributions to the thermo-osmotic response. We apply this model to a wide range of systems by studying the effects of wetting, salt type and concentration, and surface charge. We show that intense thermo-osmotic flows can be generated using slipping charged surfaces. We also predict for intermediate wettings a transition from a thermophobic to a thermophilic behavior depending on the surface charge and salt concentration. Overall, this theoretical framework opens an avenue for controlling and manipulating thermally induced flows with common charged surfaces and a pinch of salt.

Hydrodynamic slip of alkali chloride solutions in uncharged graphene nanochannels

Using non-equilibrium molecular dynamics simulations, we demonstrate the effect of concentration and alkali cation types (K⁺, Na⁺, and Li⁺) on the hydrodynamic slip of aqueous alkali chloride solutions in an uncharged graphene nanochannel. We modeled the graphene-electrolyte interactions using the potential of Williams et al. [J. Phys. Chem. Lett. 8, 703 (2017)], which uses optimized graphene-ion Lennard-Jones interaction parameters to effectively account for surface and solvent polarizability effects on the adsorption of ions in an aqueous solution to a graphene surface. In our study, the hydrodynamic slip exhibits a decreasing trend for alkali chloride solutions with increasing salt concentration. The NaCl solution shows the highest reduction in the slip length followed by KCl and LiCl solutions, and the reduction in the slip length is very much dependent on the salt type. We also compared the slip length with that calculated using a standard unoptimized interatomic potential obtained from the Lorentz-Berthelot mixing rule for the ion-carbon interactions, which is not adjusted to account for the surface and solvent polarizability at the graphene surface. In contrast to the optimized model, the slip length of alkali chloride solutions in the unoptimized model shows only a nominal change with salt concentration and is also independent of the nature of salts. Our study shows that adoption of the computationally inexpensive optimized potential of Williams et al. for the graphene-ion interactions has a significant influence on the calculation of slip lengths for electrolyte solutions in graphene-based nanofluidic devices.

Microscopic origin of the effect of substrate metallicity on interfacial free energies

We investigate the effect of the metallic character of solid substrates on solid-liquid interfacial thermodynamics using molecular simulations. Building on the recent development of a semiclassical Thomas-Fermi model to tune the metallicity in classical molecular dynamics simulations, we introduce a thermodynamic integration framework to compute the evolution of the interfacial free energy as a function of the Thomas-Fermi screening length. We validate this approach against analytical results for empty capacitors and by comparing the predictions in the presence of an electrolyte with values determined from the contact angle of droplets on the surface. The general expression derived in this work highlights the role of the charge distribution within the metal. We further propose a simple model to interpret the evolution of the interfacial free energy with voltage and Thomas-Fermi length, which allows us to identify the charge correlations within the metal as the microscopic origin of the evolution of the interfacial free energy with the metallic character of the substrate. This methodology opens the door to the molecular-scale study of the effect of the metallic character of the substrate on confinement-induced transitions in ionic systems, as reported in recent atomic force microscopy and surface force apparatus experiments.

Passive solute separation in AC electroosmosis including surface charge-coupled hydrodynamic slip effects

Separation of electrically neutral, mutually noninteracting passive solutes via AC electroosmotic slit channel flows is investigated for general asymmetric wall surface zeta potentials and apparent hydrodynamic slip lengths. We consider the nontrivial coupling between the surface potentials (or charge densities) and the apparent slip lengths, and focus our attention on the occurrence of a so called "crossover phenomenon" for separating out the slow diffusers when both slow and fast diffusers are present. Results show that regardless of the potential-slip coupling, wider bandwidths become available for crossover phenomenon to occur when the electroosmotic velocity gradient (magnitude) is greater. Contrarily, plug-like velocity profiles inhibit crossover phenomenon, and the potential-slip parametric combinations leading to such profiles can be easily identified by the conditions for minimal transport enhancement reported in recent literature. When separating out the slow diffuser or crossover phenomenon is desired, we recommend incorporating significant asymmetry in the surface potential and apparent slip boundary conditions such that the operating frequency and flow oscillation amplitude may be lowered to more practical values. Our results also agree with and strengthen the physical picture for explaining crossover phenomenon in macroscopic pressure-driven oscillatory flows.

Modulating Water Slip Using Atomic-Scale Defects: Friction on Realistic Hexagonal Boron Nitride Surfaces

Atomic-scale defects are ubiquitous in nanomaterials, yet their role in modulating fluid flow is inadequately understood. Hexagonal boron nitride (hBN) is an important two-dimensional material with applications in desalination and osmotic power. Although pristine hBN offers higher friction to the flow of water than graphene, we show here that certain defects can enhance water slippage on hBN. Using classical molecular dynamics simulations assisted by quantum-mechanical density functional theory, we compute the friction coefficient of water on hBN containing various vacancies (B, N, BN, B₂N, and B₃N) and the Stone-Wales defect. By investigating two defect concentrations, we obtain friction coefficients ranging from 0.4 to 2.6 times that of pristine hBN, leading to a maximum water slip length of 18.1 nm on hBN with a N vacancy or a Stone-Wales defect. Our work informs the use of defects to tune water flow and reveals defective hBN as an alternative high-slip surface to graphene.

Numerical Analysis of the Heterogeneity Effect on Electroosmotic Micromixers Based on the Standard Deviation of Concentration and Mixing Entropy Index

One approach to achieve a homogeneous mixture in microfluidic systems in the quickest time and shortest possible length is to employ electroosmotic flow characteristics with heterogeneous surface properties. Mixing using electroosmotic flow inside microchannels with homogeneous walls is done primarily under the influence of molecular diffusion, which is not strong enough to mix the fluids thoroughly. However, surface chemistry technology can help create desired patterns on microchannel walls to generate significant rotational currents and improve mixing efficiency remarkably. This study analyzes the function of a heterogeneous zeta-potential patch located on a microchannel wall in creating mixing inside a microchannel affected by electroosmotic flow and determines the optimal length to achieve the desired mixing rate. The approximate Helmholtz–Smoluchowski model is suggested to reduce computational costs and simplify the solving process. The results show that the heterogeneity length and location of the zeta-potential patch affect the final mixing proficiency. It was also observed that the slip coefficient on the wall has a more significant effect than the Reynolds number change on improving the mixing efficiency of electroosmotic micromixers, benefiting the heterogeneous distribution of zeta-potential. In addition, using a channel with a heterogeneous zeta-potential patch covered by a slip surface did not lead to an adequate mixing in low Reynolds numbers. Therefore, a homogeneous channel without any heterogeneity would be a priority in such a range of Reynolds numbers. However, increasing the Reynolds number and the presence of a slip coefficient on the heterogeneous channel wall enhances the mixing efficiency relative to the homogeneous one. It should be noted, though, that increasing the slip coefficient will make the mixing efficiency decrease sharply in any situation, especially in high Reynolds numbers.

Electrification of water interface

The surface charge of a water interface determines many fundamental processes in physical chemistry and interface science, and it has been intensively studied for over a hundred years. We summarize experimental methods to characterize the surface charge densities developed so far: electrokinetics, double-layer force measurements, potentiometric titration, surface-sensitive nonlinear spectroscopy, and surface-sensitive mass spectrometry. Then, we elucidate physical ion adsorption and chemical electrification as examples of electrification mechanisms. In the end, novel effects on surface electrification are discussed in detail. We believe that this clear overview of state of the art in a charged water interface will surely help the fundamental progress of physics and chemistry at interfaces in the future.

Liquid flow reversibly creates a macroscopic surface charge gradient

The charging and dissolution of mineral surfaces in contact with flowing liquids are ubiquitous in nature, as most minerals in water spontaneously acquire charge and dissolve. Mineral dissolution has been studied extensively under equilibrium conditions, even though non-equilibrium phenomena are pervasive and substantially affect the mineral-water interface. Here we demonstrate using interface-specific spectroscopy that liquid flow along a calcium fluoride surface creates a reversible spatial charge gradient, with decreasing surface charge downstream of the flow. The surface charge gradient can be quantitatively accounted for by a reaction-diffusion-advection model, which reveals that the charge gradient results from a delicate interplay between diffusion, advection, dissolution, and desorption/adsorption. The underlying mechanism is expected to be valid for a wide variety of systems, including groundwater flows in nature and microfluidic systems.

Reactions at the interface between mineral surfaces and flowing liquids are ubiquitous in nature. Here the authors explore, using surface-specific sum frequency generation spectroscopy and numeric calculations, how the liquid flow affects the charging and dissolution rates leading to flow-dependent charge gradients along the surface.

Size-Sensitive Thermoelectric Properties of Electrolyte-Based Nanofluidic Systems

In this work, we investigate the thermoelectric properties of aqueous KCl solutions confined in graphene nanochannels through molecular dynamics simulations. The channel height H ranges from 0.7 to 7.8 nm. It is found that the Seebeck coefficient, S_e, and the figure of merit, ZT, of the KCl solution are highly sensitive to H when H is small. For the nanochannel of H = 1.0 nm, S_e = 30.6 mV/K and ZT = 4.6 at room temperature, which are superior to most of the solid-state thermoelectric materials. The remarkable thermoelectric properties in small channels are attributed to the flow slip at the channel walls and the mean excess enthalpy density of the solution, which is mainly from the potential energy contribution. The molecular insight promotes the applications of nanofluidic devices for thermal energy harvesting.

Interfacial CO2-mediated nanoscale oil transport: from impediment to enhancement

CO2-based enhanced oil recovery is widely practiced. The current understanding of its mechanisms largely focuses on bulk phenomena such as achieving miscibility or reducing oil density and viscosity. Using molecular dynamics simulations, we show that CO2 adsorption on calcite surfaces impedes decane transport at moderate adsorption density but enhances decane transport when CO2 adsorption approaches surface saturation. These effects change the decane permeability through 8 nm-wide pores by up to 30% and become negligible only in pores wider than several tens of nanometers. The strongly nonlinear, non-monotonic dependence of decane permeability on CO2 adsorption is traced to CO2's modulation of interfacial structure of long-chain hydrocarbons, and thus the slippage between interfacial hydrocarbon layers and between interfacial CO2 and hydrocarbon layers. These results highlight a new and critical role of CO2-induced interfacial effects in influencing oil recovery from unconventional reservoirs, whose porosity is dominated by nanopores.

Fast increase of nanofluidic slip in supercooled water: the key role of dynamics

Nanofluidics is an emerging field offering innovative solutions for energy harvesting and desalination. The efficiency of these applications depends strongly on liquid-solid slip, arising from a favorable ratio between viscosity and interfacial friction. Using molecular dynamics simulations, we show that wall slip increases strongly when water is cooled below its melting point. For water on graphene, the slip length is multiplied by up to a factor of five and reaches 230 nm at the lowest simulated temperature, T ∼ 225 K; experiments in nanopores can reach much lower temperatures and could reveal even more drastic changes. The predicted fast increase in water slip can also be detected at supercoolings reached experimentally in bulk water, as well as in droplets flowing on anti-icing surfaces. We explain the anomalous slip behavior in the supercooled regime by a decoupling between viscosity and bulk density relaxation dynamics, and we rationalize the wall-type dependence of the enhancement in terms of interfacial density relaxation dynamics. While providing fundamental insights on the molecular mechanisms of hydrodynamic transport in both interfacial and bulk water in the supercooled regime, this study is relevant to the design of anti-icing surfaces, could help explain the subtle phase and dynamical behaviors of supercooled confined water, and paves the way to explore new behaviors in supercooled nanofluidic systems.

Flow Electrification of a Corona-Charged Polyethylene Terephthalate Film

Corona charging of a free-standing polymer film can produce a quasi-permanent potential difference across the film thickness, while the absolute amplitude of the surface voltage may be highly sensitive to the free charges. To precisely control the voltage distribution, we investigated the flow electrification technology by exposing corona-charged polyethylene terephthalate films to sodium salt solutions. The surface voltage and the free-charge density were adjusted by the salt concentration, the anion size, and the flow rate. The dipolar component of electric potential remained unchanged. This result has significant scientific interest and technological importance to surface treatment, filtration, energy harvesting, among others.

Load Impedance of Immersed Layers on the Quartz Crystal Microbalance: A Comparison with Colloidal Suspensions of Spheres

The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic, and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here, we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible submicron-sized suspended spheres and with experimental results for adsorbed micron-sized colloids, which yield a "negative acoustic mass". The parallel behavior unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should, in most cases, include hydrodynamics.