Unraveling the Molecular Interface and Boundary Problems in an Electrical Double Layer and Electroosmotic Flow

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.

Applied Electric Field Effects on Diffusivity and Electrical Double-Layer Thickness

This study utilizes molecular dynamics (MD) simulations and continuum frameworks to explore electroosmotic flow (EOF) in nanoconfined aqueous electrolytes, offering a promising alternative to conventional micro-/nanofluidic systems. Although osmotic behavior in these environments is deeply linked to local fluid properties and interfacial dynamics between the fluid and electrolyte solutions, achieving a complete molecular-level understanding has remained challenging. The findings establish a linear relationship between electric field strength and fluid velocity, uncovering two distinct transport regimes separated by a critical threshold, with a markedly intensified flow in the second regime. It is demonstrated that rising electric field strengths significantly enhance water diffusion coefficients, supported by a detailed analysis of fluid hydration structures, the potential of mean force (PMF), and local stress tensors. Due to the applied electric field strength, the motion of ions and water accelerates, leading to the redistribution of ions and intensification of electrostatic forces. This expands the thickness of the electric double layer (EDL) and amplifies fluid diffusivity, thereby enhancing nanoscale fluid activity. These insights enhance the molecular-level understanding of EOF and define the stability of flow regimes, providing valuable guidelines for advancing nanofluidic technologies, such as drug delivery systems and lab-on-a-chip devices.

Ion Transport Through Nanopores and the Effects of Pore Wall-Ion Interaction

Ion transport inside nanopores is affected by the physicochemical interactions between the ions and the internal pore wall, offering novel opportunities useful for nanopore-based applications. Here we demonstrate that the transport of Fe(CN)63-/4- is influenced by the pore wall-ion interactions in sub-10 nm pore channels of a mesoporous zirconia film (MZF) formed on an electrode based on cyclic voltammetric (CV) studies. At pH lower than the point of zero charge of zirconia, the pore wall is positively charged, enabling it to exert attractive interaction with the negatively charged analyte ions. Moreover, experimental data indicate that the attractive interaction strongly favors the more highly charged Fe(CN)64- ions over the Fe(CN)63- ions. These effects affect the ion transport through the MZF nanopore channels, which is manifested by a number of different sets of data, including the positive shift of the reduction potential, the disparity between the CV curves of the anodic and cathodic sweeps, and the splitting of the single pair of redox peaks into two pairs when the electrical double layer thickness is increased by reducing the concentration of the supporting electrolyte. Each of these observations can be explained by the wall-ion interactions. Our findings may lead to further explorations into the transport of redox ions that interact differently with the pores and into the development of novel applications based on nanopores.

Estimating water transport in carbon nanotubes: a critical review and inclusion of scale effects

The quasi-frictionless water flow across graphitic surfaces offers vast opportunities for a wide range of applications from biomedical science to energy. However, the conflicting experimental results impede a clear understanding of the transport mechanism and desired flow control. Existing literature proposes numerous modifications and updated boundary conditions to extend classical hydrodynamic theories for nanoflows, yet a consensus or definitive conclusion remains elusive. This study presents a critical review of the proposed modifications of the pressure driven flow or the Hagen-Poiseuille (HP) equations to estimate the flow enhancement through carbon nanotubes (CNTs). For such a case, we performed (semi-)classical molecular dynamics simulations of water flow in various sizes of CNTs, applied the different forms of boundary definitions from the literature, and derived HP equation models by implementing these modifications. By aggregating seven distinct experimental datasets, we tested various flow enhancement models against our measurements. Our findings indicate that including the interfacial layering-based dynamic slip-definition in the proposed HP equations yields accurate estimations. While considering interfacial viscosity predicts the individual CNT experiments well, using the experimental viscosity yields better estimations of measurements for the water flow enhancement through membranes of CNTs. This critical review testing existing literature demonstrates how to refine continuum fluid mechanics to predict water flow enhancement at the nanoscale providing holistic multiscale modeling.

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.

The validity of the continuum modeling limit in a single pore flows to the molecular scale

The discrete characteristics of molecules become dominant in the molecular regime when the surface-to-volume ratio becomes very high. Using the well-established continuum approach is questionable due to this dominant behavior. Due to the lack of perfect modeling of such a small-scale system, the experimentalist must rely on the trial and error method. Here we analyze the water transport mechanism through a nanoporous graphene membrane at the molecular level by adopting the classical molecular dynamics (MD) simulation. The results for SPC/E water molecules were compared with those obtained for liquid argon atoms and continuum Sampson's equation predictions. We find that the effect of local variants such as density layering, interatomic forces, slip velocity, and geometric boundary conditions become exponentially dominant with decreasing nanopore size. Consequently, the continuum assumptions break down at 1.5 nm pore diameter due to neglecting the dominant local properties.

Neural network predicts ion concentration profiles under nanoconfinement

Modeling the ion concentration profile in nanochannel plays an important role in understanding the electrical double layer and electro-osmotic flow. Due to the non-negligible surface interaction and the effect of discrete solvent molecules, molecular dynamics (MD) simulation is often used as an essential tool to study the behavior of ions under nanoconfinement. Despite the accuracy of MD simulation in modeling nanoconfinement systems, it is computationally expensive. In this work, we propose neural network to predict ion concentration profiles in nanochannels with different configurations, including channel widths, ion molarity, and ion types. By modeling the ion concentration profile as a probability distribution, our neural network can serve as a much faster surrogate model for MD simulation with high accuracy. We further demonstrate the superior prediction accuracy of neural network over XGBoost. Finally, we demonstrated that neural network is flexible in predicting ion concentration profiles with different bin sizes. Overall, our deep learning model is a fast, flexible, and accurate surrogate model to predict ion concentration profiles in nanoconfinement.