Electro-osmotic flow in hydrophobic nanochannels.

Electro-osmotic flow is the motion of fluid driven by an applied electric field, for which an electric double layer near a charged surface is deemed essential. Here, we find that electro-osmotic flow can occur in electrically neutral nanochannels in the absence of definable electric double layers through extensive molecular dynamics simulations. An applied electric field is shown to cause an intrinsic channel selectivity between cations and anions, by reorienting the hydration shells of these confined ions. The ion selectivity then results in a net charge density in the channel that induces the unconventional electro-osmotic flow. The flow direction is amenable to manipulation by the field strength and the channel size, which will inform ongoing efforts to develop highly integrated nanofluidic systems capable of complex flow control.

This paper presents a theoretical model for the electro-osmotic flow (EOF) of semi-dilute polyelectrolyte (PE) solutions in nanochannels. We use mean-field theories to describe the properties of electric double layer and viscosity of PE solutions that are prerequisites for constructing the EOF model. The EOF model is validated via a good match to the existing experimental results. Based on the validated EOF model, we conduct a comprehensive analysis of EOF of semi-dilute PE solutions in nanochannels. First, we observe considerable EOF of PE solutions in the uncharged nanochannels, which is in stark contrast to EOF of simple electrolyte solutions. The analyses show that the EOF of PE solutions in uncharged nanochannels is triggered by the external electric field acting on the near-wall non-electroneutral regions resulting from the confinement-induced inhomogeneous distribution of PE monomers. Although the solutions are electroneutral as a whole, the presence of local non-electroneutral regions and the mismatch between non-electroneutral regions and high-viscosity regions lead to the net EOF in uncharged nanochannels. Furthermore, we reveal that the EOF mobility $\mu _{{eof}}$ in uncharged nanochannels exhibits a scaling law $\mu _{{eof}} \propto a^{-0.44}$ (wherein $a$ denotes monomer Kuhn length) and is inversely proportional to the PE chain length, while it decreases nonlinearly with the charge fraction of the PE chains. Moreover, the EOF mobility reaches its maximum at specific bulk monomer concentration, and increases with the nanochannel height before converging to that under no confinement. Second, we analyse the EOF of PE solutions in nanochannels with various wall effects, such as surface charge density, slip length and adsorption length. When the surface charge is absent, the adsorption length significantly influences the direction and magnitude of the EOF, whereas the slip length has no effect. When the wall becomes increasingly charged, the influence of adsorption length on EOF gradually diminishes, while the importance of the slip length progressively intensifies and the EOF is highly influenced by the co-action of various wall effects in a complicated manner. When the surface wall is oppositely charged to polymer monomers, the EOF mobility varies nonlinearly with the surface charge density, while a zero net flow of EOF followed by a direction reversal is discovered when the wall is likely charged to polymer monomers.

Effect of boundary slip and surface charge on the pressure-driven flow

Velocity slip in electroosmotic flows (EOF) is investigated using an analytical solution of Poisson–Boltzmann and Stokes (PB-S) equations with slip correction, and the results are compared with the predictions from molecular dynamics (MD) simulations. Particularly, EOFs of NaCl solution in silicon nanochannels are simulated, and channel dimensions are picked to exhibit plug flow behavior in the bulk region. Electrochemical conditions are specified within the validity region of PB theory to avoid charge inversion and flow reversal effects. The analytical model shows normalization of the slip length (an interfacial property) with the Debye length determined by the ionic concentration, implying that the slip enhancement in EOFs is independent of the channel height. MD results are compared with the analytical solution using the apparent viscosity and slip lengths determined by force-driven flow simulations in charged silicon nanochannels. Onset of slip velocity within the electrical double layer and its effects on EOF are investigated as a function of the liquid–wall interaction strength. Good agreements between the analytical solutions and MD results validate PB-S equations in nanochannels as small as 3.5 nm. Results validate that slip enhancement in EOFs is independent of the channel height, which constitutes a theoretical basis for the slip-length measurements on hydrophobic dielectric surfaces using EOFs.

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.

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.

Thermal transport due to liquid jet impingement on superhydrophobic surfaces with isotropic slip

In this paper, a review of different techniques used to measure the slip length on superhydrophobic surfaces with large slip length is presented. First, we present the theoretical models used to calculate the effective slip length on superhydrophobic surfaces in different configurations of liquid flow. Then, we present the different techniques used to measure the slip past these superhydrophobic surfaces: rheometry, particle image velocimetry, pressure drop, surface force apparatus and atomic force microscopy.

Molecular dynamics simulations were used to explain the origin and properties of electrical double-layer capacitance in short graphene nanochannels with width below 2 nm. The results explain the previously reported experimental result on the non-monotonic dependence of the capacitance with the channel width. The mechanism for the anomalous increase of the capacitance in sub-1-nm in pore diameter is attributed here to the width-dependent radial location of counterions in the nanochannels, and the restricted number of co-ions. Decrease of the channel width lowers the number of co-ions and positions the counterions closer to the channel walls. For nanochannels with width ranging from 1 to 2 nm, co-ions are allowed to enter the nanochannel, and both types of ions assume alternating layered distributions leading to the decrease of the capacitance. Voltage is another control parameter which allows understanding capacitance in graphene nanochannels. As the voltage increases, due to limited space near the charged surface, more counterions need to be located in the center of the nanochannel resulting in further capacitance decrease.

Non-equilibrium molecular dynamics simulations have been carried out to investigate the effect of surface roughness and interface wettability on the nanorheology and slip boundary condition of simple fluids in a nanochannel of several atomic diameters width. The solid surfaces decorated with periodic nanostrips are considered as the rough surface in this study. The simulation results showed that the interface wettability and the surface roughness are important in determining the nanorheology of the nanochannel and fluid slip at solid–fluid interface. It is observed that the presence of surface roughness always suppresses the fluid slip for hydrophilic and hydrophobic surface nanochannels. For fluids over smooth and hydrophobic surfaces, the snapshots of fluid molecules show that an air gap or nanobubble exists at the fluid–solid interface, resulting in the apparent slip velocity. For a given surface with fixed interface wettability, the fluid velocities increase by increasing the driving force, while the driving force has no significant influence on the density structure of fluid molecules. The fluid slip and the flow rate are measured for hydrophilic and hydrophobic nanochannels. The flow rates in rough surface nanochannels are smaller than those of smooth surface walls due to the increase of drag resistance at the solid–fluid interface. The dependence between fluid slip and flow rate showed that the slip length increases approximately linearly with the flow rate for both the hydrophobic and hydrophilic surface nanochannels.

Chapter 4 - Single-Phase Electrokinetic Flow in Microchannels

The present study is an analysis of pressure-driven electrokinetic flows in hydrophobic microchannels with emphasis on the slip effects under coupling of interfacial electric and fluid slippage phenomena. Commonly used linear model with slip-independent zeta potential and the nonlinear model at limiting (high-K) condition with slip-dependent zeta potential are solved analytically. Then, numerical solutions of the electrokinetic flow model with zeta potential varying with slip length are analyzed. Different from the general notion of “the more hydrophobic the channel wall, the higher the flowrate,” the results with slip-independent and slip-dependent zeta potentials both disclose that flowrate becomes insensitive to the wall hydrophobicity or fluid slippage at sufficiently large slip lengths. Boundary slip not only assists fluid motion but also enhances counter-ions transport in EDL and, thus, results in strong streaming potential as well as electrokinetic retardation. With slip-dependent zeta potential considered, flowrate varies non-monotonically with increasing slip length due to competition of the favorable and adverse effects with more complicated interactions. The influence of the slip on the electrokinetic flow is eventually nullified at large slip lengths for balance of the counter effects, and the flowrate becomes insensitive to further hydrophobicity of the microchannel. The occurrence of maximum, minimum, and insensitivity on the flowrate-slip curves can be premature at a higher zeta potential and/or larger electrokinetic separation distance.

In this investigation, two-dimensional flow past square cylinders with slip boundary have been studied with the lattice Boltzmann method. Three modes, which are a single cylinder, an oblique cylinder, and side-by-side cylinders, are investigated with Reynolds numbers from 25 to 200 while relative slip length ranges from 0 to 0.1. It can be concluded that both the flow state and the slip boundary have a great effect on the drag reduction rate. For a single square cylinder, drag forces decrease with larger slip length while the Strouhal number is almost constant. For an oblique cylinder, the slip length also has effects on the stability of the flow except the drag and lift forces. Vortex separation delays with a slip wall of oblique cylinder. For side-by-side cylinders, the jet between two cylinders is not conducive to the drag reduction rate of the slip boundary. Moreover, the application of slip boundary may also lead to additional drag force as vortex separation intensifies, which is extremely different from simple channel flows. Studies have shown that the slip boundary does not always reduce the drag in some complex flow fields. It can be concluded that the drag reduction effect of slip boundaries is more effective in uniform flow.

Featured ApplicationDrag reduction in many applications of micro-/nano-fluidic channel.In the development of micro/nano fluid control systems, fluid resistance has always been one of the key factors restricting its development. According to previous studies, it is found that the boundary slip effect of the solid-liquid interface can effectively reduce the resistance of the microfluid and improve the transport efficiency of the microfluid. The boundary slip length is mainly affected by surface wettability, roughness, and surface charge density. Among them, the influence mechanism of surface charge density on the boundary slip is the most complicated, and there is a lack of relevant research, and further investigation is needed. In this paper, we present research on quantification of effective slip length and surface charge density, where the roughness effect is considered. The electrostatic and hydrodynamic force data obtained from atomic force microscopy (AFM) measurements were fitted and processed for comparative analysis. We obtained the variation of surface charge density and effective slip length when different oleophobic surface samples were immersed in ethylene glycol with different pH values. The effect of pH on the surface charge density and effective slip length was investigated by their variations. The mechanism of the effect of pH on the surface charge density was discussed. The experimental results show that in the ethylene glycol solution, no matter whether the pH value of the solution increases or decreases, the charge density of the surface with the same properties decreases, and the effective boundary slip length also shows a downward trend. In deionized water, the surface charge density and effective boundary slip length decreases with the decrease of PH value.

Track-etched polycarbonate (PC) membranes with nanochannels are versatile materials for electrochemical, energy-harvesting, and separation applications. Precise control over their surface charge is critical, as it governs ion selectivity, electroosmotic flow, and overall ionic transport behaviour in confined nanochannels. However, environmentally friendly and scalable strategies to precisely tune their surface charge remain limited. Amination is a practical approach for PC membrane functionalisation, as it introduces protonatable amine groups that enhance the positive surface charge and enable further chemical modifications via mild, aqueous reactions. Here, we report a simple aqueous amination method that enables systematic control of surface charge density in PC membranes between 0.0015–0.0034 C cm−2. Commercial PC membranes with nominal pore sizes of 0.015, 0.05, and 0.1 µm were functionalised with a series of amines, hexamethylenediamine (HMDA), triethylenetetramine (TETA), polyethyleneimine (PEI), and glycine (Gly), through urethane-bond formation with surface carbonyl groups under mild aqueous conditions. Elemental and spectroscopic analyses confirmed efficient functionalisation and tuneable nitrogen content (9.7–22.6 at%), related to variable surface charge density, achieved by varying reaction parameters such as concentration, time, temperature, and amine type. The highest surface charge density of 0.0034 C cm−2 was achieved using 5% w/v TETA on PC membranes with 0.1 µm diameter. This scalable, low-energy pathway for PC membrane functionalisation is even compatible with ultrasmall pores, down to ∼15 nm. The charge densities achieved through this green aqueous functionalisation are the highest among other surface charge-tuning methods, such as plasma, ultraviolet, or polymer-grafting methods. Aqueous amination-based functionalisation is suitable for fabricating charge-tuneable, ion-selective membranes for nanofluidic energy conversion, electrochemical sensing, and other surface-charge-governed applications.