Surface wettability effects on flow in rough wall nanochannels

The effect of rough-wall/fluid interaction on flow in nanochannels is investigated by NEMD. Hydrophobic and hydrophilic surfaces are studied for walls with nearly atomic-size rectangular protrusions and cavities. Our NEMD simulations reveal that the number of liquid atoms temporarily trapped in the cavities is affected by the strength of the potential energy inside the cavities. Regions of low potential energy are possible trapping locations. Fluid atom localization is also affected by the hydrophilicity/hydrophobicity of the surface. Potential energy is greater between two successive hydrophilic protrusions, compared to hydrophobic ones. Moreover, groove size and wall wettability are factors that control effective slip length. Surface roughness and wall wettability have to be taken into account in the design of nanofluidic devices.     

Water droplet properties on periodically structured superhydrophobic surfaces: a lattice Boltzmann approach to multiphase flows with high water/air density ratio

Surface roughness affects the contact angle (CA) due to the increased area of solid–liquid interface and due to the effect of sharp edges of rough surfaces. Roughness may also lead to another non-wetting regime, by forming a composite solid–liquid–air interface between the water and the textured surface; this composite interface exhibits strong water repellency due to the various pockets of air entrapped between the surface textures. The contact between water and a hydrophobic textured surface leads to one of these two regimes depending on the thermodynamics stability of the regimes. In this study, the projection method of lattice Boltzmann method is used to analyze the large density difference at the air and water interface. The method is applied to simulate two-phase flows with the density ratio of up to 1,000. A numerical model is presented to provide a relationship between roughness and CA, which is used to develop optimized texture topography and create a biomimetic superhydrophobic surface. The numerical models encompass the effects of contact area, solid–liquid–gas composite interface and shape edges. The models are reused to analyze different possible roughness distributions and to calculate the effect of the cross-sectional area of pillars, including rectangular, triangular, cross, and pyramidal pillars. The energy barrier is investigated to predict the position of the transition between the Cassie and Wenzel regime observed for each roughness parameter as well as a theoretical free surface energy model.     

Stochastic model for metastable wetting of roughness-induced superhydrophobic surfaces

A stochastic model for metastable wetting of roughness-induced hydrophobic surfaces is proposed. For a rough surface, increased solid–liquid interface area results in increased interface energy, and increases the contact angle (for non-wetting liquids) or decreases it (for wetting liquids). For a very rough surface, a composite solid–liquid–air interface may form with air pockets trapped in the valleys between asperities, as opposed to the homogeneous solid–liquid interface. Both the homogeneous and composite interface configurations correspond to local energy minima of the system and therefore, there are stable states associated with different energy levels. The system may transform from one stable state to the other due to small perturbations, such as capillary waves. Different probabilities are associated with these different stable states, depending on the energy levels. The contact zone consists of a large number of asperities and valleys, which may be in the homogeneous or composite state. The overall contact angle is calculated based on the statistical model. The model may be used for design of roughness-induced superhydrophobic surfaces.     

Fast nanofluidics by travelling surface waves

In this paper, we investigate the fast flow in nanochannels, which is induced by the travelling surface waves. The nanoscale fluid mechanism in nanochannels has been influenced by both amplitude and frequency of travelling surface waves, and the hydrodynamic characteristics have been obtained by molecular dynamics simulations. It has been found that the flow rate is an increasing function of the amplitude of travelling surface waves and can be up to a sevenfold increase. However, the flow rate is only enhanced in the limited range of frequency of travelling surface waves such as low frequencies, and a maximum fivefold increase in flow rate is pronounced. In addition, the fluid–wall interaction (surface wettability) plays an important role in the nanoscale transport phenomena, and the flow rate is significantly increased under a strong fluid–wall interaction (hydrophilicity) in the presence of travelling surface waves. Moreover, the friction coefficient on the wall of nanochannels is decreased obviously due to the large slip length, and the shear viscosity of fluid on the hydrophobic surface is increased by travelling surface waves. It can be concluded that the travelling surface wave has a potential function to facilitate the flow in nanochannels with respect to the decrease in surface friction on the walls. Our results allow to define better strategies for the fast nanofluidics by travelling surface waves.     

Slippage of binary fluid mixtures in a nanopore

This work focuses on the slip phenomenon at the fluid–solid interface accompanying Poiseuille flow of simple binary miscible fluids in a slit nanopore. To explore such flows, molecular dynamics simulations are used on Lennard–Jones binary mixtures composed of species of varying affinities with the walls. The results have shown that the apparent slip magnitude at the fluid–solid interface depends largely on the species that is dominant in contact with the walls. In addition, it has been shown that the velocity profiles of each species (of different “wettability”) does not superpose with the velocity profile of the mixture and such a result points out the limitations of the classical approaches based on a single momentum conservation equation to deal with mixtures flow in nanochannels.     

Multi-scale study of liquid flow in micro/nanochannels: effects of surface wettability and topology

The paper reports parametric study, using a molecular dynamics–continuum hybrid simulation method, of liquid flow in micro/nanochannels with surface nanostructures. The effects of channel height, shape of roughening element, ratio of pitch to length of roughening element and liquid–solid bonding strengths (representing surface wettability) on the velocity and temperature boundary conditions are investigated. The velocity boundary condition is found to shift from significant slip to locking due to the blocking of the surface nanostructure. The blocking appears weak for small pitch ratio and weak liquid–solid bonding. Distorted streamlines, small random eddies and appreciable density oscillations are seen in the vicinity of the wall for small pitch ratio and strong liquid–solid bonding. On the other hand, smooth streamlines and weak density oscillations are seen for large pitch ratio and weak liquid–solid bonding. Results also reveals that: relative slip length, relative Kapitza length and minus pressure gradient vary with channel height and pitch ratio in functions of power law and approximately linear, respectively; relative slip and Kapitza lengths vary with liquid–solid bonding strength as approximately decreasing power functions (except for the strongest case), whereas minus pressure gradient varies with liquid–solid bonding strength as approximately a logarithm-like function. The effect of shape of roughening element is found to be much less significant compared with the other factors studied.     

Hydrodynamic drainage force in a highly confined geometry: role of surface roughness on different length scales

We measured the hydrodynamic drainage force of an aqueous, Newtonian liquid squeezed between two hydrophobic or two hydrophilic surfaces by means of the colloidal probe technique. We controlled the wettability, the roughness, the topology, and also the approaching velocity of the surfaces. We found that asperities on the surfaces caused an artificial decrease of the measured drainage force that must be considered by the interpretation of the force curves. Even considering the effect of asperities, our experimental results could be interpreted only with the aid of a partial slip model. Or else, interpreted assuming that the viscosity close to the surfaces is different from bulk. On patterned hydrophilic surfaces, we demonstrated that the drainage force depends not only on the overall surface roughness or micro structuring but also on the specific length scale of the surface nanostructures.     

Contact line dynamics of a superhydrophobic surface: application for immersion lithography

The dynamic contact line behavior of water on nanotextured rough hydrophobic and superhydrophobic surfaces is studied and contrasted to smooth hydrophobic surfaces for application in immersion lithography. Liquid loss occurs at the receding meniscus when the smooth substrate is accelerated beyond a critical velocity of approximately 1 m/s. Nanotexturing the surface with average roughness values even below 10 nm results in critical velocity larger than 2.5 m/s, the upper limit of the apparatus. This unexpected increase in critical velocity is observed for both sticky hydrophobic and slippery superhydrophobic surfaces. The authors attribute this large increase in critical velocity both in increased receding contact angle and in increased slip length for such nanotextured surfaces.     

Molecular dynamics simulation of fluid containing gas in hydrophilic rough wall nanochannels

This study performed the molecular dynamic simulations to investigate the boundary behavior of liquid water with entrapped gas bubbles over various hydrophilic roughened substrates. A “liquid–gas–vapor coexistence setup” was employed to maintain a constant thermodynamic state during individual equilibrium simulations and corresponding non-equilibrium Poiseuille flow cases. The two roughened substrates (Si(100) and graphite) adopted in this study present similar contact angles and slip length with gas-free fluid. By considering the effects of argon molecules at the interface, we demonstrated that the boundary slip behavior differed dramatically between these two rough wall channels. This divergence can be attributed to differences in the morphology of argon bubble at the interface due to discrepancies in the atomic arrangement and wall–fluid interaction energy. Furthermore, the density of gas at the interface had a significant impact on the effective slip length of the roughened graphite substrate, whereas shear rate \(\dot{\gamma }\) presented no noticeable influence. On the roughened Si(100) surface, the morphology of the argon bubbles exhibited far higher meniscus curvature and unstable properties under hydrodynamic effects. Thus, this substrate exhibited no slip to slight negative slip and no remarkable influence from either the density of gas at the interface or shear rate. In the present study, we demonstrate that the morphology and behavior of interfacial gas bubbles are influenced by the parameters of wall–fluid interaction as well as the atomic arrangement of the substrate. Our results related to nanochannel flow reveal that different surfaces, such as Si(100) and graphite, may possess similar intrinsic wettability; however, properties of the interfacial gas bubbles can lead to noticeable changes in interfacial characteristics resulting in various degrees of boundary slippage.     

Numerical simulation of emergence of a water droplet from a pore into a microchannel gas stream

A numerical investigation on the dynamic behavior of liquid water entering a microchannel through a lateral opening (pore) in the wall is reported in this paper. The channel dimensions, flow conditions and transport properties are chosen to simulate those in the gas channel of a typical proton exchange membrane fuel cell (PEMFC). Two-dimensional transient simulations employing the volume of fluid method are used to explicitly track the liquid–gas interface, and to gain understanding into the dynamics of a water droplet subjected to airflow in the bulk of the microchannel. A series of parametric studies, including the effects of static contact angle, dimensions of the pore, air-inlet velocity, and water-inlet velocity are performed with a particular focus on the effect of hydrophobicity. The simulations show that the wettability of the microchannel surface has a major impact on the dynamics of the water droplet. Flow patterns are presented and analyzed showing the splitting of a droplet for a hydrophobic surface, and the tendency for spreading and film flow formation for a hydrophilic surface. The time evolution of the advancing and receding contact angles of the droplet are found to be sensitive to the wettability when the gas diffusion layer surface is hydrophilic, but independent of wettability when the surface is hydrophobic. The critical air velocity at which a droplet detaches is found to decrease with increasing hydrophobicity and with increasing initial dimension of the droplet. The critical air velocity found in the present study by taking into account the water transport and evolution of the droplet from a pore are found to differ significantly from previous works which consider a stagnant droplet sitting on the surface.     

Numerical investigation on drag reduction with superhydrophobic surfaces by lattice-Boltzmann method

The mechanism of drag reduction by using superhydrophobic surfaces whose contact angle is greater than 150° is still an open problem that needs to be investigated. The main purpose of this paper is to reveal how the pressure drop can be decreased. The lattice-Boltzmann method (LBM) is employed to investigate fluid flows through channels with different wettability conditions and topographical surfaces. The drag reduction by superhydrophobic surfaces is determined based on numerical experiments. For the smooth-surface flow, a very thin gas film is observed between the fluid and the superhydrophobic wall; hence, the liquid/solid interface is replaced by the gas/liquid interface. For the rough-surface flow, liquid sweeps over the grooves and the contact area is reduced; therefore, the friction is decreased rapidly. Additionally, the effects of surface wettability and surface roughness are analyzed as well. It is found that introducing roughness elements has a positive effect for reducing the pressure drop for the hydrophobic-surface flow, but has a negative effect for the hydrophilic-surface flow.     

Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model

The present study has numerically investigated two-dimensional electroosmotic flows in a microchannel with dielectric walls of rectangle-waved surface roughness to understand the roughness effect. For the study, numerical simulations are performed by employing the Nernst–Planck equation for the ionic species and the Poisson equation for the electric potential, together with the traditional Navier–Stokes equation. Results show that the steady electroosmotic flow and ionic-species transport in a microscale channel are well predicted by the Poisson–Nernst–Planck model and depend significantly on the shape of surface roughness such as the amplitude and periodic length of wall wave. It is found that the fluid flows along the surface of waved wall without involving any flow separation because of the very strong normal component of EDL (electric double layer) electric field. The flow rate decreases exponentially with the amplitude of wall wave, whereas it increases linearly with the periodic length. It is mainly due to the fact that the external electric-potential distribution plays a crucial role in driving the electroosmotic flow through a microscale channel with surface roughness. Finally, the present results using the Poisson–Nernst–Planck model are compared with those using the traditional Poisson–Boltzmann model which may be valid in these scales.     

Lattice Boltzmann method for microfluidics: models and applications

The lattice Boltzmann method (LBM) has experienced tremendous advances and has been well accepted as a useful method to simulate various fluid behaviors. For computational microfluidics, LBM may present some advantages, including the physical representation of microscopic interactions, the uniform algorithm for multiphase flows, and the easiness in dealing with complex boundary. In addition, LBM-like algorithms have been developed to solve microfluidics-related processes and phenomena, such as heat transfer, electric/magnetic field, and diffusion. This article provides a practical overview of these LBM models and implementation details for external force, initial condition, and boundary condition. Moreover, recent LBM applications in various microfluidic situations have been reviewed, including microscopic gaseous flows, surface wettability and solid–liquid interfacial slip, multiphase flows in microchannels, electrokinetic flows, interface deformation in electric/magnetic field, flows through porous structures, and biological microflows. These simulations show some examples of the capability and efficiency of LBM in computational microfluidics.     

Molecular dynamics-based prediction of boundary slip of fluids in nanochannels

Computational modeling and simulation can provide an effective predictive capability for flow properties of the confined fluids in micro/nanoscales. In this paper, considering the boundary slip at the fluid–solid interface, the motion property of fluids confined in parallel-plate nanochannels are investigated to couple the atomistic regime to continuum. The corrected second-order slip boundary condition is used to solve the Navier–Stokes equations for confined fluids. Molecular dynamics simulations for Poiseuille flows are performed to study the influences of the strength of the solid–fluid coupling, the fluid temperature, and the density of the solid wall on the velocity slip at the fluid boundary. For weak solid–fluid coupling strength, high temperature of the confined fluid and high density of the solid wall, the large velocity slip at the fluid boundary can be obviously observed. The effectiveness of the corrected second-order slip boundary condition is demonstrated by comparing the velocity profiles of Poiseuille flows from MD simulations with that from continuum.     

Wetting of rough three-dimensional superhydrophobic surfaces

Wetting of rough three-dimensional periodic surfaces is studied. The contact angle of liquid with a rough surface (θ) is different from that with a smooth surface (θ₀) due to the difference in the contact area and effect of the air pockets. For non-wetting liquids (θ₀>π/2), the contact angle increases with roughness and may approach the value of π (superhydrophobic surface). For high θ₀, a homogeneous solid-liquid interface, as well as a composite solid-liquid-air interface with air pockets at the valleys of rough surface are possible. These two interfaces correspond to different states of equilibrium and result in different θ. A probability-based approach is introduced to handle the multiple states of equilibrium and to calculate θ. It is found also that increasing droplet size has the same effect as increasing period of roughness (size of asperities). For larger droplets and for larger asperities, the composite interface is less likely. For applications involving liquid’s transport near rough walls of a channel, an analogy between a droplet of non-wetting liquid and a gas bubble in wetting liquid is proposed. In order to increase bubbles mobility, the contact angle and the contact angle hysteresis should be minimized. Practical recommendations for design of superhydrophobic surfaces are formulated.     

Thin film evaporation in microchannels with interfacial slip

We investigate the role of interfacial slip on evaporation of a thin liquid film in a microfluidic channel. The effective slip mechanism is attributed to the formation of a depleted layer adhering to the substrate–fluid interface, either in a continuum or in a rarefied gas regime, as a consequence of intricate hydrophobic interactions in the narrow confinement. We appeal to the fundamental principles of conservation in relating the evaporation mechanisms with fluid flow and heat transfer over interfacial scales. We obtain semi-analytical solutions of the pertinent governing equations, with coupled heat and mass transfer boundary conditions at the liquid–vapor interface. We observe that a general consequence of interfacial slip is to elongate the liquid film, thereby leading to a film thickening effect. Thicker liquid films, in turn, result in lower heat transfer rates from the wall to liquid film, and consequently lower mass transfer rates from the liquid film to the vapor phase. Nevertheless, the total mass of evaporation (or equivalently, the net heat transfer) turns out to be higher in case of interfacial slip due to the longer film length. We also develop significant physical insights on the implications of the relative thickness of the depleted layer with reference to characteristic length scales of the microfluidic channel on the evaporation process, under combined influences of the capillary pressure, disjoining pressure, and the driving temperature differential for the interfacial transport.     

Roughness optimization for biomimetic superhydrophobic surfaces

For non-wetting liquids the contact angle with a rough surface is greater than with a flat surface and may approach 180°, as reported for leaves of water-repellent plants, such as lotus. Roughness affects the contact angle due to the increased area of solid–liquid interface and due to the effect of sharp edges of rough surfaces. High roughness may lead to composite solid–liquid–air interface, which may be either stable or unstable. A comprehensive analytical model is proposed to provide a relationship between local roughness and contact angle, which is used to develop roughness distribution and to create biomimetic superhydrophobic surfaces. Various roughness distributions are considered, including periodic and surfaces with rectangular, hemispherically topped cylindrical, conical and pyramidal asperities and the random Gaussian height distribution. Verification of the model is conducted using experimental data for the contact angle of water droplet on a lotus leaf surface. For two solid bodies in contact, for wetting liquids, wetting leads to the meniscus force, which affects friction. Dependence of the meniscus force on roughness, previously ignored, is considered in the paper and it is found that with increasing roughness meniscus force can grow due to scale effect.

Hybrid atomistic�Ccontinuum simulations of fluid flows involving interfaces

In this work, we use an hybrid atomistic–continuum (HAC) simulation method to study transient and steady isothermal flows of Lennard-Jones fluids near interfaces. Our hybrid method is based on a domain decomposition algorithm. The flow domain is composed of two overlapping regions: an atomistic region described by molecular dynamics, and a continuum region described by a finite volume discretization of the incompressible Navier–Stokes equations. To show the interest of such an hybrid method to compute flows near fluid/solid interface, we first applied our hybrid scheme to the classical Couette flow, where the moving wall is modelled at the atomistic scale. In addition, we also studied an oscillatory shear flow. Then, to compute flows near fluid/fluid interface, we applied our method to a two-phase Couette flow (liquid/gas), where the interface is modelled at the molecular scale. We show that hybrid results can sometimes differ from those provided by analytical solutions deduced from continuum mechanics equations combined with usual boundary/interface relations. For the Couette and oscillatory shear flows, a good agreement is found between hybrid simulations and macroscopic analytical solutions, however, we noticed that the fluid in contact with the wall can be more entailed than what expected. For the liquid/gas Couette flow, the hybrid simulation exhibits an unexpected jump of the velocity in the interfacial region, corresponding to a partial slip between the two fluid phases. Those interesting results highlight the interest of using an HAC method to deal with systems for which surfaces/interfaces effects are important.     

Transient analysis of sliding contact of layered elastic/plastic solids with rough surfaces

 Based on the boundary element method (BEM) and a variational principle, a numerical model is developed to analyze the time – transient sliding contact of two layered elastic/plastic solids. Two cases are considered: one is the loading/sliding/unloading of a rough surface on a smooth surface, and the other is of two rough surfaces. Contact statistics, contact pressure profile and stress distribution are predicted at each time step with updated surface roughness. The results are used to study the effect of surface roughness, physical properties of the layer and the substrate, and lubricant film thickness on friction, stiction, and wear. Discussion on the integration of this contact model into advanced tribological models, e.g., wear model, is also presented. Received: 28 June 2002/Accepted: 23 October 2002 Currently at: Seagate Technology, Pittsburgh, PA Paper presented at the 13th Annual Symposium on Information Storage and Processing Systems, Santa Clara, CA, USA, 17–18 June, 2002     

Gated transport in nanofluidic devices

The surface property of the nanochannel plays an important role in controlling the ion transport through the nanochannel. Embedding electrodes outside the nanochannel (referred to as gated nanochannels) is a simple way to control the surface charge density of the nanochannel. Based on the numerical simulations using coupled Poisson–Nernst–Planck and Stokes equations, we show that a relative difference between the applied voltage and the gate voltage would alter the space charge density along the nanochannel. Thus, the gate voltage can tune the nanochannel into a p- or n-type field effect transistor, enabling the control of fluid flow in the nanochannel. The ionic currents reveal that the ionic flux can be controlled by the gate voltage. Analytical expressions are derived to estimate the effective space charge density and the fluid flow in the nanochannels for a fixed gate voltage. We also suggest potential applications of the gated nanochannels.