Effects of interface curvature on Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse grooves and ribs

This paper presents numerical results pertaining to the effects of interface curvature on the effective slip behavior of Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse ribs and grooves. The effects of interface curvature are systematically investigated for different normalized channel heights or tube diameters, shear-free fractions, and flow Reynolds numbers. The numerical results show that in the low Reynolds number Stokes flow regime, when the channel height or tube diameter (normalized using the groove–rib spacing) is sufficiently large, the critical interface protrusion angle at which the effective slip length becomes zero is θ _c ≈ 62°–65°, which is independent of the shear-free fraction, flow geometry (channel and tube), and flow driving mechanism. As the normalized channel height or tube diameter is reduced, for a given shear-free fraction, the critical interface protrusion angle θ _c decreases. As inertial effects become increasingly dominant corresponding to an increase in Reynolds number, the effective slip length decreases, with the tube flow exhibiting a more pronounced reduction than the channel flow. In addition, for the same corresponding values of shear-free fraction, normalized groove–rib spacing, and interface protrusion angle, longitudinal grooves are found to be consistently superior to transverse grooves in terms of effective slip performance.     

Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves

Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in micro- and nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shear-free fraction and the periodic extent of each groove–rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove–rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove–rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.     

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.     

Liquid flow through microchannels with grooved walls under wetting and superhydrophobic conditions

Recent developments in superhydrophobic surfaces have enabled significant reduction in the frictional drag for liquid flow through microchannels. There is an apparent risk when using such surfaces, however, that under some conditions the liquid meniscus may destabilize and, consequently, the liquid will wet the entire patterned surface. This paper presents analytical and experimental results that compare the laminar flow dynamics through microchannels with superhydrophobic walls featuring ribs and cavities oriented both parallel and transverse to the direction of flow under both wetting and non-wetting conditions. The results show the reduction in the total frictional resistance is much greater in channels when the liquid phase does not enter the cavity regions. Further, it is demonstrated that the wetting and non-wetting cavity results represent limiting cases between which the experimental data lie. Generalized expressions enabling prediction of the classical friction factor-Reynolds number product as a function of the relevant governing dimensionless parameters are also presented for both the superhydrophobic and wetting states. Experimental results are presented for a range of parameters in the laminar flow regime.     

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.     

A microgrooved membrane based gas–liquid contactor

This research presents an approach for applying microgrooved membranes for improved gas–liquid contacting. The study involves analysis of the performance of the microdevice by quantifying the flux enhancement for different membrane configurations. Two kinds of configurations, continuous and non-continuous grooves, were investigated. The microgrooves provide shear-free gas–liquid interfaces, which result in local slip velocity at the gas–liquid interface. Exploiting this physical phenomenon, it is possible to reduce mass transport limitations in gas–liquid contacting. An experimental study using grooved membranes suggests enhancement in flux up to 20–30 %. The flux enhancement at higher liquid flow rates is observed due to a partial shear-free gas–liquid interface. The performance of the membrane devices decreased with wetted microgrooves due to the mass transport limitations. The flow visualization experiments reveal wetting of the microgrooves at higher liquid flow rates. According to the numerical and experimental study, we have shown that microgrooved membranes can be employed to improve gas–liquid contacting processes.     

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.     

Effects of surface roughness and interface wettability on nanoscale flow in a nanochannel

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.     

Thermohydrodynamic analysis of micro spherical spiral groove gas bearings under slip flow and surface roughness coupling effect

The effects of gas rarefaction and surface roughness are temperature-related and always neglected in macroscale. These effects were considered in the analysis of the thermohydrodynamic performance of micro spherical spiral groove bearings. The Reynolds equation and the energy equation incorporated with Wu’s slip model and the Weierstrass–Mandelbrot function to analysis the coupling effect of slip flow and surface roughness. The effects of spherical grooves on computational accuracy were reduced through parameter transformation and oblique coordinates. To describe the temperature boundary condition at the grooved region, a simple gas-mixing model was presented for the grooves. Prediction results showed that temperature reduced bearing forces and friction torque through the slip flow effect. Surface roughness increased not only temperature significantly but also bearing forces and friction torque through a high eccentricity ratio and a low bearing clearance.

     

Boundary conditions for shear flow past a permeable interface modeled as an array of cylinders

The boundary condition relating the macroscopic jump in the tangential velocity across a permeable interface consisting of a particulate lattice to the shear rate prevailing on either side of the interface is discussed. The computation of the velocity jump hinges on the realization that shear flow on one side of the interface induces a slip velocity on that side and a streaming drift velocity on the other side. The direction and magnitude of the slip and drift velocities depend on the interface constitution, solid fraction, and Reynolds number. Numerical computations are performed for a model two-dimensional interface consisting of a periodic array of cylinders. In the case of longitudinal unidirectional flow, the boundary conditions are defined in terms of previously computed drift and slip velocity coefficients for any ratio of the shear rates above and below the interface and any Reynolds number. To study the behavior in the complementary case of transverse flow, the Navier-Stokes equation is solved numerically using a finite-difference method on an orthogonal grid generated by conformal mapping, using the stream function/vorticity formulation. The results reveal that inertial effects promote the magnitude of the slip and drift velocity, and illustrate the streamline pattern near the interface.     

Liquid-state motion sensing

This paper demonstrates a liquid droplet-based motion sensing system which has the advantages of simple fabrication, low power consumption and digital signal processing. The sensor consists of a dielectric substrate patterned with an array of microelectrodes, and a saline droplet as the proof mass. Once an external linear acceleration is applied, the inertial force moves the droplet on the micropatterned substrate. The acceleration is determined from the movement profile detected by the microelectrodes. In order to enhance the threshold and the sensitivity of motion sensing, two surface treatment approaches are utilized to create superhydrophobic surfaces. The result shows that the minimal sliding angle that can move a 20 μl droplet on the superhydrophobic surface is lower than 1°, corresponding to a threshold of lower than 0.017 g. A lumped-parameter model is developed to estimate the dynamic behavior of the proposed system. The result shows that the frequency response of the droplet-based sensor is more significant at low frequencies than at high frequencies, which is distinct from solid-state accelerometers. Measurement under a constant acceleration shows that the predicted value derived from the measurement has a good match with the actual applied acceleration, validating the proposed system as a viable alternative for motion sensing.     

Role of interface shape on the laminar flow through an array of superhydrophobic pillars

In this study, measurements of the pressure drop and the velocity vector fields through a regular array of superhydrophobic pillars were systematically taken to investigate the role of air–water interface shape on laminar drag reduction. A polydimethylsiloxane microfluidic channel was created with a regular array of apple-core-shaped and circular pillars bridging across the entire channel. Due to the shape and hydrophobicity of the apple-core-shaped pillars, air was trapped on the side of the pillars after filling the microchannel with water. The measurements were taken at a capillary number of Ca = 6.6 × 10^?5. The shape of the air–water interface trapped within the superhydrophobic apple-core-shaped pillars was systematically modified from concave to convex by changing the static pressure within the microchannel. The pressure drop through the microchannel containing the superhydrophobic apple-core-shaped pillars was found to be sensitive to the shape of the air–water interface. For static pressures which resulted in the apple-core-shaped superhydrophobic pillars having a circular cross section, D/D ₀ = 1, a drag reduction of 7% was measured as a result of slip along the air–water interface. At large static pressures, the interface was driven into the apple-core-shaped pillars, resulting in decrease in the effective size of the pillars and an increase in the effective spacing between pillars. When combined with a slip velocity measured to be 10% of the average velocity between the pillars, the result was a pressure drop reduction of 18% compared to the circular pillars at a non-dimensional interface diameter of D/D ₀ = 0.8. At low static pressures, the pressure drop increased significantly as the expanded air–water interface constricted flow through the array of pillars even as large interfacial slip velocity was maintained. At D/D ₀ = 1.1, for example, the pressure drop increased by 17% compared to the circular pillar. This drag increase was the result of an increased form drag due to a decrease in porosity and permeability of the pillar array and a decrease in the skin friction drag due to the presence of the air–water interface. For D/D ₀ = 1.1, the slip velocity was measured to be 45% of the average streamwise velocity between the pillars. When compared to no-slip pillars of similar shape, the drag reduction was found to increase from 6 to 9% with increasing convex curvature of the air–water interface.     

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.     

Hydrodynamic structures of droplets engineered in rectangular micro-channels

This paper reports on numerical simulations of the hydrodynamics inside droplets in rectangular micro-channels. Two- and three-dimensional simulations are performed thanks to a finite-volume/front-capturing method. Droplet interface deformation and velocity fields inside both droplets and continuous phase can then be followed. This study leads to important results about droplet deformation and inner streamlines for mass and heat transfer studies. More particularly, the capillary number seems to have a great influence on the liquid/liquid flow hydrodynamics and this impact on film thickness and slip velocity is quantified through correlations.     

Dewetting of thin liquid films on chemically patterned substrates: front propagation along narrow lyophobic stripes and stripe arrays

Using experiments and numerical simulations, we investigate the dewetting of thin liquid films on chemically patterned substrates. The patterns consist of long and narrow hydrophobic stripes, separated by larger hydrophilic domains. We characterize the morphology and dynamics of the dewetting front starting from an initially present dry-spot. Moreover, we study the distortion of the liquid film on the adjacent hydrophilic domains as a function of film thickness, hydrophobic contact angle and pattern dimensions. Implications of our results on the solution processing of organic electronic devices on chemically patterned surfaces are discussed.     

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.     

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.