A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with the flow. The pressure difference between the liquid and the gas in the grooves causes a curvature of the liquid surface resisted by surface tension. The effects of this surface deformation are studied in this paper. The corrections to the effective slip length produced by the curvature are analyzed theoretically and a comparison with available data and related mathematical models is presented.
In this contribution we review recent efforts on investigations of the effect of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We demonstrate the applicability of the method to treat fundamental questions in microfluidics by investigating fluid flow in hydrophobic and rough microchannels as well as over surfaces covered by nano- or microscale gas bubbles.
Surface effects become important in microfluidic setups because the surface to volume ratio becomes large. In such setups the surface roughness is not any longer small compared to the length scale of the system and the wetting properties of the wall have an important influence on the flow. However, the knowledge about the interplay of surface roughness and hydrophobic fluid-surface interaction is still very limited because these properties cannot be decoupled easily in experiments. We investigate the problem by means of lattice Boltzmann (LB) simulations of rough microchannels with a tunable f…
Substantial experimental, theoretical, as well as numerical effort has been invested to understand the effect of boundary slippage in microfluidic devices. However, even though such devices are becoming increasingly important in scientific, medical, and industrial applications, a satisfactory understanding of the phenomenon is still lacking. This is due to the extremely precise experiments needed to study the problem and the large number of tunable parameters in such systems. In this paper we apply a recently introduced algorithm to implement hydrophobic fluid-wall interactions in the lattice …
Dissipative Particle Dynamics (DPD) is becoming a popular particle based method to study flow through microchannels due to the ease with which the presence of biological cells or DNA chains can be modeled. Many Lab-On-Chip (LOC) devices require the ability to manipulate the transport of cells or DNA chains in the fluid flow. Microchannel surfaces coated with combinations of hydrophilic and hydrophobic materials have been found useful for this purpose. In this work, we have numerically studied the hydrodynamics of a steady nonuniform developing flow between two infinite parallel plates with hyd…
Various experiments have found a boundary slip in hydrophobic microchannel flows, but a consistent understanding of the results is still lacking. While Molecular Dynamics (MD) simulations cannot reach the low shear rates and large system sizes of the experiments, it is often impossible to resolve the needed details with macroscopic approaches. We model the interaction between hydrophobic channel walls and a fluid by means of a multi-phase lattice Boltzmann model. Our mesoscopic approach overcomes the limitations of MD simulations and can reach the small flow velocities of known experiments. We…
Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in the assumption of perfectly smooth boundaries. We investigate the problem by means of lattice Boltzmann (LB) simulations and introduce an ``effective no-slip plane'' at an intermediate position between peaks and valleys of the surface. Our simulations show good agreement with analytical results for sinusoidal boundaries, but can be extended to arbitrary geo…
Liquid-gas-liquid interfaces stabilized by hydrophobic beads behave as ball bearings under shear and exhibit a giant slip. Using a scaling analysis and molecular dynamics simulations we predict that, when the contact angle theta between the beads and the liquid is large, the slip length diverges as R rho(-1) (pi -theta)(-3) where R is the bead radius, and theta is the bead density. DOI: 10.1103/PhysRevLett.110.104504
Experiments and simulations suggest that simple liquids may experience slip while flowing near a smooth, hydrophobic surface. Here we show how precursors to molecular slip can be observed in the complex response of a liquid to oscillatory shear. We measure both the change in frequency and bandwidth of a quartz crystal microbalance (QCM) during the growth of a single drop of water immersed in an ambient liquid. By varying the hydrophobicity of the surface using self-assembled monolayers, our results show little or no slip for water on all surfaces. However, we observe excess transverse motion n…
Super-hydrophobic array of grooves containing trapped gas (stripes), have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes, with limited guidance. Here, we analyze the experimentally relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive analytical formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that can be used for any surface slip fraction (validated by …
Inertial microfluidic is able to focus and separate particles in microchannels based on the characteristic geometry and intrinsic hydrodynamic effect. Yet, the vertical position of suspended particles in the microchannel cannot be manipulated in real time. In this study, we utilize the boundary slip effect to regulate the parabolic velocity distribution of fluid in the microchannel and present a scheme to active control the vertical position of particles in inertial microfluidics. The flow field of a microchannel with a unilateral slip boundary is equivalent to that of the microchannel widened…
Recent experiments (Zhu & Granick (2001) Phys. Rev. Lett. 87 096105) have measured a large shear dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such slip, motivated by the recent observations of nanobubbles on hydrophobic surfaces. The model considers the dynamic response of bubbles to change in hydrodynamic pressure due to the oscillation of a solid surface. Both the compression and diffusion of gas in the bubbles decrease the force on the oscillating surface by a ``leaking mattress'' effect, thereby creating an apparent shear-dependent slip. Wit…
We show that an electro-osmotic flow near the slippery hydrophobic surface depends strongly on the mobility of surface charges, which are balanced by counter-ions of the electrostatic diffuse layer. For a hydrophobic surface with immobile charges the fluid transport is considerably amplified by the existence of a hydrodynamic slippage. In contrast, near the hydrophobic surface with mobile adsorbed charges it is also controlled by an additional electric force, which increases the shear stress at the slipping interface. To account for this, we formulate electro-hydrodynamic boundary conditions a…
We present a mesoscopic model of the fluid-wall interactions for flows in microchannel geometries. We define a suitable implementation of the boundary conditions for a discrete version of the Boltzmann equations describing a wall-bounded single phase fluid. We distinguish different slippage properties on the surface by introducing a slip function, defining the local degree of slip for mesoscopic molecules at the boundaries. The slip function plays the role of a renormalizing factor which incorporates, with some degree of arbitrariness, the microscopic effects on the mesoscopic description. We …
We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semi-analytical theory of an effective slip in a parallel-plate channel with one super-hydrophobic striped and one hydrophilic surface. Our approach is valid for an…
We employ micro-particle image velocimetry ($μ$-PIV) to investigate laminar micro-flows in hydrophobic microstructured channels, in particular the slip length. These microchannels consist of longitudinal micro-grooves, which can trap air and prompt a shear-free boundary condition and thus slippage enhancement. Our measurements reveal an increase of the slip length when the width of the micro-grooves is enlarged. The result of the slip length is smaller than the analytical prediction by Philip et al. [1] for an infinitely large and textured channel comprised of alternating shear-free and no-sli…
We give a general theoretical description of electro-osmotic flow at striped super-hydrophobic surfaces in a thin double layer limit, and derive a relation between the electro-osmotic mobility and hydrodynamic slip-length tensors. Our analysis demonstrates that electro-osmotic flow shows a very rich behavior controlled by slip length and charge at the gas sectors. In case of uncharged liquid-gas interface, the flow is the same or inhibited relative to flow in homogeneous channel with zero interfacial slip. By contrast, it can be amplified by several orders of magnitude provided slip regions ar…
We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured super-hydrophobic plane, that contains trapped gas bubbles. A super-hydrophobic wall is characterized by parameters $L$ (texture characteristic length), $b_1$ and $b_2$ (local slip lengths at solid and gas areas), and $ϕ_1$ and $ϕ_2$ (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and $H$ (local separation). The effect of effective slip is p…
Electrokinetic energy conversion provides a scheme for energy harvesting and storage for on-chip applications. However, the major drawback of electrokinetic energy conversion is its low conversion efficiency. Researchers are in a quest to find ways to improve this efficiency. With the same motive, we investigated the generation of streaming potential by applying surface modification and employing a non-Newtonian fluid to flow through the microchannel under constant pressure difference across its ends. Shear-thickening liquids tend to lessen electrokinetic effects, whereas shear-thinning liquid…
Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a correction function to the Reynolds equation, which is shown to be the harmonic mean of corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (co…
In this paper, we applied the Shan-Chen multiphase Lattice Boltzmann method to simulate two different parameters, contact angle (a static parameter) and slip length (a dynamic parameter), and we proposed a relationship between them by fitting those numerical simulation results. By changing the values of the strength of interaction between fluid particles (SIF) and the strength of interaction between fluid and solid surface (SIFS), we simulated a series of contact angles and slip lengths. Our numerical simulation results show that both SIF and SIFS have little effects on the relationship betwee…
When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to significant reduction of viscous friction in the laminar regime, so it is of interest to quantify their effective slipping properties as a function of their geometric characteristics. Most previous studies have considered flows bounded by arrays of either long grooves, or isolated solid pillars on an otherwise flat solid substrate, and for which therefore the sur…
Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of super-hydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length. We derive approximate formulae for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Bolzmann simulations for any surface slip fraction. The cosine texture can provide a very large effective (forward) slip…
Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to greatly enhance electrokinetic phenomena. Existing theories assume either homogeneous flat surfaces or patterned surfaces with thin double layers (compared to the texture correlation length) and thus predict simple surface-averaged, isotropic flows (independent of orientation). By analyzing electro-osmotic flows over striped slip-stick surfaces with arbitrary double-layer thickness, we show that surface anisotropy generally leads to a tensorial electro-…
A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and super-hydrophobic surfaces display strong drag-reduction in the laminar regime. Here we consider theoretically a super-hydrophobic surface composed of circular posts (so called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially-dependent strength, we derive the effective surfa…
Liquid slip flow with a Knudsen number Kn = 0.001-0.1 plays a dominant role in confined flow channels. Its physical origin can be attributed to the intermolecular fluid-solid (F-S) interaction force. To this end, we propose herein continuous force functions (decaying either exponentially or by a power law) between fluid particles and two confined flat walls in the framework of the mesoscopic lattice Boltzmann model (LBM). The analytical solutions for density profile, velocity profile, slip length, and permeability ratio are derived and related to the mesoscale F-S interaction parameters and th…
Gas flow and heat transfer in confined geometries at micro and nano scales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. The nonequilibrium effects enhance with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier-Stokes-Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte-Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannel…
On microstructured hydrophobic surfaces, geometrical patterns may lead to the appearance of a superhydrophobic state, where gas bubbles at the surface can have a strong impact on the fluid flow along such surfaces. In particular, they can strongly influence a detected slip at the surface. We present two-phase lattice Boltzmann simulations of a flow over structured surfaces with attached gas bubbles and demonstrate how the detected slip depends on the pattern geometry, the bulk pressure, or the shear rate. Since a large slip leads to reduced friction, our results allow to assist in the optimiza…
The paper addresses the hydrodynamic behavior of a sphere close to a micro-patterned superhydrophobic surface described in terms of alternated no-slip and perfect-slip stripes. Physically, the perfect-slip stripes model the parallel grooves where a large gas cushion forms between fluid and solid wall, giving rise to slippage at the gas-liquid interface. The potential of the boundary element method (BEM) in dealing with mixed no-slip/perfect-slip boundary conditions is exploited to systematically calculate the mobility tensor for different particle-to-wall relative positions and for different p…
Numerical analyses of transient electro-osmosis of a typical non-Newtonian liquid induced by DC and AC electric fields in a rectangular microchannel are conducted in the framework of continuum fluid mechanics. The famous power-law constitutive model is used to express the fluid dynamic viscosity in terms of the velocity gradient. Transient start-up characteristics of electro-osmotic power-law liquid flow in rectangular microchannels are simulated by using finite element method. Under a DC electric field, it is found out and the fluid is more inert to the external electric field and the steady-…
In the CLB method, a Bosanquet-type effective viscosity is employed to account for the rarefaction effect on the gas viscosity. To gain accurate simulations and to match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection boundary scheme with a modified second-order slip boundary condition is adopted in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel (the ratio of the length to the height L/H=100) with pressure boundary condition over a wide range of Knudsen n…
The shape of a microchannel during flow through it is instrumental to understanding the physics that govern various phenomena ranging from rheological measurements of fluids to separation of particles and cells. Two commonly used approaches for obtaining a desired channel shape (for a given application) are (i) fabricating the microchannel in the requisite shape and (ii) actuating the microchannel walls during flow to obtain the requisite shape. However, these approaches are not always viable. We propose an alternative, passive approach to {\it a priori} tune the elastohydrodynamics in a micro…
We study hydrodynamics, heat transfer and entropy generation in pressure-driven microchannel flow of a power-law fluid. Specifically, we address the effect of asymmetry in the slip boundary condition at the channel walls. Constant, uniform but unequal heat fluxes are imposed at the walls in this thermally developed flow. The effect of asymmetric slip on the velocity profile, on the wall shear stress, on the temperature distribution, on the Bejan number profiles, and on the average entropy generation and the Nusselt number are established through the numerical evaluation of exact analytical exp…
Molecular dynamics simulations have been performed to study frictional slip and its influence on energy dissipation and momentum transfer at atomically smooth solid/water interfaces. By modifying surface chemistry, we investigate the relationship between slip and the mechanical response of a vibrating solid for both hydrophilic and hydrophobic surfaces. We discover physical phenomena that emerge at high frequencies and that have significant contributions to energy dissipation. A new analytical model is developed to describe mechanical response of the resonators in this high frequency regime, w…
The influence of the texture of a hydrophobic surface on the electro-osmotic slip of the second kind and the electrokinetic instability near charge-selective surfaces (permselective membranes, electrodes, or systems of micro- and nanochannels) is investigated theoretically using a simple model based on the Rubinstein-Zaltzman approach. A simple formula is derived to evaluate the decrease in the instability threshold due to hydrophobicity. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a hydrophobic membrane surface. Theory predicts a signi…
At finite Reynolds numbers, Re, particles migrate across laminar flow streamlines to their equilibrium positions in microchannels. This migration is attributed to a lift force, and the balance between this lift and gravity determines the location of particles in channels. Here we demonstrate that velocity of finite-size particles located near a channel wall differs significantly from that of an undisturbed flow, and that their equilibrium position depends on this, referred to as slip velocity, difference. We then present theoretical arguments, which allow us to generalize expressions for a lif…
We experimentally explore pressure-driven flow of water and n-hexane across nanoporous silica (Vycor glass monoliths with 7 or 10 nm pore diameters, respectively) as a function of temperature and surface functionalization (native and silanized glass surfaces). Hydraulic flow rates are measured by applying hydrostatic pressures via inert gases (argon and helium, pressurized up to 70 bar) on the upstream side in a capacitor-based membrane permeability setup. For the native, hydrophilic silica walls, the measured hydraulic permeabilities can be quantitatively accounted for by bulk fluidity provid…
We consider the effective hydrophobicity of a periodically grooved surface immersed in liquid, with trapped shear-free bubbles protruding between the no-slip ridges at a $π/2$ contact angle. Specifically, we carry out a singular-perturbation analysis in the limit $ε\ll1$ where the bubbles are closely spaced, finding the effective slip length (normalised by the bubble radius) for longitudinal flow along the the ridges as $π/{\sqrt{2ε}}-(12/π)\ln 2 + (13π/24)\sqrt{2ε}+ o(\sqrtε)$, the small parameter $ε$ being the planform solid fraction. The square-root divergence highlights the strong hydropho…
Compact and small-scale heat exchangers can handle high heat dissipation rates due to their large surface area to volume ratios. Applications involving high heat dissipation rates include, but are not limited to, compact microelectronic processing units, high power laser arrays, fuel cells, as well as fission batteries. Low maintenance cost, small size and dimensions, as well as high convective heat transfer coefficients, make micro-scale heat sinks an efficient and reliable cooling solution for applications with high heat dissipation rates. Despite these advantages, the large pressure drop th…
In this Letter, the falling of super-hydrophobic spheres is investigated experimentally at low Reynolds numbers. In particular, we show that super-hydrophobic coatings become ineffective at reducing drag unlike predicted by theoretical and numerical approaches. A time scale analysis describing both Marangoni-induced stresses and air/liquid interface deformation shows that these mechanisms are unlikely to account for the slippage effect disappearance observed in our study. Instead, we propose a simple model based on an isotropic porous medium approach, derived to account for losses induced by t…
We consider the flow of a Newtonian fluid in a nano or microchannel with walls that have patterned variations in slip length. We formulate a set of equations to describe the effects on an incompressible Newtonian flow of small variations in slip, and solve these equations for slow flows. We test these equations using molecular dynamics simulations of flow between two walls which have patterned variations in wettability. Good qualitative agreement and a reasonable degree of quantitative agreement is found between the theory and the molecular dynamics simulations. The results of both analyses sh…
The interaction of rarefied gases with functionalized surfaces is of great importance in technical applications such as gas separation membranes and catalysis. To investigate the influence of functionalization and rarefaction on gas flow rate in a defined geometry, pressure-driven gas flow experiments with helium and carbon dioxide through plain and alkyl-functionalized microchannels are performed. The experiments cover Knudsen numbers from 0.01 to 200 and therefore the slip flow regime up to free molecular flow. To minimize the experimental uncertainty which is prevalent in micro flow experim…
Experimental two-phase invasion percolation flow patterns were observed in hydrophobic micro-porous networks designed to model fuel cell specific porous media. In order to mimic the operational conditions encountered in the porous electrodes of polymer electrolyte membrane fuel cells (PEMFCs), micro-porous networks were fabricated with corresponding microchannel size distributions. The inlet channels were invaded homogeneously with flow rates corresponding to fuel cell current densities of 1.0 to 0.1 A/cm2 (Ca 10e-7-10e-8). A variety of fractal breakthrough patterns were observed and analyzed …
Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for …
Symmetric drainage flow of a compressible fluid from a fracture modeled as a long narrow channel is studied on the basis of linearized compressible Navier-Stokes equations with no-slip condition. The Helmholtz decomposition theorem is used to decompose the velocity field into an irrotational part and a solenoidal part. The irrotational velocity is driven by the fluid's volumetric expansion whilst the role of the solenoidal velocity is to enforce the no-slip condition for the overall velocity and it does not contribute to the mass flow rate. It is found that at large times this no-slip flow exh…
This paper studies the nature of the effective velocity boundary conditions for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that, to lowest order in the area fraction $β$ covered by free-slip regions with characteristic size $a$, a macroscopic Navier-type slip condition emerges with a slip length of the order of $aβ$. The study is motivated by recent experiments which suggest that gas nano-bubbles may form on solid walls and may be responsible for the appearance of a partial slip boundary conditions for liquid flow. The results are a…
We discuss how the wettability and roughness of a solid impacts its hydrodynamic properties. We see in particular that hydrophobic slippage can be dramatically affected by the presence of roughness. Owing to the development of refined methods for setting very well-controlled micro- or nanotextures on a solid, these effects are being exploited to induce novel hydrodynamic properties, such as giant interfacial slip, superfluidity, mixing, and low hydrodynamic drag, that could not be achieved without roughness.
The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been know that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential…
Super Hydrophobic (SH) coatings are widely used to mitigate drag in various applications. Numerous studies have demonstrated that the beneficial wall-slip effect produced by these materials disappears in laminar flow regimes. The main mechanisms considered to be behind the decrease in performance are Marangoni-induced stresses and air/liquid interface deformation. In the present study, a new mechanism is proposed to explain the loss of performances of SH-surfaces in laminar flow regimes. Here we consider the flow of air inside the plastron and the associated momentum loses induced by roughness…
The composite torsional ultrasonic oscillator, a versatile experimental system, can be used to investigate slip of Newtonian fluid at a smooth surface. A rigorous analysis of slip-dependent damping for the oscillator is presented. Initially, the phenomenon of finite surface slip and the slip length are considered for a half-space of Newtonian fluid in contact with a smooth, oscillating solid surface. Definitions are revisited and clarified in light of inconsistencies in the literature. We point out that, in general oscillating flows, Navier's slip length b is a complex number. An intuitive vel…
