Roughness induced boundary slip in microchannel flows

High-Pressure CO2 and CH4 Transport in Smooth Crystalline Silica Mesopores: A Molecular Dynamics Study

In this study, we use molecular dynamics (MD) simulation to study pressure-driven CO2 and CH4 flows and their slippage behaviors in β-cristobalite mesopores. The result illustrates that both CO2 and CH4 have an apparent adsorption layer on pore surface. However, significant differences in gas slippage are observed: CH4 flow shows considerable slippage, while it is negligible for CO2 flow. This disparity is attributed to the collective effect of gas molecular configurations and surface structure. The linear molecular structure of CO2 allows it to align perpendicular to the surface, even penetrating into the surface. Notably, the perpendicular orientation of CO2 molecules is energetically favored near the center of the equilateral triangle formed by adjacent oxygen atoms on β-cristobalite surface. Conversely, the symmetric molecular structure of CH4, coupled with its larger size, prevents its penetration into pore surfaces. Therefore, despite smooth crystalline surfaces, CO2 topological accessible plane is much more curved than that of CH4. Consequently, CO2 displays hesitating motions undergoing rotational movements, which significantly hinders its slippage. This study highlights the collective influences of gas molecular characteristics and surface structure on gas slippage, affording important insights into gas sequestration and the development of functional materials for gas separation.

Multiscale analysis of the particles on demand kinetic model

We present a thorough investigation of the particles on demand kinetic model. After a brief introduction of the method, an appropriate multiscale analysis is carried out to derive the hydrodynamic limit of the model. In this analysis, the effect of the time-space dependent comoving reference frames are taken into account. This could be regarded as a generalization of the conventional Chapman-Enskog analysis applied to the lattice Boltzmann models which feature global constant reference frames. Further simulations of target benchmarks provide numerical evidence confirming the theoretical predictions.

A review on slip boundary conditions at the nanoscale: recent development and applications

The slip boundary condition for nanoflows is a key component of nanohydrodynamics theory, and can play a significant role in the design and fabrication of nanofluidic devices. In this review, focused on the slip boundary conditions for nanoconfined liquid flows, we firstly summarize some basic concepts about slip length including its definition and categories. Then, the effects of different interfacial properties on slip length are analyzed. On strong hydrophilic surfaces, a negative slip length exists and varies with the external driving force. In addition, depending on whether there is a true slip length, the amplitude of surface roughness has different influences on the effective slip length. The composition of surface textures, including isotropic and anisotropic textures, can also affect the effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed.

Unexpected Frictional Behavior of Laser-Textured Hydrophobic Surfaces

Hydrophobic surfaces can allow a liquid to slip over the surface and can thus reduce friction in lubricated contact working in a full film regime. Theory supports that the amount of slip can be increased if super-hydrophobic surfaces that are composed of a textured low surface energy material are used. In this work, polytetrafluoroethylene (PTFE) polymer samples were textured with a femto second laser to create super-hydrophobic surfaces by machining a hexagonal network of small circular holes with 10 and 20 μm lattice sides. The frictional behavior of these surfaces was compared to the smooth PTFE samples. Surprisingly, the textured surfaces revealed higher friction coefficients than the smooth surfaces. This higher friction can be explained by a change of wetting regime due to high pressure in fluid and a possible generation of vortices in the cavities.

Kinetic Simulations of Compressible Non-Ideal Fluids: From Supercritical Flows to Phase-Change and Exotic Behavior

We investigate a kinetic model for compressible non-ideal fluids. The model imposes the local thermodynamic pressure through a rescaling of the particle’s velocities, which accounts for both long- and short-range effects and hence full thermodynamic consistency. The model is fully Galilean invariant and treats mass, momentum, and energy as local conservation laws. The analysis and derivation of the hydrodynamic limit is followed by the assessment of accuracy and robustness through benchmark simulations ranging from the Joule–Thompson effect to a phase-change and high-speed flows. In particular, we show the direct simulation of the inversion line of a van der Waals gas followed by simulations of phase-change such as the one-dimensional evaporation of a saturated liquid, nucleate, and film boiling and eventually, we investigate the stability of a perturbed strong shock front in two different fluid mediums. In all of the cases, we find excellent agreement with the corresponding theoretical analysis and experimental correlations. We show that our model can operate in the entire phase diagram, including super- as well as sub-critical regimes and inherently captures phase-change phenomena.

Particles on Demand for Kinetic Theory

A novel formulation of fluid dynamics as a kinetic theory with tailored, on-demand constructed particles removes restrictions on flow speed and temperature as compared to its predecessors, the lattice Boltzmann methods and their modifications. In the new kinetic theory, discrete particles are determined by a rigorous limit process which avoids ad hoc assumptions about their velocities. Classical benchmarks for incompressible and compressible flows demonstrate that the proposed discrete-particles kinetic theory opens up an unprecedented wide domain of applications for computational fluid dynamics.

Wall slip for complex liquids - Phenomenon and its causes

In this review, we tried to qualify different types and mechanisms of wall slip phenomenon, paying particular attention to the most recent publications and issues. The review covers all type of fluids - homogeneous low molecular weight liquids, polymer solution, multi-component dispersed media, and polymer melts. We focused on two basic concepts - fluid-solid wall interaction and shear-induced fluid-to-solid transitions - which are the dominant mechanisms of wall slip. In the first part of the review, the theoretical and numerical studies of correlation of wetting properties and wall slip of low molecular weight liquids and polymeric fluids are reviewed along with some basic experimental results. The influence of nanobubbles and microcavities on the effectiveness of wall slip is illuminated with regard to the bubble dynamics, as well as their stability at smooth and rough interfaces, including superhydrophobic surfaces. Flow of multi-component matter (microgel pastes, concentrated suspensions of solid particles, compressed emulsions, and colloidal systems) is accompanied by wall slip in two cases. The first one is typical of viscoplastic media which can exist in two different physical states, as solid-like below the yield point and liquid-like at the applied stresses exceeding this threshold. Slip takes place at low stresses. The second case is related to the transition from fluid to solid states at high deformation rates or large deformations caused by the strain-induced glass transition of concentrated dispersions. In the latter case, the wall effects consist of apparent slip due to the formation of a low viscous thin layer of fluid at the wall. The liquid-to-solid transition is also a dominant mechanism in wall slip of polymer melts because liquid polymers are elastic fluids which can be in two relaxation states depending on the strain rate. The realization of these mechanisms is determined by polymer melt interaction with the solid wall.

Interface conditions of roughness-induced superoleophilic and superoleophobic surfaces immersed in hexadecane and ethylene glycol

Interface conditions are an important property that can affect the drag of fluid flow. For surfaces with different oleophobicity, the boundary slip at the solid-oil interface is mostly larger than that at the solid-water interface. Roughness is a key factor for the wettability of superoleophilic/superoleophobic surfaces, and it has been found to affect the effective value of slip length in measurements. Moreover, there are no studies on the effect of roughness on slip at interfaces between oil and superoleophilic/superoleophobic surfaces. A theoretical description of the real surface roughness is yet to be found. Results show that the effective slip length is negative and decreases with an increasing root mean squared (RMS) roughness of surfaces, as the increasing roughness enhances the area with discontinuous slip at the solid-liquid interface. The underlying mechanisms are analyzed. The amplitude parameters of surface roughness could significantly inhibit the degree of boundary slip on both superoleophilic surfaces in Wenzel state and superoleophobic surfaces in Cassie state immersed in oil. The oleic systems were likely to enhance boundary slip and resulted in a corresponding reduction in drag with decreasing roughness on the solid-oil interfaces.

Droplet Transport in a Nanochannel Coated by Hydrophobic Semiflexible Polymer Brushes: The Effect of Chain Stiffness

We study the influence of chain stiffness on droplet flow in a nanochannel, coated with semiflexible hydrophobic polymers by means of nonequilibrium molecular dynamics simulations. The studied system is then a moving droplet in the slit channel, coexisting with its vapor and subjected to periodic boundary conditions in the flow direction. The polymer chains, grafted by the terminal bead to the confining walls, are described by a coarse-grained model that accounts for chain connectivity, excluded volume interactions and local chain stiffness. The rheological, frictional and dynamical properties of the brush are explored over a wide range of persistence lengths. We find a rich behavior of polymer conformations and concomitant changes in the friction properties over the wide range of studied polymer stiffnesses. A rapid decrease in the droplet velocity was observed as the rigidity of the chains is increased for polymers whose persistence length is smaller than their contour length. We find a strong relation between the internal dynamics of the brush and the droplet transport properties, which could be used to tailor flow properties by surface functionalization. The monomers of the brush layer, under the droplet, present a collective "treadmill belt" like dynamics which can only be present due the existence of grafted chains. We describe its changes in spatial extension upon variations of polymer stiffness, with bidimensional velocity and density profiles. The deformation of the polymer brushes due to the presence of the droplet is analyzed in detail. Lastly, the droplet-gas interaction is studied by varying the liquid to gas ratio, observing a 16% speed increase for droplets that flow close to each other, compared to a train of droplets that present a large gap between consecutive droplets.

Study of the Relationship between Boundary Slip and Nanobubbles on a Smooth Hydrophobic Surface

Surface nanobubbles, which are nanoscopic or microscopic gaseous domains forming at the solid/liquid interface, have a strong impact on the interface by changing the two-phase contact to a three-phase contact. Therefore, they are believed to affect the boundary condition and liquid flow. However, there are still disputes in the theoretical studies as to whether the nanobubbles can increase the slip length effectively. Furthermore, there are still no direct experimental studies to support either side. Therefore, an intensive study on the effective slip length for flows over bare surfaces with nanobubbles is essential for establishing the relation between nanobubbles and slip length. Here, we study the effect of nanobubbles on the slippage experimentally and theoretically. Our experimental results reveal an increase from 8 to 512 nm in slip length by increasing the surface coverage of nanobubbles from 1.7 to 50.8% and by decreasing the contact angle of nanobubbles from 42.8 to 16.6°. This is in good agreement with theoretical results. Our results indicate that nanobubbles could always act as a lubricant and significantly increase the slip length. The surface coverage, height, and contact angle are key factors for nanobubbles to reduce wall friction.

Lattice Kinetic Theory in a Comoving Galilean Reference Frame

We prove that the fully discrete lattice Boltzmann method is invariant with respect to Galilean transformation. Based on this finding, a novel class of shifted lattices is proposed which dramatically increases the operating range of lattice Boltzmann simulations, in particular, for gas dynamics applications. A simulation of vortex-shock interaction is used to demonstrate the accuracy and efficiency of the proposed lattices. With one single algorithm it is now possible to simulate a broad range of applications, from low Mach number flows to transonic and supersonic flow regimes.

Numerical simulation of gas flow and heat transfer in a rough microchannel using the lattice Boltzmann method

In microfluidics, two important factors responsible for the differences between the characteristics of the flow and heat transfer in microchannels and conventional channels are rarefaction and surface roughness which are studied in the present work. An incompressible gas flow in a microchannel is simulated two dimensionally using the lattice Boltzmann method. The flow is in the slip regime and surface roughness is modeled by both regular and Gaussian random distribution of rectangular modules. The effects of relative surface roughness height and Knudsen number on gaseous flow and heat transfer are studied. It was shown that as the relative roughness height increases, the Poiseuille number increases and the Nusselt number has a decreasing or increasing trend, depending on the degree of rarefaction. A comparison between the flow and heat transfer characteristics in regular and random distribution of surface roughness demonstrates that in regular roughness, circular flows are more pronounced; Poiseuille number is higher and Nusselt number is lower than that of its equivalent random roughness.

Interfacial slip on rough, patterned and soft surfaces: a review of experiments and simulations

Advancements in the fabrication of microfluidic and nanofluidic devices and the study of liquids in confined geometries rely on understanding the boundary conditions for the flow of liquids at solid surfaces. Over the past ten years, a large number of research groups have turned to investigating flow boundary conditions, and the occurrence of interfacial slip has become increasingly well-accepted and understood. While the dependence of slip on surface wettability is fairly well understood, the effect of other surface modifications that affect surface roughness, structure and compliance, on interfacial slip is still under intense investigation. In this paper we review investigations published in the past ten years on boundary conditions for flow on complex surfaces, by which we mean rough and structured surfaces, surfaces decorated with chemical patterns, grafted with polymer layers, with adsorbed nanobubbles, and superhydrophobic surfaces. The review is divided in two interconnected parts, the first dedicated to physical experiments and the second to computational experiments on interfacial slip of simple (Newtonian) liquids on these complex surfaces. Our work is intended as an entry-level review for researchers moving into the field of interfacial slip, and as an indication of outstanding problems that need to be addressed for the field to reach full maturity.

Thermal slip for liquids at rough solid surfaces

Molecular dynamics simulation is used to examine the thermal slip of liquids at rough solid surfaces as characterized by fractal Cantor structures. The temperature profiles, potential energy distributions, thermal slip, and interfacial thermal resistance are investigated and evaluated for a variety of surface topographies. In addition, the effects of liquid-solid interaction, surface stiffness, and boundary condition on thermal slip length are presented. Our results indicate that the presence of roughness expands the low potential energy regions in adjacent liquids, enhances the energy transfer at liquid-solid interface, and decreases the thermal slip. Interestingly, the thermal slip length and thermal resistance for liquids in contact with solid surfaces depends not only on the statistical roughness height, but also on the fractal dimension (i.e., topographical spectrum).

Effective slip-length tensor for a flow over weakly slipping stripes

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, b(y), is assumed to be small compared to the scale of the heterogeneities, L, but finite. For such weakly slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has steplike jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of max[b(y)/L] becomes comparable to the leading-order term, but anisotropic, even at very small b(y)/L. This leads to an anisotropy of the effective slip and to its significant reduction compared to the surface-averaged value. The asymptotic formulas are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.

Friction and slip at the solid/liquid interface in vibrational systems

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 the 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 the mechanical response of the resonators in this high-frequency regime, which is relevant in such applications as microelectromechanical-system-based biosensors. We find a linear relationship between the slip length and the ratio of the damping rate shift to the resonant frequency shift, which provides a new way to obtain information about the slip length from experiments.

Calculation of effective slip on rough chemically heterogeneous surfaces using a homogenization approach

We present an expression for the effective slip length of a nanoscale rough chemically heterogeneous surface. A heterogeneous surface may be regarded as having an effective slip length generated by extrapolating the uniform velocity profile found in the far field. We consider two-dimensional steady-state Stokes flow over a surface that has periodic roughness and an intrinsic slip length varying over the same period. Using weak convergence methods for partial differential equations, we derive an expression for the effective slip length in terms of the intrinsic slip length and contact area of the surface. The result predicts that roughness causes a significant reduction in effective slip and that slip effects are dominated by the minimum intrinsic slip length of the system.

Role of rough surface topography on gas slip flow in microchannels

We conduct a lattice Boltzmann simulation of gas slip flow in microchannels incorporating rough surface effects as characterized by fractal geometry with a focus on gas-solid interaction. The gas slip flow in rough microchannels, which is characterized by Poiseuille number and mass flow rate, is evaluated and compared with smooth microchannels. The effects of roughness height, surface fractal dimension, and Knudsen number on slip behavior of gas flow in microchannels are all investigated and discussed. The results indicate that the presence of surface roughness reduces boundary slip for gas flow in microchannels with respect to a smooth surface. The gas flows at the valleys of rough walls are no-slip while velocity slips are observed over the top of rough walls. We find that the gas flow behavior in rough microchannels is insensitive to the surface topography irregularity (unlike the liquid flow in rough microchannels) but is influenced by the statistical height of rough surface and rarefaction effects. In particular, decrease in roughness height or increase in Knudsen number can lead to large wall slip for gas flow in microchannels.

Effect of molecular structure on liquid slip

Slip behavior of three liquids with distinct molecular shapes--linear (hexadecane), branched (pentaerythritol tetra), and a chain of rings (polyphenylether)--is studied using molecular dynamics simulation and reduced-order modeling. Slip at a liquid-solid interface is shown to be affected by the molecular structure of the liquid. A two-dimensional Frenkel-Kontorova model captures the fundamental structural features of the liquid molecules and gives insight into how molecules flex and slip along the surface. We formulate an approximation to the Peierls-Nabarro energy which incorporates both the position of liquid atoms relative to substrate atoms and molecular flexibility. We find that increased molecular flexibility can lead to reduced slip by allowing the liquid to conform epitaxially to the substrate with only a small energetic penalty. Liquid molecules which are less flexible can conform to the substrate only with greater expense of conformational energy, and so exhibit larger slip.

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (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 predicted to decrease the force as compared with what is expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1, and b2, implies that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of a superhydrophobic surface.

Pinning and avalanches in hydrophobic microchannels

Rare events appear in a wide variety of phenomena such as rainfall, floods, earthquakes, and risk. We demonstrate that the stochastic behavior induced by the natural roughening present in standard microchannels is so important that the dynamics for the advancement of a water front displacing air has plenty of rare events. We observe that for low pressure differences the hydrophobic interactions of the water front with the walls of the microchannel put the front close to the pinning point. This causes a burstlike dynamics, characterized by series of pinning and avalanches, that leads to an extreme-value Gumbel distribution for the velocity fluctuations and a nonclassical time exponent for the advancement of the mean front position as low as 0.38.

Simulations of slip flow on nanobubble-laden surfaces

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 give assistance in the optimization of microchannel flows for large throughput.

Wetting, roughness and flow boundary conditions

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.

Diffusion between evolving interfaces

Diffusion in an evolving environment is studied by continuous-time Monte Carlo simulations. Diffusion is modeled by continuous-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution dominates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, diffusion is found to depend strongly on the details of the dynamical rules of particles close to the interfaces.

Random-roughness hydrodynamic boundary conditions

We report results of lattice Boltzmann simulations of a high-speed drainage of liquid films squeezed between a smooth sphere and a randomly rough plane. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. However, this force reduction does not represent slippage. The computed force is exactly the same as that between equivalent smooth surfaces obeying no-slip boundary conditions, but located at an intermediate position between peaks and valleys of asperities. The shift in hydrodynamic thickness is shown to depend on the height and density of roughness elements. Our results do not support some previous experimental conclusions on a very large and shear-dependent boundary slip for similar systems.

Slip effects in polymer thin films

Probing the fluid dynamics of thin films is an excellent tool for studying the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid, due to the fact that the dewetting process, an internal mechanism, acts as a driving force for liquid flow. Viscous dissipation, within the liquid, and slippage balance interfacial forces. Thus, friction at the solid/liquid interface plays a key role towards the flow dynamics of the liquid. Probing the temporal and spatial evolution of growing holes or retracting straight fronts gives, in combination with theoretical models, information on the liquid flow field and, especially, the boundary condition at the interface. We review the basic models and experimental results obtained during the last several years with exclusive regard to polymers as ideal model liquids for fluid flow. Moreover, concepts that aim to explain slippage on the molecular scale are summarized and discussed.

Front pinning in capillary filling of chemically coated channels

The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven oscillator, an analytical criterion for front pinning is derived under the condition of diluteness of the coating spots. The criterion is tested against two-dimensional lattice Boltzmann simulations and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the chemical coating.

Structured surfaces for a giant liquid slip

We study experimentally how two key geometric parameters (pitch and gas fraction) of textured hydrophobic surfaces affect liquid slip. The two are independently controlled on precisely fabricated microstructures of posts and grates, and the slip length of water on each sample is measured using a rheometer system. The slip length increases linearly with the pitch but dramatically with the gas fraction above 90%, the latter trend being more pronounced on posts than on grates. Once the surfaces are designed for very large slips (>20 microm), however, further increase is not obtained in regular practice because the meniscus loses its stability. By developing near-perfect samples that delay the transition from a dewetted (Cassie) to a wetted (Wenzel) state until near the theoretical limit, we achieve giant slip lengths, as large as 185 microm.

Roughness of microspheres for force measurements

We have investigated the morphology and surface roughness of several commercially available microspheres to determine their suitability for force measurements using the atomic force microscope. The roughness varies considerably, depending on sphere size and material, ranging from nearly ideally flat up to micrometer-sized features. Because surface roughness significantly influences the magnitude and accuracy of measurement of surface forces, the results presented here should be helpful for colloid physicists and in particular for those performing force measurements.

Slip flow over structured surfaces with entrapped microbubbles

On hydrophobic surfaces, roughness may lead to a transition to a superhydrophobic state, where gas bubbles at the surface can have a strong impact on a detected slip. We present two-phase lattice Boltzmann simulations of a Couette flow over structured surfaces with attached gas bubbles. Even though the bubbles add slippery surfaces to the channel, they can cause negative slip to appear due to the increased roughness. The simulation method used allows the bubbles to deform due to viscous stresses. We find a decrease of the detected slip with increasing shear rate which is in contrast to some recent experimental results implicating that bubble deformation cannot account for these experiments. Possible applications of bubble surfaces in microfluidic devices are discussed.

Wetting on nanorough surfaces

We present in this Letter a free-energy approach to the dynamics of a fluid near a nanostructured surface. The model accounts both for the static phase equilibrium in the vicinity of the surface (wetting angles, Cassie-Wenzel transition) and the dynamical properties like liquid slippage at the boundary. This method bridges the gap between phenomenological phase-field approaches and more macroscopic lattice-Boltzmann models.