Beyond the lotus effect: roughness influences on wetting over a wide surface-energy range

To enhance our understanding of liquids in contact with rough surfaces, a systematic study has been carried out in which water contact angle measurements were performed on a wide variety of rough surfaces with precisely controlled surface chemistry. Surface morphologies consisted of sandblasted glass slides as well as replicas of acid-etched, sandblasted titanium, lotus leaves, and photolithographically manufactured golf-tee shaped micropillars (GTMs). The GTMs display an extraordinarily stable, Cassie-type hydrophobicity, even in the presence of hydrophilic surface chemistry. Due to pinning effects, contact angles on hydrophilic rough surfaces are shifted to more hydrophobic values, unless roughness or surface energy are such that capillary forces become significant, leading to complete wetting. The observed hydrophobicity is thus not consistent with the well-known Wenzel equation. We have shown that the pinning strength of a surface is independent of the surface chemistry, provided that neither capillary forces nor air enclosure are involved. In addition, pinning strength can be described by the axis intercept of the cosine-cosine plot of contact angles for rough versus flat surfaces with the same surface chemistries.     

Roughness effects of cellulose and paper substrates on water drop impact and recoil

The impact dynamics of water drops on sized and unsized smooth cellulose films and paper surfaces with controlled roughness levels were studied. The objective was to better understand the effect of roughness on the liquid drop impact dynamics on paper surfaces, isolating from the effect chemical heterogeneity. Drop impact in the first few milliseconds were recorded using high-speed CCD camera and the three-phase contact line movement of the water drop was analyzed. Smooth cellulose film surface and rough paper surface showed similar impact dynamics, suggesting that the surface energy plays a more dominant role than surface roughness. Significantly different dynamic contact angles of water drop on the sized and unsized surfaces were observed during drop impact. The Laplace pressure of the curved spreading front pointing to the centre of a spreading drop on these sized cellulose and paper surfaces reduces the three-phase contact line movement, and leads to smaller maximum spreading diameter. Our results suggest that the water drop spreads on the rough surface is most likely via a “roll-over” action rather than “stick and jump” movements.     

Influence of surface roughness on dispersion forces

Surface roughness occurs in a wide variety of processes where it is both difficult to avoid and control. When two bodies are separated by a small distance the roughness starts to play an important role in the interaction between the bodies, their adhesion, and friction. Control of this short-distance interaction is crucial for micro and nanoelectromechanical devices, microfluidics, and for micro and nanotechnology. An important short-distance interaction is the dispersion forces, which are omnipresent due to their quantum origin. These forces between flat bodies can be described by the Lifshitz theory that takes into account the actual optical properties of interacting materials. However, this theory cannot describe rough bodies. The problem is complicated by the nonadditivity of the dispersion forces. Evaluation of the roughness effect becomes extremely difficult when roughness is comparable with the distance between bodies. In this paper we review the current state of the problem. Introduction for non-experts to physical origin of the dispersion forces is given in the paper. Critical experiments demonstrating the nonadditivity of the forces and strong influence of roughness on the interaction between bodies are reviewed. We also describe existing theoretical approaches to the problem. Recent advances in understanding the role of high asperities on the forces at distances close to contact are emphasized. Finally, some opinions about currently unsolved problems are also presented.     

Generalization of Kelvin's equation for compressible liquids in nanoconfinement

The Kelvin equation for a compressible liquid in nanoconfinement is written in a form that takes into account not only Laplace's pressure, but also the oscillatory compression pressure. This leads to a simple analytical equation for pressure in nanocapillaries. The corrected equation is used to analyze properties of aqueous systems, including the oscillatory structural forces between attractive surfaces and inert surfaces, repulsive "hydration" forces between hydrophilic surfaces, and attractive "hydrophobic" forces between hydrophobic surfaces. Relative vapor pressure in a nanocapillary also is discussed.     

A generalized analysis of capillary flows in channels

Investigations on the motion of a fluid in capillary geometries have been extensively reported in the literature using both experimental and theoretical approaches. In this paper, the theories for capillary flow are generalized to a unified nonlinear second-order differential equation which takes the effects of the entrance, the inertial forces, and the dynamic contact angle into account. An analytical solution of the differential equation is obtained in the form of a double Dirichlet series. The readily evaluated analytical solution is compared with experimental and numerical results in the literature, which shows a good agreement. It is demonstrated that this analytical approach can be used to predict capillary flows for a wide range of fluids and parallel-plate and tube geometries in a unified manner.     

Wagging the contact line: transverse and longitudinal waves

Kinetics of wetting has been explored where the contact line not only sees a steady spreading but also has longitudinal or transverse oscillations imposed on it. The latter case is realized when spreading takes place over a rough surface. The effects of the imposed motion are small, which seem to be due to low spreading rates and small dynamic contact angles used in this study. However, a singularity is seen in viscous dissipation during the movement on the model rough surface, which is interpreted here as an instability that is similar to Haines' jumps and stick-slip phenomena, with possible entrainment of the displaced fluid. This is the first time that all of these have been associated with each other.     

Friction and adhesion forces of Bacillus thuringiensis spores on planar surfaces in atmospheric systems

The kinetic friction force and the adhesion force of Bacillus thuringiensis spores on planar surfaces in atmospheric systems were studied using atomic force microscopy. The influence of relative humidity (RH) on these forces varied for different surface properties including hydrophobicity, roughness, and surface charge. The friction force of the spore was greater on a rougher surface than on mica, which is atomically flat. As RH increases, the friction force of the spores decreases on mica whereas it increases on rough surfaces. The influence of RH on the interaction forces between hydrophobic surfaces is not as strong as for hydrophilic surfaces. The friction force of the spore is linear to the sum of the adhesion force and normal load on the hydrophobic surface. The poorly defined surface structure of the spore and the adsorption of contaminants from the surrounding atmosphere are believed to cause a discrepancy between the calculated and measured adhesion forces.     

Plasma-based processes for surface wettability modification

In this article, we describe a method to create rough features on silicon surfaces by reactive etching of a photoresist layer. The roughness and, consequently, the wettability of the surfaces can be modified by modifying the duration of plasma etching. Hydrophobic materials deposited on the rough silicon surface can be modified until a superhydrophobic behavior is obtained, whereas hydrophilic materials become more hydrophilic. The elaboration technique described herein offers an inexpensive and rapid method for the creation of tunable roughness on silicon surfaces with large areas.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Friction and Adhesion of Gecko-Inspired PDMS Flaps on Rough Surfaces

Geckos have developed a unique hierarchical structure to maintain climbing ability on surfaces with different roughness, one of the extremely important parameters that affect the friction and adhesion forces between two surfaces. Although much attention has been paid on fabricating various structures that mimic the hierarchical structure of a gecko foot, yet no systematic effort, in experiment or theory, has been made to quantify the effect of surface roughness on the performance of the fabricated structures that mimic the hierarchical structure of geckos. Using a modified surface forces apparatus (SFA), we measured the adhesion and friction forces between microfabricated tilted PDMS flaps and optically smooth SiO(2) and rough SiO(2) surfaces created by plasma etching. Anisotropic adhesion and friction forces were measured when sliding the top glass surface along (+y) and against (-y) the tilted direction of the flaps. Increasing the surface roughness first increased the adhesion and friction forces measured between the flaps and the rough surface due to topological matching of the two surfaces but then led to a rapid decrease in both of these forces. Our results demonstrate that the surface roughness significantly affects the performance of gecko mimetic adhesives and that different surface textures can either increase or decrease the adhesion and friction forces of the fabricated adhesives.     

Wettability of clean metal surfaces

Experimental and theoretical investigations bearing on the question of the wettability, by water, of clean oxygen-free metal surfaces are reviewed. Results on gold, silver, and copper are discussed in terms of surface cleanliness, surface structure, and extent of dispersion (London) force interaction. It is concluded that clean solid metal surfaces are hydrophilic. They will yield a zero degree contact angle when prepared in the amorphous state and possibly in the perfect crystalline state as well. These results do not necessarily preclude the possibility that physical interaction at the metal-water interface consists solely of dispersion forces.     

Nanodrop on a nanorough solid surface: density functional theory considerations

The density distributions and contact angles of liquid nanodrops on nanorough solid surfaces are determined on the basis of a nonlocal density functional theory. Two kinds of roughness, chemical and physical, are examined. The former considers the substrate as a sequence of two kinds of semi-infinite vertical plates of equal thicknesses but of different natures with different strengths for the liquid-solid interactions. The physical roughness involves an ordered set of pillars on a flat homogeneous surface. Both hydrophobic and hydrophilic surfaces were considered. For the chemical roughness, the contact angle which the drop makes with the flat surface increases when the strength of the liquid-solid interaction for one kind of plates decreases with respect to the fixed value of the other kind of plates. Such a behavior is in agreement with the Cassie-Baxter expression derived from macroscopic considerations. For the physical roughness on a hydrophobic surface, the contact angle which a drop makes with the plane containing the tops of the pillars increases with increasing roughness. Such a behavior is consistent with the Wenzel formula developed for macroscopic drops. For hydrophilic surfaces, as the roughness increases the contact angle first increases, in contradiction with the Wenzel formula, which predicts for hydrophilic surfaces a decrease of the contact angle with increasing roughness. However, a further increase in roughness changes nonmonotonously the contact angle, and at some roughness, the drop disappears and only a liquid film is present on the surface. It was also found that the contact angle has a periodic dependence on the volume of the drop.     

Three- and two-dimensional effects in wetting kinetics

Wetting at equilibrium is reviewed in brief, and it is then suggested that a wider class of nonequilibrium problems can exist where an equilibrium-like behaviour is reached simply because the mechanisms for spreading are suppressed.The mechanisms of spreading are reviewed to suggest that experiments of wetting kinetics of liquids with varying volatilities on mica would lead to interesting results. Such experiments were conducted and the results are supportive of the models. It was also observed that when volatility and surface roughness, two important mechanisms of spreading, are removed, the drop motion presumed to be controlled by surface diffusion at the contact line virtually ceases, although scanning electron microscopy results show that they are indeed moving.The role of films of ultra-low thicknesses are examined. It is seen that the dynamics of molecular scale droplets are understandable, and can be modelled in many ways, and the features these moving molecular scale drops exhibit can in some cases affect the movement of microscale drops as well.We are able to identify and define two- and three-dimensional volatilities and mobilities that help one to classify the spreading phenomena, as far as the liquids are concerned. The surfaces can be smooth or rough, a difference that has a strong effect.     

On the adhesion between fine particles and nanocontacts: an atomic force microscope study

In this study we measured the adhesion forces between atomic force microscope (AFM) tips or particles attached to AFM cantilevers and different solid samples. Smooth and homogeneous surfaces such as mica, silicon wafers, or highly oriented pyrolytic graphite, and more rough and heterogeneous surfaces such as iron particles or patterns of TiO2 nanoparticles on silicon were used. In the first part, we addressed the well-known issue that AFM adhesion experiments show wide distributions of adhesion forces rather than a single value. Our experiments show that variations in adhesion forces comprise fast (i.e., from one force curve to the next) random fluctuations and slower fluctuations, which occur over tens or hundreds of consecutive measurements. Slow fluctuations are not likely to be the result of variations in external factors such as lateral position, temperature, humidity, and so forth because those were kept constant. Even if two solid bodies are brought into contact under precisely the same conditions (same place, load, direction, etc.) the result of such a measurement will often not be the same as that of the previous contact. The measurement itself will induce structural changes in the contact region, which can change the value for the next adhesion force measurement. In the second part, we studied the influence of humidity on the adhesion of nanocontacts. Humidity was adjusted relatively fast to minimize tip wear during one experiment. For hydrophobic surfaces, no signification change in adhesion force with humidity was observed. Adhesion force versus humidity curves recorded with hydrophilic surfaces either showed a maximum or continuously increased. We demonstrate that the results can be interpreted with simple continuum theory of the meniscus force. The meniscus force is calculated based on a model that includes surface roughness and takes into account different AFM tip (or particle) shapes by a two-sphere model. Experimental and theoretical results show that the precise contact geometry has a critical influence on the humidity dependence of the adhesion force. Changes in tip geometry on the sub-10-nm length scale can completely change adhesion force versus humidity curves. Our model can also explain the differences between earlier AFM studies, where different dependencies of the adhesion force on humidity were observed.     

A review of the role of wetting and spreading phenomena on the flotation practice

Wetting and spreading phenomena are the most important parameters for understanding of froth flotation practice. The wetting and spreading of fluids on the solid surface should be considered in the high efficiency flotation process. These phenomena involve surface tension forces, contact line dynamics, surface roughness and heterogeneity, contact angles, bubble–particle interactions and other factors. This review highlights the various concepts of contact angles and well-known equations in this respect and compares these equations. Based on this review, flotation selectivity and efficiency are highly dependent on solid–liquid contact angles and collision, collection, attachment, and stability efficiency could be predicted by wetting and spreading roles. In order to control flotation performance, efforts should be made to determine wetting characteristic of the flotation process. It is imperative that an improved understanding of wetting and spreading phenomena in the phase's interfaces will provide an improved and efficient flotation practice. It is proposed that future research should focus on the scientific and engineering aspect of wetting and spreading phenomena on flotation and on the development of a method to enhance flotation performance by controlling these phenomena.     

The surface tension of a solid at the solid-vacuum interface, an evaluation from adsorption and wall potential calculations

A method for the evaluation of quantities that are experimentally inaccessible such as the surface tension at the solid-vacuum interface and the superficial tension of the fluid in contact with the solid is presented. The approach is based on consideration of an equilibrium of a fluid in solid capillary wherein a balance between surface and capillary forces has been replaced by conceptual alternative interfacial and centrifugal forces. This approach involves the simultaneous numerical solution one the special forms of the Gibbs equation for solid-fluid interface and a generalized Kelvin equation derived earlier. The latter equation takes into account interactions between the solid thick cylindrical wall and confined fluid, this body-body interaction potential has been primarily calculated using the Lennard-Jones (6-12) expression for the atom-atom pair potentials and expressed by hypergeometrical functions having good convergences. All numerical calculations shown here have been performed for the model graphite-argon system at 90 K. Finally, an analysis of the accuracy of the proposed method is considered.     

The Molecular Spreading of Nonpolar Perfluoropolyether Films on Amorphous Carbon Surfaces

The spreading mechanism of nonpolar perfluoropolyether films on carbon surfaces is examined in the mesoscopic regime, including both submonolayer and multilayer films. For the submonolayer film, adsorption-desorption is a main mechanism for spreading, and the surface diffusion coefficients increase as the film thickness increases. The driving force for the spreading in the submonolayer regime is the gradient of the disjoining pressure, which is described by the two-dimensional virial equation. For the multilayer film regime, the spreading characteristics are determined by the molecular weight and the disjoining pressure gradient, which is assumed to be purely van der Waals in nature. We adopt a partial slip boundary condition to analyze the multilayer film, which qualitatively explains the dependence of the surface diffusion coefficient on film thickness. Copyright 2000 Academic Press.     

The Neumann and Young equations for nematic contact lines

The Neumann and Young equations for three-phase nematic contact lines have been derived using the momentum balance equation and classical liquid crystal physics theories. The novel finding is the presence of bending forces, originating from the anchoring energy of nematic interfaces, and acting on the contact line. The classical Neumann triangle or tensile force balance becomes in the presence of a nematic phase the Neumann pentagon, involving the usual three tensile forces and two additional bending forces. The Young equation that describes the static contact angle of a fluid in contact with a rigid solid is again a tensile force balance along the solid, but for nematics it also involves an additional bending force. The effects of the bending forces on contact angles and wetting properties of nematic liquid crystals are thoroughly characterized. It is found that in terms of the spreading coefficient, bending forces enlarge the partial wetting window that exists between dewetting and spontaneous spreading. Bending forces also affect the behaviour of the contact angle, such that spreading occurs at contact angles greater than zero and dewetting at values greater than pi. Finally, the contact angle range in the partial wetting regime is always less than pi.     

The Neumann and Young equations for nematic contact lines

The Neumann and Young equations for three-phase nematic contact lines have been derived using the momentum balance equation and classical liquid crystal physics theories. The novel finding is the presence of bending forces, originating from the anchoring energy of nematic interfaces, and acting on the contact line. The classical Neumann triangle or tensile force balance becomes in the presence of a nematic phase the Neumann pentagon, involving the usual three tensile forces and two additional bending forces. The Young equation that describes the static contact angle of a fluid in contact with a rigid solid is again a tensile force balance along the solid, but for nematics it also involves an additional bending force. The effects of the bending forces on contact angles and wetting properties of nematic liquid crystals are thoroughly characterized. It is found that in terms of the spreading coefficient, bending forces enlarge the partial wetting window that exists between dewetting and spontaneous spreading. Bending forces also affect the behaviour of the contact angle, such that spreading occurs at contact angles greater than zero and dewetting at values greater than pi. Finally, the contact angle range in the partial wetting regime is always less than pi.     

Capillary rise of liquids over a microstructured solid surface

The location of the triple line as a function of time has been recorded for a series of organic liquids, with various surface tension to viscosity ratios, wicking upward a rough Cu(6)Sn(5)/Cu intermetallic (IMC) substrate. The complex topographical features of such an IMC rough surface are characterized by surface porosity and surface roughness. A theoretical model for wicking upward a rough surface has been established by treating the rough IMC surface as a two-dimensional porous medium featuring a network of open microtriangular grooves. The model is verified against experimental data. The study confirms that the kinetics of capillary rise of organic liquids in a nonreactive flow regime over a porous surface having arbitrary but uniformly distributed topographical features involves (i) surface topography metrics (i.e., permeability, tortuosity/porosity, and geometry of the microchannel cross section); (ii) wicking features (i.e., contact angle and filling factor); and (iii) physical properties of liquids (i.e., surface tension and viscosity). An excellent agreement between theoretical predictions and experimentally obtained data proves, for a selected filling factor η, validity of the analytically established model. Scaled data sets show that, for a given rough surface topography, (i) wicking kinetics of considered liquids depend on properties of liquids, that is, surface tension to viscosity ratios and contact angles; (ii) the filling factor for all tested liquids is an invariant, offering good prediction within the range of ~0.9-1.0. The distance of the wicking front versus square root of time relationship was well established throughout the whole considered wicking evolution time.