Partial wetting of chemically patterned surfaces: the effect of drop size

Partial wetting of chemically heterogeneous substrates is simulated. Three-dimensional sessile drops in equilibrium with smooth surfaces supporting ordered chemical patterns are considered. Significant features are observed as a result of changing the drop volume. The number of equilibrated drops is found either to remain constant or to increase with growing drop volume. The shape of larger drops appears to approach that of a spherical cap and their three-phase contact line seems, on a larger scale, more circular in shape than that of smaller drops. In addition, as the volume is increased, the average contact angle of drops whose free energy is lowest among all equilibrium-shaped drops of the same volume appears to approach the angle predicted by Cassie. Finally, contrary to results obtained with two-dimensional drops, contact angle hysteresis observed in this system is shown to exhibit a degree of volume dependence in the advancing and receding angles. Qualitative differences in the wetting behavior associated with the two different chemical patterns considered here, as well as differences between results obtained with two-dimensional and three-dimensional drops, can possibly be attributed to variations in the level of constraint imposed on the drop by the different patterns and by the dimensionality of the system.     

Wetting and absorption of water drops on Nafion films

Water drops on Nafion films caused the surface to switch from being hydrophobic to being hydrophilic. Contact angle hysteresis of >70 degrees between advancing and receding values were obtained by the Wilhelmy plate technique. Sessile drop measurements were consistent with the advancing contact angle; the sessile drop contact angle was 108 degrees . Water drop adhesion, as measured by the detachment angle on an inclined plane, showed much stronger water adhesion on Nafion than Teflon. Sessile water and methanol drops caused dry Nafion films to deflect. The flexure went through a maximum with time. Flexure increased with contact area of the drop, but was insensitive to the film thickness. Methanol drops spread more on Nafion and caused larger film flexure than water. The results suggest that the Nafion surface was initially hydrophobic but water and methanol drops caused hydrophilic sulfonic acid domains to be drawn to the Nafion surface. Local swelling of the film beneath the water drop caused the film to buckle. The maximum flexure is suggested to result from motion of a water swelling front through the Nafion film.     

Comparison of sessile drop and captive bubble methods on rough homogeneous surfaces: a numerical study

Quasi-static experiments using sessile drops and captive bubbles are the most employed methods for measuring advancing and receding contact angles on real surfaces. These observable contact angles are the most easily accessible and reproducible. However, some properties of practical surfaces induce certain phenomena that cause a built-in uncertainty in the estimation of advancing and receding contact angles. These phenomena are well known in surface thermodynamics as stick-slip phenomena. Following the work of Marmur (Marmur, A. Colloids Surf., A 1998, 136, 209-215), where the stick-slip effects were studied with regard to sessile drops and captive bubbles on heterogeneous surfaces, we developed a novel extension of this study by adding the effects of roughness to both methods for contact angle measurement. We found that the symmetry between the surface roughness problem and the chemical heterogeneity problem breaks down for drops and bubbles subjected to stick-slip effects.     

Contact angles and their hysteresis as a measure of liquid-solid adhesion

The wetting behavior of a series of aliphatic polyamides was examined. Polyamides and polyethylene were molded against glass to produce smooth surfaces. After cleaning, chemical composition of the surfaces was verified with X-ray photoelectron spectroscopy. Advancing and receding contact angles were measured from small sessile water drops. Contact angles decreased with amide content while contact angle hysteresis increased. Wetting free energies calculated from contact angles were equal to those from dewetting, suggesting that contact angle hysteresis did not arise from surface anomalies, but from hydrogen bonding between water and the amide groups in the polyamide surfaces.     

Dynamic behavior of polymer surface and the time dependence of contact angle

The increased attention has been focused on the re-searches of soft materials proposed by Pierre-Gilles de Gennes, a Nobel Prize Laureate in Physics. A special issue of “Science” on soft surfaces was published in 2002 to review specific surface properti…     

Constitutive modeling of contact angle hysteresis

We introduce a phase field model of wetting of surfaces by sessile drops. The theory uses a two-dimensional non-conserved phase field variable to parametrize the Gibbs free energy of the three-dimensional system. Contact line tension and contact angle hysteresis arise from the gradient term in the free energy and the kinetic coefficient respectively. A significant advantage of this approach is in the constitutive specification of hysteresis. The advancing and receding angles of a surface, the liquid-vapor interfacial energy and three-phase line tension are the only required constitutive inputs to the model. We first simulate hysteresis on a smooth chemically homogeneous surface using this theory. Next we show that it is possible to study heterogeneous surfaces whose component surfaces are themselves hysteretic. We use this theory to examine the wetting of a surface containing a circular heterogeneous island. The contact angle for this case is found to be determined solely by the material properties at the contact line in accord with recent experimental data.     

Anisotropic wetting characteristics on submicrometer-scale periodic grooved surface

Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference. The wetting characteristics on the patterned surfaces were studied by contact angle measurements. Macroscopic distortion of water drops was found on such small-scale surface structures, and the contact angles measured from the direction parallel to the grooves were larger than those measured from the perpendicular direction. A thermodynamic model was developed to calculate the change in the surface free energy as a function of the instantaneous contact angle when the three-phase contact line (TPCL) moves along the two orthogonal directions. It was found that the fluctuations, i.e., energy barriers, on the energy versus contact angle curves are crucial to the analysis of wetting anisotropy and contact angle hysteresis. The calculated advancing and receding contact angles from the energy versus contact angle curves were in good agreement with those measured experimentally. Furthermore, with the groove depth increasing, both the degree of wetting anisotropy and the contact angle hysteresis perpendicular to the grooves increased as a result of the increase in the energy barrier. The theoretical critical value of the groove depth, above which the anisotropic wetting appears, was determined to be 16 nm for the grooved surface with a wavelength of 396 nm. On the other hand, the effect of the groove wavelength on the contact angle hysteresis perpendicular to the grooves was also interpreted on the basis of the thermodynamic model. That is, with the wavelength decreasing, the contact angle hysteresis increased due to the increase in the number of energy barriers. These results may provide theoretical evidence for the design and application of anisotropic wetting surface.     

Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces

A simulation study of liquid drops on inclined surfaces is performed in order to understand the evolution of drop shapes, contact angles, and retention forces with the tilt angle. The simulations are made by means of a method recently developed for dealing with contact angle hysteresis in the public-domain Surface Evolver software. The results of our simulations are highly dependent on the initial contact angle of the drop. For a drop with an initial contact angle equal to the advancing angle, we obtain results similar to those of experiments in which a drop is placed on a horizontal surface that is slowly tilted. For drops with an initial contact angle equal to the mean between the advancing and the receding contact angles, we recover previous results of finite element studies of drops on inclined surfaces. Comparison with experimental results for molten Sn-Ag-Cu on a tilted Cu substrate shows excellent agreement.     

Effect of oxidation on the wettability of poly(dimethylsiloxane) surfaces

The wetting of amorphous poly(dimethylsiloxane) (PDMS) surfaces by water has been studied using molecular dynamics simulations. PDMS surfaces were generated by compressing a long PDMS chain between two elastic boundaries at atmospheric pressure. Oxidation of the PDMS surface, achieved in real systems by exposure to air plasma or corona discharge, was modeled by replacing methyl groups on the PDMS chain with hydroxyl groups. Three surfaces of varying degrees of oxidation were characterized by measuring the water contact angle and the roughness. The dependence of the microscopic contact angle on drop size was measured from time averaged density profiles. The macroscopic contact angle was measured directly using a cylindrical drop of infinite length with zero contact line curvature. The measured macroscopic contact angle ranged from approximately 125 degrees on the untreated surface to 75 degrees on the most oxidized surface studied. The line tension was found to increase with increasing degree of oxidation, from a negligible value on the untreated surface to approximately 5x10(-11) J m(-1) on the most heavily oxidized surface.     

Evaporation of pure liquid sessile and spherical suspended drops: a review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by a contact line and characterized by contact angle, contact radius and drop height. Diffusion-controlled evaporation of a sessile drop in an ambient gas is an important topic of interest because it plays a crucial role in many scientific applications such as controlling the deposition of particles on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, drop wise cooling, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials in the last decades. This paper presents a review of the published articles for a period of approximately 120 years related to the evaporation of both sessile drops and nearly spherical droplets suspended from thin fibers. After presenting a brief history of the subject, we discuss the basic theory comprising evaporation of micrometer and millimeter sized spherical drops, self cooling on the drop surface and evaporation rate of sessile drops on solids. The effects of drop cooling, resultant lateral evaporative flux and Marangoni flows on evaporation rate are also discussed. This review also has some special topics such as drop evaporation on superhydrophobic surfaces, determination of the receding contact angle from drop evaporation, substrate thermal conductivity effect on drop evaporation and the rate evaporation of water in liquid marbles.     

Anisotropic drop morphologies on corrugated surfaces

The spreading of liquid drops on surfaces corrugated with micrometer-scale parallel grooves is studied both experimentally and numerically. Because of the surface patterning, the typical final drop shape is no longer spherical. The elongation direction can be either parallel or perpendicular to the direction of the grooves, depending on the initial drop conditions. We interpret this result as a consequence of both the anisotropy of the contact line movement over the surface and the difference in the motion of the advancing and receding contact lines. Parallel to the grooves, we find little hysteresis due to the surface patterning and that the average contact angle approximately conforms to Wenzel's law as long as the drop radius is much larger than the typical length scale of the grooves. Perpendicular to the grooves, the contact line can be pinned at the edges of the ridges, leading to large contact angle hysteresis.     

Three-dimensional equilibrium shapes of drops on hysteretic surfaces

In this paper, we study equilibrium three-dimensional shapes of drops on hysteretic surfaces. We develop a function coupled with the publicly available surface energy minimization code Surface Evolver to handle contact angle hysteresis. The function incorporates a model for the mobility of the triple line into Surface Evolver. The only inputs to the model are the advancing and receding contact angles of the surface. We demonstrate this model’s versatility by studying three problems in which parts of the triple line advance while other parts either recede or remain stationary. The first problem focuses on the three-dimensional shape of a static pendant drop on a vertical surface. We predict the finite drop volume when impending sliding motion is observed. In the second problem, we examine the equilibrium shapes of coalescing sessile drops on hysteretic surfaces. Finally, we study coalescing puddles in which gravity plays a leading role in determining the equilibrium puddle shape along with hysteresis.     

Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force

Contact angle hysteresis, drop shape, and drop retention were studied with a tiltable plane. Contact liquids were water and ethylene glycol. Four polymers and silicon wafers were used as substrates. When the plane was inclined, the shape of drops distorted, exhibiting advancing and receding contact angles. Drops remained stationary until a critical angle of tilt was exceeded, and then they began to move. The difference in the advancing and receding contact angles, or contact angle hysteresis, ranged from 9° to 66°, depending on the liquid and the substrate. Roughness did not seem to influence the hysteresis as much as the chemical nature of the surfaces. Elongation and back-to-front asymmetry were greater on surfaces with high hysteresis. We found a linear correlation between the aspect ratio of drops and their contact angle hysteresis. Also, the retentive force increased with elongation of the drops.     

Photon control of liquid motion on reversibly photoresponsive surfaces

The movement of a liquid droplet on a flat surface functionalized with a photochromic azobenzene may be driven by the irradiation of spatially distinct areas of the drop with different UV and visible light fluxes to create a gradient in the surface tension. In order to better understand and control this phenomenon, we have measured the wetting characteristics of these surfaces for a variety of liquids after UV and visible light irradiation. The results are used to approximate the components of the azobenzene surface energy under UV and visible light using the van Oss-Chaudhury-Good equation. These components, in combination with liquid parameters, allow one to estimate the strength of the surface interaction as given by the advancing contact angle for various liquids. The azobenzene monolayers were formed on smooth air-oxidized Si surfaces through 3-aminopropylmethyldiethoxysilane linkages. The experimental advancing and receding contact angles were determined following azobenzene photoisomerization under visible and ultraviolet (UV) light. Reversible light-induced advancing contact-angle changes ranging from 8 to 16 degrees were observed. A large reversible change in contact angle by photoswitching of 12.4 degrees was achieved for water. The millimeter-scale transport of 5 microL droplets of certain liquids was achieved by creating a spatial gradient in visible/UV light across the droplets. A criterion for light-induced motion of droplets is shown to be consistent with the response of a variety of liquids. The type of light-driven fluid movement observed could have applications in microfluidic devices.     

Retention forces and contact angles for critical liquid drops on non-horizontal surfaces

Retention forces and drop parameters are investigated for drops on the verge of sliding on vertical and inclined surfaces. Using earlier observations of drop geometry, the retentive-force factor relating surface-tension forces to contact-angle hysteresis is reliably determined. The retention force for a drop is found to be insignificantly affected by the aspect ratio of its contour. The maximum size of a drop is predicted with good accuracy, based on the two-circle method for approximating shapes of drops. The Bond number of a critical drop is found to be constant for a given surface and liquid. A general relation is proposed between the characteristic advancing and receding contact angles. The relation is supported by a large set of contact-angle data. In the absence of theta R data, the relation allows estimating the receding contact angle and the critical drop size, using only the advancing angle.     

Simultaneous spreading and evaporation: Recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1–2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.     

Liquid–paper interactions during liquid drop impact and recoil on paper surfaces

The spreading and recoiling of water drops on several flat and macroscopically smooth model surfaces and on sized paper surfaces were studied over a range of drop impaction velocities using a high-speed CCD camera. The water drop spreading and recoiling results on several model hydrophobic and hydrophilic surfaces were found to be in agreement with observations reported in the literature. The maximum drop spreading diameter for those model surfaces at impact was found to be dependent upon the initial drop kinetic energy and the degree of hydrophobicity/hydrophilicity of the surface. The extent of the maximum drop recoiling was found to be much weaker for hydrophilic substrates than for hydrophobic substrates. Sized papers, however, showed an interesting switch of behaviour in the process of water drop impaction. They behave like a hydrophobic substrate when a water drop impacts on it, but like a hydrophilic substrate when water drop recoils. Although the contact angle between water and hydrophilic or hydrophobic non-porous surfaces changes from advancing to receding as reported in literature, the change of contact angle during water impact on paper surface is unique in that the level of sizing was found to have a smaller than expected influence on the degree of recoil. Atomic force microscopy (AFM) was used to probe fibres on a sized filter paper surface under water. The AFM data showed that water interacted strongly with the fibre even though the paper was heavily sized. Implications of this phenomenon were discussed in the context of inkjet print quality and of the surface conditions of sized papers. Results of this study are very useful in the understanding of inkjet ink droplet impaction on paper surfaces which sets the initial condition for ink penetration into paper after impaction.     

Nanoparticle flotation collectors II: the role of nanoparticle hydrophobicity

The ability of polystyrene nanoparticles to facilitate the froth flotation of glass beads was correlated to the hydrophobicity of the nanoparticles. Contact angle measurements were used to probe the hydrophobicity of hydrophilic glass surfaces decorated with hydrophobic nanoparticles. Both sessile water drop advancing angles, θ(a), and attached air bubble receding angle measurements, θ(r), were performed. For glass surfaces saturated with adsorbed nanoparticles, flotation recovery, a measure of flotation efficiency, increased with increasing values of each type of contact angle. As expected, the advancing water contact angle on nanoparticle-decorated, dry glass surfaces increased with surface coverage, the area fraction of glass covered with nanoparticles. However, the nanoparticles were far more effective at raising the contact angle than the Cassie-Baxter prediction, suggesting that with higher nanoparticle coverages the water did not completely wet the glass surfaces between the nanoparticles. A series of polystyrene nanoparticles was prepared to cover a range of surface energies. Water contact angle measurements, θ(np), on smooth polymer films formed from organic solutions of dissolved nanoparticles were used to rank the nanoparticles in terms of hydrophobicity. Glass spheres were saturated with adsorbed nanoparticles and were isolated by flotation. The minimum nanoparticle water contact angle to give high flotation recovery was in the range of 51° < θ(np(min)) ≤ 85°.     

Comparison of the relaxation of sessile drops driven by harmonic and stochastic mechanical excitations

Currently, there is no conclusive evidence regarding the global equilibrium condition of vibrated drops. However, it is well-known that vibration of sessile drops effectively reduces the contact angle hysteresis. In this work, applying a recent methodology for evaluating the most-stable contact angle, we examined the impact of the type of excitation signal (random signal versus periodical signal) on the values of the most-stable contact angle for polymer surfaces. Using harmonic signals, the oscillation frequency affected the postvibration contact angle. Instead, the white noise signal enabled sessile drops to relax regardless of their initial configuration. In spite of that, the values of most-stable contact angle obtained with different signals mostly agreed. We concluded that not only the amount of relaxation can be important for relaxing a sessile drop but also the rate of relaxation. Together with receding contact angle, most-stable contact angle, measured with the proposed methodology, was able to capture the thermodynamic changes of "wetted" polymer surfaces.     

Water microdroplets on molecularly tailored surfaces: correlation between wetting hysteresis and evaporation mode switching

The evaporation of water microdroplets from solid surfaces was studied using digital contact angle analysis techniques. An inclusive trend for the evaporation process, that is, a switch from the initial constant contact area to the subsequent constant contact angle mode was observed for all surfaces examined, including mixed self-assembled monolayers (SAMs) on gold and "conventional" surfaces such as silicon wafers, polycarbonate, and Teflon. More importantly, it has been shown that the change in contact angle during the evaporation process (i.e., evaporation hysteresis, delta theta(evap), the difference between the initial and "equilibrated" contact angle) correlates well with the wetting hysteresis determined directly (i.e., measuring the advancing and receding contact angles on these surfaces by changing the drop volume). The comparison between mixed SAM surfaces and conventional solids revealed that the evaporation/wetting hysteresis is dominated by the roughness (from nanometer to micrometer scale) rather than the chemical heterogeneity of the surface. The evaporation rates of water microdroplets on these surfaces were also monitored and modeled.