Contact angles of drops on curved superhydrophobic surfaces

Superhydrophobic surfaces have contact angles that exceed 150 degrees and are known to reduce surface fouling, protect surfaces, and improve liquid-liquid separations. Electrospun sub-micron fiber mats can perform as superhydrophobic surfaces. Superhydrophobic behavior is typically measured on planar surfaces, whereas applications may require curved surfaces. This paper discuses the measurement of water contact angles of fiber mats formed on cylindrical surfaces to create superhydrophobic behavior on curved surfaces. Equations are derived that relate the radius of curvature of spherical and cylindrical surfaces and drop size to the observed contact angle on the curved surfaces. Calculations from the equations agree well with experimental observations on spherical surfaces reported in literature and on cylindrical surfaces created in our lab.     

Contact angles on spherical surfaces

In this paper, we explore the influence of curved surfaces on contact angles. Small liquid drops were deposited at the apex of spheres. Liquid was added to advance the contact line (or withdrawn to cause recession). As drop volume increased, the contact line advanced outward and downward. With the addition of each increment of liquid, the contact line encountered a steeper slope and showed progressively larger apparent advancing contact angles. Observed apparent contact angles could be explained in terms of intrinsic contact angles and surface orientation. We found that if curvature and geometry were correctly accounted for, the classic Gibbs relation held. The experimental approach and analysis used here for estimating intrinsic wettability from curved surfaces could easily be integrated into automated contact angle measurement systems.     

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.     

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.     

Motion of liquid drops on surfaces induced by asymmetric vibration: role of contact angle hysteresis

Hysteresis of wetting, like the Coulombic friction at solid/solid interface, impedes the motion of a liquid drop on a surface when subjected to an external field. Here, we present a counterintuitive example, where some amount of hysteresis enables a drop to move on a surface when it is subjected to a periodic but asymmetric vibration. Experiments show that a surface either with a negligible or high hysteresis is not conducive to any drop motion. Some finite hysteresis of contact angle is needed to break the periodic symmetry of the forcing function for the drift to occur. These experimental results are consistent with simulations, in which a drop is approximated as a linear harmonic oscillator. The experiment also sheds light on the effect of the drop size on flow reversal, where drops of different sizes move in opposite directions due to the difference in the phase of the oscillation of their center of mass.     

Vapour adsorption and contact angles on hydrophobic solid surfaces

To test the effects of vapour adsorption on contact angle measurements, contact angles of high-vapour-pressure liquids and low-vapour-pressure liquids on a hydrophobic solid surface (FC721) were measured by using the axisymmetric drop shape analysis-profile (ADSA-P) technique. Details of the surface preparation and the experiments are presented. By plotting the experimental data in terms of _1v cos vs. _1v, this study shows that the vapour adsorption on a fluorocarbon surface, FC721, is negligible.     

Nanolayer liquid density on hydrophobic surfaces

 The excess volumes of dispersions of hydrophobic silica particles and hydrophobized layer silicates were studied in ethanol– cyclohexane mixtures. A plot of the excess volume vs. composition [V ^σ=f (x ₁)] indicates that the components, ethanol and cyclohexane, on hydrophobic SiO₂ are ordered to a considerable extent. The excess volumes which are positive in the pure solvent, i.e. without dispersed particles, take on negative values over the entire composition range. On the other hand, excess volumes for layer silicates the surface of which had been modified by long (n _c=18) alkyl chains were calculated by a combination of adsorption isotherms with X-ray diffraction data and were positive in the entire composition range. It is established that the density of the adsorption layer on the solid/liquid interface in colloid dispersions significantly differs from that of the bulk phase. The differences depend on the surface structure of the adsorbent. Received: 4 June 1998 Accepted: 7 July 1998     

Contact angle hysteresis on regular pillar-like hydrophobic surfaces

A series of pillar-like patterned silicon wafers with different pillar sizes and spacing are fabricated by photolithography and further modified by a self-assembled fluorosilanated monolayer. The dynamic contact angles of water on these surfaces are carefully measured and found to be consistent with the theoretical predictions of the Cassie model and the Wenzel model. When a water drop is at the Wenzel state, its contact angle hysteresis increases along with an increase in the surface roughness. While the surface roughness is further raised beyond its transition roughness (from the Wenzel state to the Cassie state), the contact angle hysteresis (or receding contact angle) discontinuously drops (or jumps) to a lower (or higher) value. When a water drop is at the Cassie state, its contact angle hysteresis strongly depends on the solid fraction and has nothing to do with the surface roughness. Even for a superhydrophobic surface, the contact angle hysteresis may still exhibit a value as high as 41 degrees for the solid fraction of 0.563.     

Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.     

Spreading of liquid drops over dry surfaces

Spreading of thin, axisymmetric, non-volatile, Newtonian liquid drops over a dry, smooth, flat solid surface is considered both theoretically and experimentally in the case of complete wetting. The drop profile is solved analytically by matching the “outer” solution for large film thicknesses, where only the capillary effects are important, with the “inner” solution for small film thicknesses, where the viscous and disjoining pressure effects are comparable to capillary effects. It is shown that the apparent radius of the wetted spot, the apex height of the drop, and the apparent advancing dynamic contact angle follow different power laws in time and the advancing dynamic contact angle follows a power law in capillary number. Both the prefactor and the exponent of each power law are derived theoretically. Good agreement between the theory predictions and experimental measurements is shown for both the prefactor and exponent of each power law. It is necessary to emphasize that the theory suggested does not include any fitting parameters.     

Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of constant volume is considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy, we derive an equation for the apparent contact angle, which is similar but different from the well-known Cassie's law. Next, using this modified Cassie's law as a guide to predict the behavior of a droplet on a heterogeneous striped surface, we examine several scenarios of contact angle hysteresis using a periodically striped surface model. By changing the volume of the droplet, we predict a sudden jump of the droplet edge, and a continuous change of the apparent contact angle at the edge of two stripes. Our results suggest that as drop volume is increased (advancing contact lines), the predominant drop configuration observed is the one whose contact angle is large; whereas, decreasing drop volume from a large value (receding contact lines) yields drop configuration that predominantly exhibit the smaller contact angle.     

Studies of the wetting kinetics of liquid drops on solid surfaces

The viscosity _L and the surface tension _L of the liquid as well as the equilibrium contact angle _e are essential parameters governing the wetting kinetics of liquids on solids. By means of a contact angle apparatus with video image digitization, the dynamic contact angle and the radiusr of the contact area of sessile drops on solid surfaces have simultaneously been determined in dependence on time after drop application between about 3·10^–2 s and long times.The measurements were performed with series of liquids: polydimethylsiloxanes with different molecular masses and solutions of polyisobutylene in decalin and polyacrylic acid in water, covering a wide range of concentrations. The liquids in each series have a constant surface tension, but viscosities ranging over about four orders of magnitude, allowing the influence of _L and _L to be studied independently. Solids such as glass, polyethylene and polytetrafluoroethylene were chosen so that the cases of complete wetting (spreading) and partial wetting ( _e) could be studied.The curves of cos andr/R ₀ vs. time for the different liquids of a series can be superimposed to a master curve by plotting them against _L·t _L·R ₀, whereR ₀ is the radius of the original drop. All these master curves coincide at small wetting times, with exception of the data for the polysiloxanes. That means that the early stage of the wetting process is determined only by the properties of the wetting liquid. The influence of the solid surface, characterized by the equilibrium contact angle _e becomes significant only at the end of the wetting process.Dedicated to Professor Dr. H. Willersinn on the occasion of his 65^th birthday     

Contact angles on metal and polymer surfaces in mass transfer environments

Contact angles of pure and binary liquid mixtures measured where the surrounding vapor is not in equilibrium with the liquid are reviewed. Two physical situations were examined which simulated conditions of distillation and condensation. An explanation was afforded as to why at low concentrations when mass transfer took place, some binary mixtures exhibited poor wetting characteristics on metal surfaces but not on polymers. Furthermore, under condensation conditions, the dropwise-filmwise transition was shown to occur at the contact angle of 90° for real systems.     

Model and experimental studies for contact angles of surfactant solutions on rough and smooth hydrophobic surfaces

Despite the practical need, no models exist to predict contact angles or wetting mode of surfactant solutions on rough hydrophobic or superhydrophobic surfaces. Using Gibbs' adsorption equation and a literature isotherm, a new model is constructed based on the Wenzel and Cassie equations. Experimental data for aqueous solutions of sodium dodecyl sulfate (SDS) contact angles on smooth Teflon surfaces are fit to estimate values for the adsorption coefficients in the model. Using these coefficients, model predictions for contact angles as a function of topological f (Cassie) and r (Wenzel) factors and SDS concentration are made for different intrinsic contact angles. The model is also used to design/tune surface responses. It is found that: (1) predictions compare favorably to data for SDS solutions on five superhydrophobic surfaces. Further, the model predictions can determine which wetting mode (Wenzel or Cassie) occurred in each experiment. The unpenetrated or partially penetrated Cassie mode was the most common, suggesting that surfactants inhibit the penetration of liquids into rough hydrophobic surfaces. (2) The Wenzel roughness factor, r, amplifies the effect of surfactant adsorption, leading to larger changes in contact angles and promoting total wetting. (3) The Cassie solid area fraction, f, attenuates the lowering of contact angles on rough surfaces. (4) The amplification/attenuation is understood to be due to increased/decreased solid-liquid contact-area.     

Wetting transition on hydrophobic surfaces covered by polyelectrolyte brushes

We study the wetting by water of complex "hydrophobic-hydrophilic" surfaces made of a hydrophobic substrate covered by a hydrophilic polymer brush. Polystyrene (PS) substrates covered with polystyrene- block-poly(acrylic acid) PS- b-PAA diblock copolymer layers were fabricated by Langmuir-Schaefer depositions and analyzed by atomic force microscopy (AFM) and ellipsometry. On bare PS substrate, we measured advancing angles theta A = 93 +/- 1 degrees and receding angles theta R = 81 +/- 1 degrees . On PS covered with poorly anchored PS- b-PAA layers, we observed large contact angle hysteresis, theta A approximately 90 degrees and theta R approximately 0 degrees , that we attributed to nanometric scale dewetting of the PS- b-PAA layers. On well-anchored PS- b-PAA layers that form homogeneous PAA brushes, a wetting transition from partial to total wetting occurs versus the amount deposited: both theta A and theta R decrease close to zero. A model is proposed, based on the Young-Dupre equation, that takes into account the interfacial pressure of the brush Pi, which was determined experimentally, and the free energy of hydration of the polyelectrolyte monomers Delta G PAA (hyd), which is the only fitting parameter. With Delta G PAA (hyd) approximately -1300 J/mol, the model renders the wetting transition for all samples and explains why the wetting transition depends mainly on the average thickness of the brush and weakly on the length of PAA chains.     

Dynamic wetting and spreading characteristics of a liquid droplet impinging on hydrophobic textured surfaces

We report on the wetting dynamics of a 4.3 μL deionized (DI) water droplet impinging on microtextured aluminum (Al 6061) surfaces, including microhole arrays (hole diameter 125 μm and hole depth 125 μm) fabricated using a conventional microcomputer numerically controlled (μ-CNC) milling machine. This study examines the influence of the texture area fraction ?(s) and drop impact velocity on the spreading characteristics from the measurement of the apparent equilibrium contact angle, dynamic contact angle, and maximum spreading diameter. We found that for textured surfaces the measured apparent contact angle (CA) takes on values of up to 125.83°, compared to a CA of approximately 80.59° for a nontextured bare surface, and that the spreading factor decreases with the increased texture area fraction because of increased hydrophobicity, partial penetration of the liquid, and viscous dissipation. In particular, on the basis of the model of Ukiwe and Kwok (Ukiwe, C.; Kwok, D. Y. Langmuir 2005, 21, 666), we suggest a modified equation for predicting the maximum spreading factor by considering various texturing effects and wetting states. Compared with predictions by using earlier published models, the present model shows better agreement with experimental measurements of the maximum spreading factor.     

Contact angles in thin liquid films : III. Interaction forces in Newton black soap films

The interaction parameters of Newton black soap films stabilized by NaDS, as derived from contact angle experiments, have been interpretated in terms of the structure and the interaction forces in the films. From the film thickness and the difference between the surface excess of the salt in the film and at the bulk surface it is concluded that (a) the diffuse double-layer overlap in the film is practically complete; (b) the film only contains absorbed DS⁻ ions and an equal amount of Na⁺ counterions, but no salt; and (c) the double layer at the bulk surface is still partly diffuse. A model for the structure of the NB films is proposed according to which the adsorbed DS⁻ ions with their counterions form a two-dimensional square lattice at each film surface. It is found that the interaction free energy of the NB films can be explained by taking into account the electrostatic interactions between the discrete ions in the two opposing surface lattices. The model of the NB film is qualitatively in agreement with the experimental results of other workers.     

Restructuring of hydrophobic surfaces created by surfactant adsorption to mica surfaces

Hydrophobic surfaces created by the adsorption of a monolayer of surfactants, such as CTAB or DODAB, to mica display long-range mutual attraction when placed in water. Initially, this attraction was considered to be due to hydrophobic interaction, but more careful measurements using AFM showed that the surfactant monolayer undergoes rearrangements to produce charged patches on the surface; therefore, the nature of the long-range interaction is due to the electrostatic interaction between patches. The monolayer rearrangement depends on the nature of the surfactant and its counterion. To study possible monolayer rearrangements in molecular detail, we performed detailed molecular dynamics computer simulations on systems containing a monolayer of surfactants RN(CH(3))(3)(+)Cl(-) (R indicates a saturated hydrocarbon chain) adsorbed on a mica surface and immersed in water. We observe that when chain R is 18 carbons long the monolayer rearranges into a micelle but it remains a monolayer when the chain contains 24 carbons.     

Interfacial behavior of cubic liquid crystalline nanoparticles at hydrophilic and hydrophobic surfaces

The adsorption behavior of self-assembled lipid liquid crystalline nanoparticles at different model surfaces was investigated in situ by use of ellipsometry. The technique allows time-resolved monitoring of the adsorbed amount and layer thickness under transient and steady-state conditions. The system under study was cubic-phase nanoparticle (CPNP) dispersions of glycerol monooleate stabilized by a nonionic block copolymer, Pluronic F-127. Depending on the surface properties and presence of electrolytes, different adsorption scenarios were discerned: At hydrophilic silica thick surface layers of CPNPs are generated by particle adsorption from dispersions containing added electrolyte, but no adsorption is observed in pure water. Adsorption at the hydrophobic surface involves extensive structural relaxation and formation, which is not electrolyte sensitive, of a classic monolayer structure. The different observations are rationalized in terms of differences in interactions among the CPNP aggregates, their unimer constituents, and the surface and show a strong influence of interfacial interactions on structure formation. Surface self-assembly structures with properties similar to those of the corresponding bulk aggregates appear exclusively in the weak interaction limit. This observation is in agreement with observations for surfactant self-assembly systems, and our findings indicate that this behavior is applicable also to complex self-assembly structures such as the CPNP structures discussed herein.