Contact angles of liquid drops on super hydrophobic surfaces: understanding the role of flattening of drops by gravity

Measurement of contact angles on super hydrophobic surfaces by conventional methods can produce ambiguous results. Experimental difficulties in constructing tangent lines, gravitational distortion or erroneous assumptions regarding the extent of spreading can lead to underestimation of contact angles. Three models were used to estimate drop shape and perceived contact angles on completely nonwetting super hydrophobic surfaces. One of the models employed the classic numerical solutions from Bashforth and Adams. Additionally, two approximate models were derived as part of this work. All three showed significant distortion of microliter-sized drops and similar trends in perceived contact angles. Liquid drops of several microliters are traditionally used in sessile contact angle measurements. Drops of this size are expected to and indeed undergo significant flattening on super hydrophobic surfaces, even if the wetting interactions are minimal. The distortion is more pronounced if the liquid has a lesser surface tension or greater density. For surfaces that are completely nonwetting, underestimation of contact angles can be tens of degrees. Our modeling efforts suggest that accurate contact angle measurements on super hydrophobic surfaces would require very small sessile drops, on the order of hundreds of picoliters.     

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 Liquid was added to advance the contact line (or withdrawn to cause recession).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.     

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.     

Thickness, stability and contact angle of liquid films on and inside nanofibres, nanotubes and nanochannels

While the stability of liquid films on substrates is a classical topic of colloidal science, the availability of nanostructured materials, such as nanotubes, nanofibres and nanochannels, has raised the question of how the stability of liquid films and their wetting behaviour is affected by nanoscale confinement. This paper will present the conditions for the stability of liquid films on and inside cylindrical solid substrates with nanometre scale characteristic dimensions. It is shown that the stability is determined by an effective disjoining/conjoining pressure isotherm which differs from the corresponding disjoining/conjoining pressure isotherm of flat liquid films on flat solid substrates. From the former, the equilibrium contact angles of drops on an outer or inner surface of a cylindrical capillary have been calculated as a function of surface curvature, showing that the expressions for equilibrium contact angles vary for different geometries, in view of the difference in thickness of the film of uniform thickness with which the bulk liquid (drops or menisci) is at equilibrium. These calculations have been extended to the case of glass nanocapillaries and carbon nanotubes, finding good agreement with experimental results in the literature.     

Drop shape visualization and contact angle measurement on curved surfaces

The shape and contact angles of drops on curved surfaces is experimentally investigated. Image processing, spline fitting and numerical integration are used to extract the drop contour in a number of cross-sections. The three-dimensional surfaces which describe the surface-air and drop-air interfaces can be visualized and a simple procedure to determine the equilibrium contact angle starting from measurements on curved surfaces is proposed. Contact angles on flat surfaces serve as a reference term and a procedure to measure them is proposed. Such procedure is not as accurate as the axisymmetric drop shape analysis algorithms, but it has the advantage of requiring only a side view of the drop-surface couple and no further information. It can therefore be used also for fluids with unknown surface tension and there is no need to measure the drop volume. Examples of application of the proposed techniques for distilled water drops on gemstones confirm that they can be useful for drop shape analysis and contact angle measurement on three-dimensional sculptured surfaces.     

Criteria for ultralyophobic surfaces

Very rough surfaces can suspend small liquid drops and produce very large contact angles. This behavior often is referred to as ultralyophobicity or super repellency. It is proposed that two criteria must be met to invoke ultralyophobicity: a contact line density criterion and asperity height criterion. The proposed criteria were tested using experimental data available in the literature and were found to correctly predict suspension of small water drops on model rough surfaces with a wide variety of asperity shapes, sizes, and spacing.     

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.     

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.     

Assessing the accuracy of contact angle measurements for sessile drops on liquid-repellent surfaces

Gravity-induced sagging can amplify variations in goniometric measurements of the contact angles of sessile drops on super-liquid-repellent surfaces. The very large value of the effective contact angle leads to increased optical noise in the drop profile near the solid-liquid free surface and the progressive failure of simple geometric approximations. We demonstrate a systematic approach to determining the effective contact angle of drops on super-repellent surfaces. We use a perturbation solution of the Bashforth-Adams equation to estimate the contact angles of sessile drops of water, ethylene glycol, and diiodomethane on an omniphobic surface using direct measurements of the maximum drop width and height. The results and analysis can be represented in terms of a dimensionless Bond number that depends on the maximum drop width and the capillary length of the liquid to quantify the extent of gravity-induced sagging. Finally, we illustrate the inherent sensitivity of goniometric contact angle measurement techniques to drop dimensions as the apparent contact angle approaches 180°.     

Liquid drops on vertical and inclined surfaces; II. A method for approximating drop shapes

In this article, a new method is proposed to approximate the shapes of liquid drops on vertical and inclined surfaces. Based on observations from Part I, the profile of a drop at a given azimuthal angle is approximated by two circles sharing a common tangent at the maximum height. The drop volume is obtained by integrating all profiles over the circumference of the base. The volume is thus described as a function of the contact angles and the three-phase contact line. The new method accurately predicts the volumes of drops tested in Part I and independent measurements from the literature. Simplifying the drop shape to a spherical cap can lead to a 75% error in drop-volume prediction. The proposed method is used to study the effect of drop parameters on volume prediction. The two-circle geometry can also be used to measure contact angles from profile images.     

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.     

Contact angle measurements by confocal microscopy for non-destructive microscale surface characterization

Contact angle measurements are of great importance in surface characterization but the practical use has often been limited to macroscopic dimensions (millimeters). Therefore, we have developed a confocal microscopy method that allows non-destructive measurements of both low (<30 degrees ) and high (30 degrees -90 degrees ) contact angles. Low contact angles were measured by reconstructing the drop profile from the interference patterns in droplets condensed from atmospheric humidity. At higher contact angles water droplets with a small amount of fluorescein were sprayed onto the surfaces and 3D-image stacks were recorded and used to extract the contact angle. Suitable drop sizes were between a few up to about 50 mum radius, using a 40x magnification objective. Using drops >10 micrometers radius for microcontact angle measurements a good correlation was obtained between measured micro- and macrocontact angles. After microcontact angle measurements the surfaces were rinsed and heavy meromyosin motor fragments were adsorbed to the surface. Importantly, the sensitive actin propelling function of these motor proteins was not affected by the previous contact angle measurements using fluorescent droplets. This suggests that the methodology should be suitable for non-destructive characterization of different parts of micropatterned surfaces being developed for biological assays.     

Water contact angles and hysteresis of polyamide surfaces

The wetting behavior of a series of aliphatic polyamides (PAs) has been examined. PAs with varying amide content and polyethylene (PE) were molded against glass to produce surfaces with similar roughness. 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 hysteresis increased. Hysteresis arose primarily from molecular interactions between the contact liquid and the solid substrates, rather than moisture absorption, variations in crystallinity, surface deformation, roughness, reorientation of amide groups, or surface contamination. Free energies of hysteresis were calculated from contact angles. For PE, which is composed entirely of nonpolar methylene groups, free energies were equivalent to the strength of dispersive van der Waals bonds. For PAs, free energies corresponded to fractional contributions from the dispersive methylene groups and polar amide groups.     

Drop size dependence of contact angles on two fluoropolymers

Young’s equation predicts that the contact angle of a liquid drop is independent of its size. Nevertheless, large drop size dependences of contact angles have been observed, especially for millimetre-sized drops, on a variety of solid surfaces. We report new measurements of drop size dependence of contact angles for several liquids on two fluoropolymer surfaces, Teflon AF 1600 and EGC-1700. We demonstrate a new strategy for contact angle measurement that allows detection of approximately 0.1° changes in the contact angle during the growth of a drop. We find that on the surfaces examined, drop size dependence of contact angles is ten times smaller than on all previously studied fluoropolymers at the millimetre scale. The data are insensitive to various attempted surface modifications. We discuss the interpretation of the data and possible physical sources.     

Dip-coating crystallization on a superhydrophobic surface: a million mounted crystals in a 1 cm2 array

Silicon wafers (silicon dioxide surfaces) were patterned by photolithograpy to contain 3 μm (width) × 6 μm (length) × 40 μm (height) staggered rhombus posts in a square array (20 μm center-to-center spacing). These surfaces were hydrophobized using a vapor phase reaction with tridecafluorooctyldimethylchlorosilane and exhibit "superhydrophobicity" (water contact angles of θ(A)/θ(R) = 169°/156°). When a section of a wafer is submerged in and withdrawn from water, the superhydrophobic surface emerges, apparently completely dry. If the same procedure is performed using aqueous sodium chloride as the liquid bath, individual crystals of the salt can be observed on the top of each of the posts. "Dip-coating crystallization" using an aqueous sodium chloride solution of 4.3 M produces crystals with ～1 μm dimensions. A less concentrated solution, 1 M NaCl, renders crystals with ～500 nm dimensions. These experiments suggest that superhydrophobic surfaces that emerge from water and are "apparently completely dry" are, in fact, decorated with micrometer-size (several femtoliters) sessile water drops that rapidly evaporate. This simple technique is useful for preparation of very small liquid drops or puddles (of controlled composition) and for preparation of arrays of controlled size, crystalline substances (dip-coating crystallization).     

Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasistatically increased and decreased. We consider both two (cylindrical drops) and three (spherical drops) dimensions using analytical and numerical approaches to minimize the free energy of the drop. In two dimensions, we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions, this behavior persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions, we identify analytically the advancing and receding contact angles on the different surfaces, and we use numerical insights to argue that these provide bounds for the three-dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.     

Liquid drops on vertical and inclined surfaces; I. An experimental study of drop geometry

Experiments have been conducted to investigate the geometric parameters necessary to describe the shapes of liquid drops on vertical and inclined plane surfaces. Two liquids and eight surfaces have been used to study contact angles, contact lines, profiles, and volumes of drops of different sizes for a range of surface conditions. The results show the contact-angle variation along the circumference of a drop to be best fit by a third-degree polynomial in the azimuthal angle. This contact-angle function is expressed in terms of the maximum and minimum contact angles of the drop, which are determined for various conditions. The maximum contact angle, thetamax, is approximately equal to the advancing contact angle, thetaA, of the liquid on the surface. As the Bond number, Bo, increases from 0 to a maximum, the minimum contact angle, thetamin, decreases almost linearly from the advancing to the receding angle. A general relation is found between thetamin/thetaA and Bo for different liquid-surface combinations. The drop contour can be described by an ellipse, with the aspect ratio increasing with Bo. These experimental results are valuable in modeling drop shape, as presented in Part II of this work.     

Contact angles of colloid silica and gold particles at air-water and oil-water interfaces determined with the gel trapping technique

We have used the recently developed gel trapping technique (GTT) to determine the three-phase contact angles of submicrometer silica particles partially coated with octadecyl groups. The particles were spread at air-water and decane-water surfaces, and the aqueous phase was subsequently gelled with a nonadsorbing polysaccharide. The particles trapped at the surface of the aqueous gel were lifted by molding with curable poly(dimethylsiloxane) and imaged with scanning electron microscopy (SEM) to determine the particle contact line diameter which allows their contact angle at the original air-water or oil-water interface to be estimated. We report for the first time the use of the GTT for characterizing the contact angle of individual submicrometer particles adsorbed at liquid interfaces. The SEM images also reveal the structure of the particle monolayer at the interface and the structure of adsorbed particle aggregates. We have also determined the contact angles of agglomerated gold powder microparticles at the air-water and the decane-water interfaces. It was found that agglomerated gold particles demonstrate considerably higher contact angles than those on flat gold-coated surfaces.     

Slip-stick wetting and large contact angle hysteresis on wrinkled surfaces

Wetting on a corrugated surface that is formed via wrinkling of a hard skin layer formed by UV oxidation (UVO) of a poly(dimethylsiloxane) (PDMS) slab is studied using advancing and receding water contact angle measurements. The amplitude of the wrinkled pattern can be tuned through the pre-strain of the PDMS prior to surface oxidation. These valleys and peaks in the surface topography lead to anisotropic wetting by water droplets. As the droplet advances, the fluid is free to move along the direction parallel to the wrinkles, but the droplet moving orthogonal to the wrinkles encounters energy barriers due to the topography and slip-stick behavior is observed. As the wrinkle amplitude increases, anisotropy in the sessile droplet increases between parallel and perpendicular directions. For the drops receding perpendicular to the wrinkles formed at high strains, the contact angle tends to decrease steadily towards zero as the drop volume decreases, which can result in apparent hysteresis in the contact angle of over 100°. The wrinkled surfaces can exhibit high sessile and advancing contact angles (>115°), but the receding angle in these cases is generally vanishing as the drop is removed. This effect results in micrometer sized drops remaining in the grooves for these highly wrinkled surfaces, while the flat analogous UVO-treated PDMS shows complete removal of all macroscopic water drops under similar conditions. These wetting characteristics should be considered if these wrinkled surfaces are to be utilized in or as microfluidic devices.     

Contact angle kinetics of human albumin solutions at solid surfaces

Contact angle kinetics of sessile drops of albumin solution on hydrophilic acetal and hydrophobic FC 721 surfaces were measured using axisymmetric drop shape analysis. Young's equation is used to calculate the solid/liquid interfacial tension from measured contact angles and surface tensions as a function of time. The change in solid/liquid interfacial tension is a result of protein adsorption. It indicates that at the hydrophilic acetal surface the albumin molecules, interact only weakly, whereas the interaction with the hydrophobic FC 721 surface is quite strong.