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.     

On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces

This paper presents a systematic study of liquid droplet impact on three polymer surfaces: poly(methyl methacrylate), poly(methyl methacrylate/n-butyl methacrylate), and poly(n-butyl methacrylate). Changing from one surface to the next represents an incremental variation in solid surface tensions of 5-6 mJ/m2. These surfaces were prepared through careful experimental procedures that were used for the determination of solid surface tensions from contact angles. Our data for the maximum spreading diameter of water and formamide impacting on these surfaces were compared with those predicted from literature models. Of the models selected, we modified the model of Pasandideh-Fard et al. [Phys. Fluids 1996, 8, 650] and the results yielded a least error of only 5.09 +/- 5.05% in the determination of the maximum spreading diameter. The improved model was also compared with literature data, and good agreement was found. Of course, any such comparisons would rely on accurate experimental impact dynamics data on carefully prepared surfaces.     

Contact-angle hysteresis on super-hydrophobic surfaces

The relationship between perturbations to contact angles on a rough or textured surface and the super-hydrophobic enhancement of the equilibrium contact angle is discussed theoretically. Two models are considered. In the first (Wenzel) case, the super-hydrophobic surface has a very high contact angle and the droplet completely contacts the surface upon which it rests. In the second (Cassie-Baxter) case, the super-hydrophobic surface has a very high contact angle, but the droplet bridges across surface protrusions. The theoretical treatment emphasizes the concept of contact-angle amplification or attenuation and distinguishes between the increases in contact angles due to roughening or texturing surfaces and perturbations to the resulting contact angles. The theory is applied to predicting contact-angle hysteresis on rough surfaces from the hysteresis observable on smooth surfaces and is therefore relevant to predicting roll-off angles for droplets on tilted surfaces. The theory quantitatively predicts a "sticky" surface for Wenzel-type surfaces and a "slippy" surface for Cassie-Baxter-type surfaces.     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

Chain length effect of alkanethiol self-assembled monolayers on the maximum spreading ratio of impacting water droplets

This paper presents a systematic study of de-ionized water droplets impact on five different self-assembled monolayer surfaces: octadecanethiol, hexadecanethiol, dodecanethiol, heptanethiol and pentanethiol. Our data for the maximum spreading diameter of water impacting on these surfaces were compared with those predicted from literature models. Of the models selected, the model [M. Pasandideh-Fard, S. Chandra, J. Mostaghimi, Phys. Fluids 8 (1996) 650] was modified and the results yielded a least mean error of 7.55 ± 1.73% in the determination of the maximum spreading diameter, which is among the best from those selected.     

Molecular dynamics simulations of water droplets on polymer surfaces

Molecular dynamics simulations were used to study the wetting of polymer surfaces with water. Contact angles of water droplets on crystalline and two amorphous polyethylene (PE) and poly(vinyl chloride) (PVC) surfaces were extracted from atomistic simulations. Crystalline surfaces were produced by duplicating the unit cell of an experimental crystal structure, and amorphous surfaces by pressing the bulk polymer step by step at elevated temperature between two repulsive grid surfaces to a target density. Different-sized water droplets on the crystalline PE surface revealed a slightly positive line tension on the order of 10(-12)-10(-11) N, whereas droplets on crystalline PVC did not yield a definite line tension. Microscopic contact angles produced by the simple point charge (SPC) water model were mostly a few degrees smaller than those produced by the extended SPC model, which, as the model with lowest bulk energy, presents an upper boundary for contact angles. The macroscopic contact angle for the SPC model was 94 degrees on crystalline PVC and 113 degrees on crystalline PE. Amorphicity of the surface increased the water contact angle on PE but decreased it on PVC, for both water models. If the simulated contact angles on crystalline and amorphous surfaces are combined in proportion to the crystallinity of the polymer in question, simulated values in relatively good agreement with measured values are obtained.     

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.     

On the Problem of the Relationship between the Contact Angle and Surface Roughness Coefficient: Quartz Wettability with Melted Germanium

Equilibrium contact angles of melted geranium have been measured at fused quartz surfaces. The surfaces were preliminarily grinded, polished, and, in some cases, etched. Then, the roughness coefficients are determined for the relief profile and the surface itself by optical interferometry using a NanoMap 1000 WLI profilometer. The contact angle has been found to vary in a range of 147°–164° depending on the method of surface pretreatment. The measured values of the contact angles agree with the data of other researchers. At the same time, the analysis of the obtained data has led to the conclusion that Wenzel’s equation, which relates the contact angles at smooth and rough surfaces, is not valid for germanium droplets on quartz surface.     

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.     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

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.     

Wetting of nanogrooved polymer surfaces

Molecular dynamics simulations were used to study the wetting of nanogrooved PE and PVC polymer surfaces. The contact angles, equilibrium states, and equilibrium shapes of two nanosized water droplets were analyzed on surfaces with 1D-arranged periodic roughness of various dimensions. The composite solid-liquid contact, which is preferred in practical applications and in which a droplet rests on top of the surface asperities, was observed on the roughest PE surfaces, whereas water filled the similar but slightly deeper grooves on PVC surfaces. The transition from the wetted to composite contact regime occurred when the contact angle with a flat surface reached the value at which the apparent Wenzel and Cassie contact angles are equal. Droplets on grooved PE surfaces with the composite contact exhibited contact angles in agreement with Cassie's equation, but the increase in hydrophobicity on smoother surfaces with the wetted contact was less than expected from Wenzel's equation. The difference between the simulated and theoretical values decreased as the dimensions of the surface grooves increased. Only a slight increase or even a slight decrease in the contact angles was observed on the grooved PVC surfaces, owing to the less hydrophobic nature of the flat PVC surface. On both polymers, the nanodroplet assumed a spherical shape in the composite contact. Only minor anisotropy was observed in the wetted contact on PE surfaces, whereas even a highly anisotropic shape was seen on the grooved PVC surfaces. The contact angle in the direction of the grooves was smaller than that in the perpendicular direction, and the difference between the two angles decreased with the increasing size of the water droplet.     

Contact angle measurement on rough surfaces

A new method for the measurement of apparent contact angles at the global energy minimum on real surfaces has been developed. The method consists of vibrating the surface, taking top-view pictures of the drop, monitoring the drop roundness, and calculating the contact angle from the drop diameter and weight. The use of the new method has been demonstrated for various rough surfaces, all having the same surface chemistry. In order to establish the optimal vibration conditions, the proper ranges for the system parameters (i.e., drop volume, vibration time, frequency of vibration, and amplitude of vibration) were determined. The reliability of the method has been demonstrated by the fact that the ideal contact angles of all surfaces, as calculated from the Wenzel equation using the measured apparent contact angles, came out to be practically identical. This ideal contact angle has been compared with three methods of calculation from values of advancing and receding contact angles.     

Thermodynamic modeling of contact angles on rough, heterogeneous surfaces

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.     

VOF simulations of the contact angle dynamics during the drop spreading: Standard models and a new wetting force model

Introduction

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas–liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

Methodology

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an “adhesion-like” force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid–air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

Results

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θ_adv = 10° – 70°) and hydrophobic (θ_adv = 105° – 120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

Conclusion

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We < ˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.     

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.     

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°.     

Determination of contact angles, silane coverage, and hydrophobicity heterogeneity of methylated quartz surfaces using ToF-SIMS

Methylated quartz surfaces are extensively used in colloid science for wettability studies and the control and impact of hydrophobicity in key physicochemical processes. In this study, time-of-flight secondary ion mass spectrometry (ToF-SIMS) has been used to correlate the surface chemistry of trimethylchlorosilane-methylated quartz surfaces with the contact angle. Models have been developed for the calculation of both advancing and receding contact angles based on measurements of the ToF-SIMS signals for SiC(3)H(9)(+) (TMCS) and Si(+) (quartz). These models enable the contact angle across surfaces and, more importantly, that of individual particles to be determined on a micrometer scale. Distributions of contact angles in large ensembles of particles, therefore, can now be determined. In addition, from the ToF-SIMS analysis, the surface coverage of the methylated species can be quantitatively determined, in line with the Cassie equation. Moreover, advancing and receding contact angle maps can be calculated from ToF-SIMS images, and hence the variation in microscopic hydrophobicity (e.g., at the particle level) can be extracted directly from the images.     

Ratchetlike slip angle anisotropy on printed superhydrophobic surfaces

The fabrication and properties of superhydrophobic surfaces that exhibit ratchet-like anisotropic slip angle behavior is described. The surface is composed of arrays of poly(dimethylsiloxane) (PDMS) posts fabricated by a type of 3D printing. By controlling the dispense parameters, regular arrays of asymmetric posts were deposited such that the slope of the posts was varied from 0 to 50 relative to the surface normal. Advancing and receding contact angles as well as slip angles were measured as a function of the post slope and droplet volume. Ratchetlike slip angle anisotropy was observed on surfaces composed of sloped features. The maximum slip angle difference (for a 180° tilt angle variation) was 32° for 20 μL droplets on surfaces with posts fabricated with a slope of 50°. This slip angle anisotropy is attributed to an increase in the triple contact line (TCL) length as the droplet is tilted in a direction against the post slope whereas the TCL decreases continuously when the drop travels in a direction parallel to the post slope. The increasing length of the TCL creates an increased energy barrier that accounts for the higher slip angles in this direction.     

Validity of the "sharp-kink approximation" for water and other fluids

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, on the basis of a comparison of predicted and measured contact angles near room-temperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.