The dynamics of evaporating sessile droplets

Experiments on sessile drops evaporating in a normal atmosphere without an applied thermal gradient are reported and compared with an available theoretical model. The liquids used are alkanes; water; and, more recently, polydimethylsiloxane oligomers. The substrates are silicon wafers, completely wetted by the liquid. Experiments with hanging drops allow us first to discard any influence of convection in the gas phase on the drop dynamics. The model assumes the process to be controlled by the stationary diffusion of the evaporating molecules in the gas phase. For alkanes and water, and in a limited range of drop sizes where gravity can be ignored, the model accounts very well for the dynamics of the drop radius, and rather well for the contact angle. This is no longer the case with the polydimethylsiloxane oligomers, where the very small contact angles require a more elaborated analysis of the drop edge. The text was submitted by the authors in English.     

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.     

Theory and simulation of angular hysteresis on planar surfaces

A simple model is proposed to simulate contact angle hysteresis in drops on a planar surface. The model is based on assuming a friction force acting on the triple contact line in such a way that the contact line keeps fixed for contact angles comprised between the advancing angle and the receding one and is allowed to move in order to avoid angles outside this interval. The model is straightforwardly applied to axisymmetric drops for which a simple solution of the Young-Laplace equation can be obtained. A variation of the method has also been implemented for nonaxisymmetric drops by resorting to the public-domain "Surface Evolver" software. Comparison with experiments shows the excellent performance of the model.     

Coalescence of two drops on partially wettable substrates

The present work contains the results of the experiments with two tiny drops on partially wettable substrates with contact angles of 10°, 24°, 27°, and 56°, which coalesce in the regime entirely dominated by viscous forces. Both side and bottom views are examined. The results for these three-dimensional coalescence flows are compared with scaling laws and the numerical two-dimensional model developed in the present work.     

Contact angles of oils on solid substrates in aqueous media: correlation with AFM data on protein adhesion

This study presents a method to measure the contact angles of oils on a substrate in water. Diiodomethane and perfluorodecalin were used as model oils. Self-assembled monolayers (SAMs) were prepared by adjusting the mole ratio of CH 3- and OH-terminated alkanethiols. The contact angles of the two oils in water increased with increasing hydrophilicity of the SAMs, and the results are contrasted with the contact angles of oils on these surfaces in air. In addition, perfluorodecalin showed higher contact angles than diiodomethane on the same surface. On the poly(N-isopropylacrylamide) (PNiPAAM) monolayer surface, the contact angles of the two oils in water decreased sharply at the transition temperature of PNiPAAM (approximately 30 degrees C), but the surface retained fairly high hydrophilicity even after the transition. The above results are correlated with atomic force microscopy (AFM) measurements of the adhesion force between protein-immobilized AFM tips (human fibrinogen and bovine serum albumin) and these monolayers.     

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.     

Directional self-cleaning superoleophobic surface

In this work, we report the creation of a grooved surface comprising 3 μm grooves (height ～4 μm) separated by 3 μm from each other on a silicon wafer by photolithography. The grooved surface was then modified chemically with a fluorosilane layer (FOTS). The surface property was studied by both static and dynamic contact angle measurements using water, hexadecane, and a polyethylene wax ink as the probing liquids. Results show that the grooved surface is both superhydrophobic and superoleophobic. Its observed contact angles agree well with the calculated Cassie-Baxter angles. More importantly, we are able to make a replica of the composite wax ink-air interface and study it by SEM. Microscopy results not only show that the droplet of the wax ink "sits" on air in the composite interface but also further reveal that the ink drop actually pins underneath the re-entrant structure in the side wall of the grooved structure. Contact angle measurement results indicate that wetting on the grooved surface is anisotropic. Although liquid drops are found to have lower static and advancing contact angles in the parallel direction, the drops are found to be more mobile, showing smaller hysteresis and lower sliding angles (as compared to the FOTS wafer surface and a comparable 3-μm-diameter pillar array FOTS surface). The enhanced mobility is attributable to the lowering of the resistance against an advancing liquid because 50% of the advancing area is made of a solid strip where the liquid likes to wet. This also implies that the contact line for advancing is no longer smooth but rather is ragged, having the solid strip area leading the wetting and the air strip area trailing behind. This interpretation is supported by imaging the geometry of the contact lines using molten ink drops recovered from the sliding angle experiments in both the parallel and orthogonal directions. Because the grooved surface is mechanically stronger against mechanical abrasion, the self-cleaning effect exhibited in the parallel direction suggests that groove texturing is a viable approach to create mechanically robust, self-cleaning, superoleophobic surfaces.     

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.     

Experiments on the motion of drops on a horizontal solid surface due to a wettability gradient

Results from experiments performed on the motion of drops of tetraethylene glycol in a wettability gradient present on a silicon surface are reported and compared with predictions from a recently developed theoretical model. The gradient in wettability was formed by exposing strips cut from a silicon wafer to dodecyltrichlorosilane vapors. Video images of the drops captured during the experiments were subsequently analyzed for drop size and velocity as functions of position along the gradient. In separate experiments on the same strips, the static contact angle formed by small drops was measured and used to obtain the local wettability gradient to which a drop is subjected. The velocity of the drops was found to be a strong function of position along the gradient. A quasi-steady theoretical model that balances the local hydrodynamic resistance with the local driving force generally describes the observations; possible reasons for the remaining discrepancies are discussed. It is shown that a model in which the driving force is reduced to accommodate the hysteresis effect inferred from the data is able to remove most of the discrepancy between the observed and predicted velocities.     

Force driven separation of drops by deterministic lateral displacement

We investigate the separation of drops in force-driven deterministic lateral displacement (f-DLD), a promising high-throughput continuous separation method in microfluidics. We perform scaled-up macroscopic experiments in which drops settle through a square array of cylindrical obstacles. These experiments demonstrate the separation capabilities-and provide insight for the design-of f-DLD for drops of multiple sizes, including drops that are larger than the gaps between cylinders and exhibit substantial deformation as they move through the array. We show that for any orientation of the driving force relative to the array of obstacles, the trajectories of the drops follow selected locking directions in the lattice. We also found that a simple collision model accurately describes the average migration angles of the drops for the entire range of sizes investigated here, and for all forcing directions. In addition, we found a difference of approximately 20° between the critical angles at which the smallest and largest drops first move across a line of obstacles (column) in the array, a promising result in terms of potential size resolution of this method. Finally, we demonstrate that a single line of cylindrical obstacles rotated with respect to the driving force is capable of performing binary separations. The critical angles obtained in such single line experiments, moreover, agree with those obtained using the full array, thus validating the assumption in which the trajectory (and average migration angle) of the drops is calculated from individual obstacle-drop collisions.     

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.     

Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates

Drop shape techniques, such as axisymmetric drop shape analysis, are widely used to measure surface properties, as they are accurate and reliable. Nevertheless, they are not applicable in experimental studies dealing with fluid configurations that do not present an apex. A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates. The theoretical shape of the interface is generated numerically as a function of surface tension and some geometrical parameters at the starting point of the interface, e.g., contact angle and radius of the interface. Then, the numerical shape is fitted to the experimental profile, taking the interfacial properties as adjustable parameters. The best fit identifies the true values of surface tension and contact angle. Comparison between the experimental and the theoretical profiles is performed using the theoretical image fitting analysis (TIFA) strategy. The new method, TIFA-axisymmetric interfaces (TIFA-AI), is applicable to any axisymmetric experimental configuration (with or without apex). The versatility and accuracy of TIFA-AI is shown by considering various configurations: liquid bridges, sessile and pendant drops, and liquid lenses.     

Moving contact lines and Langmuir-Blodgett film deposition

The objective of this paper is to point out the close relationship between contact line dynamics and LB film depositions, and it is designed to serve as a blueprint for future analysis of the LB technique. Moving contact lines and contact angles play a major role in Langmuir-Blodgett ultrathin film depositions. Although the effect of contact angles has been recognized for many years, a fundamental and comprehensive explanation of the phenomena taking place at the contact line has not been formulated before. Our understanding of contact line dynamics has improved thanks to careful experiments and new theoretical developments. Flow patterns depend on dynamic contact angle and the ratio of viscosities of the gas and liquid phases. More recently dynamic contact angles-and flow patterns-have been linked to forces of molecular and double-layer origin. The dynamic relationship of flow patterns to interfacial and transport properties can be used to explain seemingly contradictory experimental results reported by researchers during more than 60 years of experience with the L-B technique. Windows of operability can be defined for X-type and Z-type depositions that are useful in the design of experimental and industrial L-B deposition equipment.     

Indirect methods to measure wetting and contact angles on spherical convex and concave surfaces

In this work, a method was developed for indirectly estimating contact angles of sessile liquid drops on convex and concave surfaces. Assuming that drops were sufficiently small that no gravitational distortion occurred, equations were derived to compute intrinsic contact angles from the radius of curvature of the solid surface, the volume of the liquid drop, and its contact diameter. These expressions were tested against experimental data for various liquids on polytetrafluoroethylene (PTFE) and polycarbonate (PC) in the form of flat surfaces, spheres, and concave cavities. Intrinsic contact angles estimated indirectly using dimensions and volumes generally agreed with the values measured directly from flat surfaces using the traditional tangent method.     

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.     

Application of Young’s equation to two immiscible liquids resting on a solid substrate

The geometry of two immiscible liquid drops (water and mercury) resting on a solid substrate is reported. The problem under investigation is a very simple situation of a non-miscible two-phase liquid system which is properly documented. The simple experimental observation of water micro drop on top of a mercury drop on polypropylene substrate is discussed. The static situation of the drops is explored, and a new equation is derived for such situation by applying Young’s equation to the contact angles. The obtained equation simply represents the additive summation of Young equations for two independent drops, and may be applied for the case when the interfaces of two drops are close to each other and hence interact. The forces at the contact lines of each drop are treated separately as well as in correlation. This paper shows a schematic representation of two-liquid phase contact angle system. The value of this work may be appreciated from a pedagogical point of view.     

Hydrophobic waterborne coating for cellulose containing hybrid organic nanoparticle pigments with vegetable oils

Vegetable oils were combined with recent nanotechnology as a sustainable method for tuning the hydrophobicity of cellulose and paper surfaces. Different soy-, sunflower-, corn-, castor-, rapeseed- and hydrogenated oils were incorporated into an aqueous dispersion of hybrid styrene maleimide nanoparticles. Here, we investigate the formation of novel coatings from these dispersions and their performance on paper and paperboard, compared with model aluminum substrates. The coated papers are evaluated by static and dynamic contact angles, microscopy, atomic force microscopy, infrared and Raman spectroscopy. The nanoparticle pigments form a porous coating after drying, while the water repellence and hydrophobicity of paperboard and paper improved with contact angles of 90–99° after drying and 98–112° after ageing. The coatings with poly(unsaturated) oils have best hydrophobicity for dispersions with an optimum viscosity of 115–150 cp required for good coverage of the paper. While homogeneous coverage of the cellulose fibers is a primary requirement, thin coatings often provide higher contact angles on paper due to roughness of the underlaying fibrous surface. After ageing, the coatings are chemically stable without oil leakage and constant imide content, while an increase in contact angles is attributed to variations in coating morphology through local re-arrangements over the paper substrate.     

Advancing contact lines on chemically patterned surfaces

We report an experimental investigation on advancing contact lines of large drops spreading on chemically patterned surfaces. The model substrates were prepared using microphotolithography allowing precise control of the position and the size of the wettability patterns. Experiments were performed exploring different surface geometries: from ordered to disordered fields of defects and from low to high surface densities. The shape of the contact line between two isolated defects was investigated as a function of the distance. Portions of the contact line on the defects and on the matrix were studied during spreading experiments and were related to the apparent contact angles measured from the final thickness of the drops. A modified Cassie equation based on the line fraction of defects is proposed.     

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.     

A method for correcting the contact angle from the θ/2 method

The θ/2 method, a widely used technique on measuring the contact angle of a sessile drop, assumes that the drop profile is part of a sphere. However, the shape profile of a sessile drop is governed by the Young–Laplace equation and is different from a sphere, especially for drops with a large bound number (e.g. large volume or small surface tension). The spherical assumption, therefore, causes errors on evaluating the contact angles. The deviation of contact angle from the θ/2 method is evaluated from a theoretical calculation in this work. A simple means is given for correcting the measurement error. The corrected angle results from the drop volume, surface tension, liquid density and the contact angle from θ/2 method. An algorithm for finding the correct contact angle without knowing the density and surface tension is also given. At the end, two examples of pendant drops are given for the illustration.