Contact line and contact angle dynamics in superhydrophobic channels

The dynamics of the wetting and movement of a three-phase contact line confined between two superhydrophobic surfaces were studied using a mean-field free-energy lattice Boltzmann model. Principle features of superhydrophobic surfaces, such as trapped vapor/air between rough microstructures, high contact angles, reduced contact angle hysteresis, and low resistance to fluid flow, were all observed. Movement of the three-phase contact line over a well-patterned superhydrophobic surface displays a periodic stick-jump-slip behavior, while the dynamic contact angle changes accordingly from maximum to minimum. Two regimes were found for the flow velocity as a function of surface roughness and can be related directly to the balance between driving force and flow resistance. This work provides a better understanding of dynamic wetting and fluid flow behaviors over superhydrophobic surfaces and hence could be useful in related applications.     

Experimental investigation of contact angle, curvature, and contact line motion in dropwise condensation and evaporation

Image-analyzing interferometry is used to measure the apparent contact angle and the curvature of a drop and a meniscus during condensation and evaporation processes in a constrained vapor bubble (CVB) cell. The apparent contact angle is found to be a function of the interfacial mass flux. The interfacial velocity for the drop during condensation and evaporation is a function of the apparent contact angle and the rate of change of radius of curvature. The dependence of velocity on the apparent contact angle is consistent with Tanner's scaling equation. The results support the hypothesis that evaporation/condensation is an important factor in contact line motion. The main purpose of this article is to present the experimental technique and the data. The equilibrium contact angle for the drop is found experimentally to be higher than that for the corner meniscus. The contact angle is a function of the stress field in the fluid. The equilibrium contact angle is related to the thickness of the thin adsorbed film in the microscopic region and depends on the characteristics of the microscopic region. The excess interfacial free energy and temperature jump were used to calculate the equilibrium thickness of the thin adsorbed film in the microscopic region.     

Line energy and the relation between advancing, receding, and young contact angles

The line energy associated with the triple phase contact line is a function of local surface defects (chemical and topographical); however, it can still be calculated from the advancing and receding contact angles to which those defects give rise. In this study an expression for the line energy associated with the triple phase contact line is developed. The expression relates the line energy to the drop volume, the interfacial energies, and the actual contact angle (be it advancing, receding, or in between). From the expression we can back calculate the equilibrium Young contact angle, theta0, as a function of the maximal advancing, thetaA, and minimal receding, thetaR, contact angles. To keep a certain maximal hysteresis between advancing and receding angles, different line energies are required depending on the three interfacial energies and the drop's volume V. We learn from the obtained expressions that the hysteresis is determined by some dimensionless parameter, K, which is some normalized line energy. The value of K required to keep a constant hysteresis (thetaA-thetaR) rises to infinity as we get closer to theta0 = 90 degrees.     

Moving contact lines of a colloidal suspension in the presence of drying

This article presents the first experimental study of an advancing contact line for a colloidal suspension. A competition between the hydrodynamic flow due to the drop velocity and the drying is exhibited: drying accounts for particle agglomeration that pins the contact line whereas the liquid flow dilutes the agglomerated particles and allows the contact line to advance continuously. The dilution dominates at low concentration and high velocity, but at high concentration and low velocity, the contact line can be pinned by the particle agglomeration, which leads to a stick-slip motion of the contact line. The calculation of the critical speed splitting both regimes gives an order of magnitude comparable to that of experiments. Moreover, a model of agglomeration gives an estimation of both the size of the wrinkles formed during stick-slip and the force exerted by the wrinkle on the contact line.     

On the validity of the Cassie equation via a mean-field free-energy lattice Boltzmann approach

We studied wetting phenomena on heterogeneous surfaces by a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 69 (2004) 32,602]. Our results suggest that the Cassie equation in macroscopic contact angle measurements is in general not valid. It was found that the Cassie equation is valid only when the patch size is on the same order of the liquid-vapor interfacial thickness. We also demonstrated that contact angle manifests itself from local surface properties near the contact point and does not result from the specific solid-liquid interactions across the contact area.     

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.     

格子Boltzman方法数值模拟微通道内不互溶液液两相流动

利用基于场介子格子Boltzman(LB)方法对T形微通道内油-水不互溶两相流动进行了数值模拟.通过静止液滴算例改进该两相流LB模型且验证了模型的有效性,成功数值模拟了T形微通道内油水两相流的五种不同流型.数值模拟结果和实验数据定性和定量吻合很好,表明本文数值方法的有效性.此外,采用改进后的LB两相流模型模拟了不同界面张力和接触角条件下的液滴形成过程,讨论了这两个变量对流型和液滴形状的影响.结果表明LB方法是研究微通道内不互溶两相流的一种有效的数值工具,能够对各种涉及不互溶多相流微流体设备的设计提供指导.     

Estimation of line tension and contact angle from heterogeneous nucleation experimental data

Using the classical nucleation theory corrected with line tension and experimental data of heterogeneous nucleation of n-nonane, n-propanol, and their mixture on silver particles of three different sizes, the authors were able to estimate the line tensions and the microscopic contact angles for the above mentioned systems. To do this they applied generalized Young's equation for the line tension and calculated the interfacial tensions using Li and Neumann's equation [Adv. Colloid Interface Sci. 39, 299 (1992)]. It has been found that, for both unary and binary systems, the line tension is negative and the resulting microscopic contact angle derived from experimental nucleation data is most of the time larger than the macroscopic one. This is in contrast to earlier studies where the influence of line tension has not been accounted for. The values of the three phase contact line tension obtained in this way are of the same order of magnitude as the estimations for other systems reported in literature. The line tension effect also decreases considerably the nucleation barrier.     

Prediction of solid-fluid interfacial tension and contact angle

Two simple equations have been developed using the lattice theory and the regular solution assumption to predict the solid-vapor and solid-liquid interfacial tension. The required parameters are the liquid critical temperature and volume, the solid melting temperature and the molar volume of liquid and solid compounds. To confirm the models, the predicted solid-fluid interfacial tension values have been used to predict the contact angle of the liquid drop on the solid surface applying Young's equation. Agreement of the predicted contact angle with the experimental data reveals the reliability of the developed models.     

To improve alignment of isoindigo-based conjugated polymer film by controlling contact line receding velocity

The macroscopic alignment of conjugated polymers with low grain boundary is essential to carrier transport. During film forming process, the match between contact line receding velocity and the critical alignment velocity is essential to get the alignment polymer film. In this paper, the contact line receding velocity of a D-A conjugated polymer film, isoindigo and bithiophene (ⅡDDT-C3), was adjusted by solvent vapor content and film-formation temperature. Only when solvent vapor content was 0.3 mL and the film-formation temperature was 90℃, the contact line receding velocity was in accordance with the critical alignment velocity, and the highest degree of alignment was attained in the ⅡDDT-C3 film, with the dichroic ratio up to 4.08. Fibers were aligned parallel with the direction of the contact line receding and the molecules of ⅡDDT-C3 adopted an edge-on orientation with the backbone parallel with the direction of fiber long axis. The π-π stacking distance between adjacent molecules was 3.63 Å.     

Histogram analysis as a method for determining the line tension of a three-phase contact region by Monte Carlo simulations

A method is proposed for determining the line tension, which is the main physical characteristic of a three-phase contact region, by Monte Carlo (MC) simulations. The key idea of the proposed method is that if a three-phase equilibrium involves a three-phase contact region, the probability distribution of states of a system as a function of two order parameters depends not only on the surface tension, but also on the line tension. This probability distribution can be obtained as a normalized histogram by appropriate MC simulations, so one can use the combination of histogram analysis and finite-size scaling to study the properties of a three phase contact region. Every histogram and results extracted therefrom will depend on the size of the simulated system. Carrying out MC simulations for a series of system sizes and extrapolating the results, obtained from the corresponding series of histograms, to infinite size, one can determine the line tension of the three phase contact region and the interfacial tensions of all three interfaces (and hence the contact angles) in an infinite system. To illustrate the proposed method, it is applied to the three-dimensional ternary fluid mixture, in which molecular pairs of like species do not interact whereas those of unlike species interact as hard spheres. The simulated results are in agreement with expectations.     

Cusp at the three-fluid contact line in a cylindrical pore

In a cylindrical pore of arbitrary wettability, we analyse the existence of a three-fluid contact line connecting the fluid-fluid interfaces between two bulk phases and the third phase contained in a cusp near the pore wall. This analysis is supported by the very similar, but simpler, analysis for a constriction between parallel plates. From the force balance at the contact line and the equations for the interface curvatures we derive expressions for the cusp height and for the capillary entry pressure related to piston-like displacement between the two bulk phases. The latter is independent of the existence of a cusp and its phase pressure. Based on some realistic assumptions, of which the most important is that a cusp grows continuously from the onset when its phase pressure is increased, we analyse under which conditions a cusp can exist, and, when it exists, what its behaviour is as a function of the cusp phase pressure. We find a simple criterion involving (two ratios of) the three interfacial tensions and two of the three contact angles, which determines whether the three-fluid contact line and, consequently, a cusp exists. The range of contact angles, as well as the size of the cusp increases, when the cusp phase is close to spreading. Not only cusps of the wetting phase can occur, but also of the intermediate-wetting phase. Numerical examples are presented to illustrate the range of behaviour of the cusps.     

Spreading, evaporation, and contact line dynamics of surfactant-laden microdrops

An optical technique based on the reflectivity measurements of a thin film was used to experimentally study the spreading, evaporation, contact line motion, and thin film characteristics of drops consisting of a water-surfactant (polyalkyleneoxide-modified heptamethyltrisiloxane, called superspreader) solution on a fused silica surface. On the basis of the experimental observations, we concluded that the surfactant adsorbs primarily at the solid-liquid and liquid-vapor interfaces near the contact line region. At equilibrium, the completely wetting corner meniscus was associated with a flat adsorbed film having a thickness of approximately 31 nm. The calculated Hamaker constant, A = -4.47 x 10(-)(20) J, shows that this thin film was stable under equilibrium conditions. During a subsequent evaporation/condensation phase-change process, the thin film of the surfactant solution was unstable, and it broke into microdrops having a finite contact angle. The thickness of the adsorbed film associated with the drops was lower than that of the equilibrium meniscus. The drop profiles were experimentally measured and analyzed during the phase-change process as the contact line advanced and receded. The apparent contact angle, the maximum concave curvature near the contact line region, and the convex curvature of the drop increased as the drop grew during condensation, whereas these quantities decreased during evaporation. The position of the maximum concave curvature of the drop moved toward the center of the drop during condensation, whereas it moved away from the center during evaporation. The contact line velocity was correlated to the observed experimental results and was compared with the results of the drops of a pure alcohol. The experimentally obtained thickness profiles, contact angle profiles, and curvature profiles of the drops explain how the surfactant adsorption affects the contact line motion. We found that there was an abrupt change in the velocity of the contact line when the adsorbed film of the surfactant solution was just hydrated or desiccated during the phase-change processes. This result shows the effect of vesicles and aggregates of the surfactant on the shape evolution of the drops. For these surfactant-laden water drops, we found that the apparent contact angle increased during condensation and decreased during evaporation. However, for the drop of a pure liquid (n-butanol and 2-propanol) the apparent contact angle remained constant at a constant velocity during condensation and evaporation. The contact line was pinned during the evaporation and spreading of the surfactant-laden water drops, but it was not pinned for a drop of a pure alcohol (self-similar shape evolution).     

Pressure dependence of the contact angle

When a liquid and its vapor contact a smooth, homogeneous surface, Gibbsian thermodynamics indicates that the contact angle depends on the pressure at the three-phase line of an isothermal system. When a recently proposed adsorption isotherm for a solid-vapor interface is combined with the equilibrium conditions and the system is assumed to be in a cylinder where the liquid-vapor interface can be approximated as spherical, the contact-angle-pressure relation can be made explicit. It indicates that a range of contact angles can be observed on a smooth homogeneous surface by changing the pressure at the three-phase line, but it also indicates that the adsorption at the solid-liquid interface is negative, and leads to the prediction that the contact angle increases with pressure. The predicted dependence of the contact angle on pressure is investigated experimentally in a system that has an independent mechanism for determining when thermodynamic equilibrium is reached. The predictions are in agreement with the measurements. The results provide a possible explanation for contact angle hysteresis.     

Analysis of the relationship between liquid droplet size and contact angle

The purpose of this paper is to present a consistent theoretical concept that can explain the various physical phenomena associated with the effect of droplet size on contact angle for droplets on solid surfaces, and with the geometry of the liquid/gas/solid contact line in general. Two droplet geometries have been considered: uniformly elongated droplets and axisymmetric droplets. It has been shown that the contact angle for elongated droplets is size-independent and, thus, satisfies the Young equation for constant material and interfacial properties. On the other hand, whereas the contact angle for axisymmetric droplets is size-dependent and does not satisfy the original Young equation, it is shown that this contact angle can still be predicted for any combination of droplet and substrate materials, and a given mass of the droplet. The theoretical work has been combined with the development of numerical schemes of solving the Laplace-Young equation for various droplet geometries. The proposed approach has been applied to different material/substrate combinations and validated against several sets of experimental data. As a result, a method has been developed for predicting the contact angle of both long and axisymmetric sessile droplets of arbitrary sizes for given liquid/solid/gas properties.     

A refractive tilting-plate technique for measurement of dynamic contact angles

The contact angle is a critical parameter in liquid interface dynamics ranging from liquid spreading on a solid surface on earth to liquid motion in partially filled containers in space. A refractive tilting-plate technique employing a scanning laser beam is developed to conduct an experimental study of a moving contact line, with the intention of making accurate measurements of the contact angle. The technique shows promise as an accurate and potentially fully automated means to determine the velocity dependence of the contact angle at the intersection of the interface between two transparent fluids with a transparent solid surface. Ray tracing calculations are included to reinforce the measurement concept. The principal experiments were conducted at speeds ranging from 0.05 to 1.00 mm/s, both advancing and receding, using an immiscible liquid pair (nonane/formamide) in contact with glass. The contact angle was found to depend for practical purposes only on the sign of the velocity and not on its magnitude for the range of velocities studied. Other observations revealed a bimodal behavior of the contact line that depends on which liquid first contacts the glass, with resulting drift in the dynamic contact angle with time.     

Biocompatible, lactide-based surfactants for the CO2-water interface: high-pressure contact angle goniometry, tensiometry, and emulsion formation

The unique properties of compressed CO2, including its low cost, nontoxicity, easily tunable solvent strength, and favorable transport properties, make it an environmentally attractive alternative to volatile organic solvents. Suitable surface-active species can be utilized to realize the full potential of clean, CO2-based technologies, by helping to overcome the low solubility typically associated with many solutes of interest in CO2. In this work we synthesize and investigate the interfacial activity of a series of nonionic amphiphiles with a biocompatible and biodegradable CO2-phile at both the CO2-water (C|W) and CO2-water-solid (C|W|S) interfaces. We developed a high-pressure pendant drop tensiometer and contact angle goniometer that allows us to measure both tension and contact angle in tandem. The tension of the C|W interface was measured in the presence of the lactide (LA)-based surface active agents with varying molecular weight and hydrophilic-to-CO2-philic ratios. Emulsion studies with an optimum balanced surfactant were performed. The contact angle of water droplets against a silane-modified (hydrophobic) substrate under CO2 atmosphere was also measured in presence of a selected LA-based amphiphile. The results demonstrate that the nonionic copolymers with the biodegradable and biocompatible LA-based group can significantly reduce the tension of the C|W interface. The LA-based surface active species are also capable of forming stable emulsions of water and CO2 and reducing the angle of the three-phase C|W|S contact line.     

Prediction of solid-water-hydrocarbon contact angle

The reliability of a recently developed solid-vapour and solid-liquid interfacial tension models has been investigated by applying them to predict liquid-vapour and liquid-liquid interfacial tension values. The impact of the geometrical molecular packing and the molecular orientations near the surface on the predicted values are discussed. The mutual solubility data are shown to be adequate for calculation of the interaction parameters in the solid-liquid model and a new equation, using this information, is developed for prediction of water-hydrocarbon interfacial tension. The model has been applied to recent data on water-methane-n-decane and water-methane-cyclohexane-n-decane interfacial tensions at elevated temperature and pressure and its reliability demonstrated. It is shown that the solid-liquid interfacial tension model is solely adequate for predicting the contact angle by applying it to mercury-water-benzene and stearic acid-water-n-decane systems.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.