Droplets on inclined rough surfaces

The behaviour of liquid droplets on inclined heterogeneous surfaces was simulated by the lattice-Boltzmann method using the Shan-Chen multiphase model. The effect of topography of the surface on the contact angle hysteresis was investigated. It is shown in particular, by using anisotropic rough surfaces, how surface topography and thereby the continuity of the three-phase contact line, affect this hysteresis. Our results clearly indicate that the superhydrophobicity of a surface cannot be judged by the contact angle alone.     

Contact angle hysteresis on nano-structured surfaces

We present results from an experimental study on the phenomenon of contact angle hysteresis on solid surfaces decorated by a random array of nanometric hollows. For weak values of the areal density of defects φ_d, the hysteresis H increases linearly with φ_d. This evolution is described by a pinning–depinning process of the contact line by individual defects. At higher values of φ_d, a collective pinning effect appears and H decreases with increasing φ_d. In the linear regime, our experimental results are compared to theoretical predictions for contact angle hysteresis induced by a single isolated defect on the solid surface. We suggest that the crossover from the individual to the collective pinning effects could be interpreted in terms of an overlapping of wetting cross sections. Finally, we analyse the influence of both the size and the morphology (hollows/hillocks) of defects on the anchorage of the contact line.     

Structure of the surface microrelief of a droplet evaporating from a rough substrate as a possible cause of contact angle hysteresis

Based on the refraction images of a droplet evaporating on a rough substrate, we simultaneously observed the dynamics of its surface microrelief, contact angle, and contact line deformations along the entire perimeter of the contact line. This has led us conclude that the microrelief structure is directly related to the phenomenon of contact angle hysteresis and the jump-like pattern of contact line deformation. We suggest a possible mechanism for the occurrence of contact angle hysteresis during droplet evaporation and derive the relations that specify the range of possible contact angles at known microrelief parameters.     

Nanodroplets on rough hydrophilic and hydrophobic surfaces

We present results of Molecular Dynamics (MD) calculations on the behavior of liquid nanodroplets on rough hydrophobic and hydrophilic solid surfaces. On hydrophobic surfaces, the contact angle for nanodroplets depends strongly on the root-mean-square roughness amplitude, but it is nearly independent of the fractal dimension of the surface. Since increasing the fractal dimension increases the short-wavelength roughness, while the long-wavelength roughness is almost unchanged, we conclude that for hydrophobic interactions the short-wavelength (atomistic) roughness is not very important. We show that the nanodroplet is in a Cassie-like state. For rough hydrophobic surfaces, there is no contact angle hysteresis due to strong thermal fluctuations, which occur at the liquid-solid interface on the nanoscale. On hydrophilic surfaces, however, there is strong contact angle hysteresis due to higher energy barrier. These findings may be very important for the development of artificially biomimetic superhydrophobic surfaces.     

The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, wetting has been studied using contact angles of drops on solids for more than 200 years, the question remains unanswered: Is wetting of a rough and chemically heterogeneous surface controlled by the interactions within the solid/liquid contact area beneath the droplet or only at the three-phase contact line? After the publications of Pease in 1945, Extrand in 1997, 2003 and Gao and McCarthy in 2007 and 2009, it was proposed that advancing, receding contact angles, and contact angle hysteresis of rough and chemically heterogeneous surfaces are determined by interactions of the liquid and the solid at the three-phase contact line alone and the interfacial area within the contact perimeter is irrelevant. As a consequence of this statement, the well-known Wenzel (1934) and Cassie (1945) equations which were derived using the contact area approach are proposed to be invalid and should be abandoned. A hot debate started in the field of surface science after 2007, between the three-phase contact line and interfacial contact area approach defenders. This paper presents a review of the published articles on contact angles and summarizes the views of the both sides. After presenting a brief history of the contact angles and their measurement methods, we discussed the basic contact angle theory and applications of contact angles on the characterization of flat, rough and micropatterned superhydrophobic surfaces. The weak and strong sides of both three-phase contact line and contact area approaches were discussed in detail and some practical conclusions were drawn.     

A Model for the Contact Angle of Liquid Droplets on Rough Surfaces

Up to now, measured results of the contact angle on rough surfaces have been explained usually based on the Wenzel equation （1936） and the Cassie-Baxter equation （1944）. However, these equations do not take into account considerations of liquid wetting behaviors on rough surfaces, and this leads to poor understanding of the mechanisms of contact between liquid droplets and rough surfaces （e.g. contact angle hysteresis）. We propose a new model for the contact angle of liquid droplets. By means of the present model, we can well understand the evperimental data which could not be well explained by the Wenzel equation and the Cassie-Baxter equation.     

Preparation of hybrid film with superhydrophobic surfaces based on irregularly structure by emulsion polymerization

A superhydrophobic surface originated from quincunx-shape composite particles was obtained by utilizing the encapsulation and graft of silica particles to control the surface chemistry and morphology of the hybrid film. The composite particles make the surface of film form a composite interface with irregular binary structure to trap air between the substrate surface and the liquid droplets which plays an essential role in obtaining high water contact angle and low water contact angle hysteresis. The water contact angle on the hybrid film is determined to be 154 ± 2° and the contact angle hysteresis is less than 5°. This is expected to be a simple and practical method for preparing self-cleaning hydrophobic surfaces on large area.     

A new model for thermodynamic analysis on wetting behavior of superhydrophobic surfaces

Superhydrophobic surfaces have shown inspiring applications in microfluidics, and self-cleaning coatings owing to water-repellent and low-friction properties. However, thermodynamic mechanism responsible for contact angle hysteresis (CAH) and free energy barrier (FEB) have not been understood completely yet. In this work, we propose an intuitional 3-dimension (3D) droplet model along with a reasonable thermodynamic approach to gain a thorough insight into the physical nature of CAH. Based on this model, the relationships between radius of three-phase contact line, change in surface free energy (CFE), average or local FEB and contact angle (CA) are established. Moreover, a thorough theoretical consideration is given to explain the experimental phenomena related to the superhydrophobic behavior. The present study can therefore provide some guidances for the practical fabrications of the superhydrophobic surfaces.     

液滴在梯度微结构表面上的铺展动力学分析

本文通过改变肋柱宽度和间距, 构造了二级和多级梯度微结构表面, 采用格子-Boltzmann方法对液滴在两种梯度表面上的铺展过程进行了研究, 探析液滴运动的机理和调控方法. 结果表明, 在改变肋柱间距的二级梯度表面上, 当液滴处于Cassie态时, 接触角滞后大小与粗糙度梯度成正比关系; 当液滴从Cassie态转换为Wenzel态或介于两者之间的不稳定态时, 这一正比关系不再遵循. 在改变肋柱宽度的二级梯度表面上, 接触角滞后大小与粗糙度梯度始终成正比关系. 在多级梯度表面上, 随液滴初始半径增大, 接触角滞后减小, 但液滴平衡位置相较于初始位置偏离增大. 对梯度微结构表面上液滴运动和接触角滞后的定量分析, 可为实现梯度微结构表面液滴运动调控提供理论依据.     

Pinning-depinning of the contact line on nanorough surfaces

We study the pinning-depinning phenomenon of a contact line on a solid surface decorated by a random array of nanometric structures. For this purpose, we have investigated the contact angle hysteresis behaviour of six different wetting and non-wetting fluids with surface tensions varying from 25 to 72mN m^-1. For low values of the areal density of defects φ_d, the hysteresis H increases linearly with φ_d indicating that “individual” defects pin the contact line. Then, from a given value of φ_d, the hysteresis H becomes to decrease with increasing φ_d, indicating a new kind of collective depinning. These two regimes were observed for all fluids used. In both cases, our experimental results are compared with the theoretical predictions for contact angle hysteresis induced by single or multiple topographical defects. We ascribe the decrease of H to the formation of cavities along the wetting front.     

Determination of solid material elastic modulus and surface energy based on JKR contact model

The JKR contact theory is employed to study the adhesion phenomena between two solid materials in intimate contact. The elastic contact modulus and the work of adhesion of solid materials are obtained during adhesion tests by utilizing a micro force-deflection measuring apparatus. Six of the plastic materials, including polyethylene polyoxymethlene (POM), polyamide (PA), terephthalate (PET), polyvinyl chloride (PVC), polypropylene (PP), and ultra-high molecular weight polyethylene (UHMWPE) are used to evaluate the adhesion effect implied by the JKR theory. Comparison is made between surface energy obtained from the adhesion tests with that by a dynamic contact angle analyser.Results show that the load/deflection data in the loading phase are in good agreement with the predictions of JKR equation, and the experimental data of unloading phase deviate significantly from the JKR theory. The phenomena of adhesion hysteresis in loading tests are responsible for these results due to the effects of molecular reconstruction on solid surfaces in contact. The work of adhesions, and hence surface energies of plastic materials, calculated by the best fitting of JKR equation with the experimental data in the loading phase, agree satisfactorily in a comparable manner with that obtained using the contact angle analyser.     

Vibrated sessile drops: Transition between pinned and mobile contact line oscillations

We study the effects of vertical vibrations on non-wetting large water sessile drops flattened by gravity. The solid substrate is characterized by a finite contact angle hysteresis (10-15 degrees). By varying the frequency and the amplitude of the vertical displacement, we observe two types of oscillations. At low amplitude, the contact line remains pinned and the drop presents eigen modes at different resonance frequencies. At higher amplitude, the contact line moves: it remains circular but its radius oscillates at the excitation frequency. The transition between these two regimes arises when the variations of contact angle exceed the contact angle hysteresis. We interpret different features of these oscillations, such as the decrease of the resonance frequencies at larger vibration amplitudes. The hysteresis acts as solid friction on the contour oscillations, and gives rise to a stick-slip regime at intermediate amplitude.Received: 4 April 2004, Published online: 10 August 2004PACS: 47.55.Dz Drops and bubbles - 68.08.Bc Wetting - 47.35. + i Hydrodynamic waves     

Vibrations of sessile drops

This study focuses on the effects of vertical vibrations on sessile drops deposited on hydrophobic substrates. At low amplitudes the contact line remains pinned because of contact angle hysteresis and only drop surface modes areobserved. Above a first threshold the contact line starts to move and exhibits a stick-slip behavior that presents some analogies with the solid friction on amechanical oscillator. At larger amplitudes, non-axisymmetric contour modes show up (modes m=2, 3...). They can be interpreted as a coupling between surface modes and contact line motion. These subharmonic modes are welldescribed within the framework of parametric oscillators. We also discuss here why vibrations can help to measure equilibrium contact angle.     

微液滴在不同能量表面上润湿状态的分子动力学模拟

微小液滴在不同能量表面上的润湿状态对于准确预测非均相核化速率和揭示界面效应影响液滴增长微观机理具有重要意义. 通过分子动力学模拟, 研究了纳米级液滴在不同能量表面上的铺展过程和润湿形态. 结果表明, 固液界面自由能随固液作用强度增加而增加, 并呈现不同液滴铺展速率和润湿特性. 固液作用强度小于1.6的低能表面呈现疏水特征, 继续增强固液作用强度时表面变为亲水, 而固液作用强度大于3.5的高能表面上液体呈完全润湿特征. 受微尺度条件下非连续、非对称作用力影响, 微液滴气液界面存在明显波动, 呈现与宏观液滴不同的界面特征. 统计意义下, 微小液滴在不同能量表面上铺展后仍可以形成特定接触角, 该接触角随固液作用强度增加而线性减小, 模拟结果与经典润湿理论计算获得的结果呈现相似变化趋势. 模拟结果从分子尺度为核化理论中的毛细假设提供了理论支持, 揭示了液滴气液界面和接触角的波动现象, 为核化速率理论预测结果和实验测定结果之间的差异提供了定性解释.     

Ice adhesion on super-hydrophobic surfaces

In this study, ice adhesion strength on flat hydrophobic and rough super-hydrophobic coatings with similar surface chemistry (based on same fluoropolymer) is compared. Glaze ice, similar to naturally accreted, was prepared on the surfaces by spraying super-cooled water microdroplets at subzero temperature. Ice adhesion was evaluated by spinning the samples at constantly increasing speed until ice delamination occurred. Super-hydrophobic surfaces with different contact angle hysteresis were tested, clearly showing that the latter, along with the contact angle, also influences the ice-solid adhesion strength.     

Dynamics and hysteresis of the contact line between liquid hydrogen and cesium substrates

We have measured both the hysteresis and the dynamics of the edge of a liquid hydrogen meniscus on several solid cesium substrates. We find that the dynamics of the contact line is thermally activated. For all substrates, we find that the activation energy is of the order of the hysteresis. We show that the pinning of the contact line on mesoscopic defects of the Cs substrate is likely to control both the hysteresis and the dynamics of the contact line at low velocity, close to the depinning threshold. Such a mechanism could be relevant also for simple room-temperature systems.     

接触角滞后现象的理论分析

在本文的研究中，考虑表面粗糙的影响，通过引入附加“磨擦力”的概念，分别用力学方法和热力学方法导出固体表面上液滴平衡时接触角应满足的条件；并得到了液滴系统自由能－固液接触面积曲线；分析了前进接触角和后退接触角的物理意义；由此给出了接触角滞后现象的一种合理解释．这对于进一步认识接触角的滞后现象，无疑是有积极意义的．     

Contact angle hysteresis at the nanometer scale

Using atomic force microscopy with nonconventional carbon tips, the pinning of a liquid contact line on individual nanometric defects was studied. This mechanism is responsible for the occurrence of the contact angle hysteresis. The presence of weak defects which do not contribute to the hysteresis is evidenced for the first time. The dissipated energy associated with strong defects is also measured down to values in the range of kT, which correspond to defect sizes in the order of 1 nm.     

Quasi-static motion of microparticles at the depinning contact line of an evaporating droplet on PDMS surface

In this paper, evaporation of sessile water droplets containing fluorescent polystyrene(PS) microparticles on polydimethylsiloxane(PDMS) surfaces with different curing ratios was studied experimentally using laser confocal microscopy. At the beginning, there were some microparticles located at the contact line and some microparticles moved towards the line. Due to contact angle hysteresis, at first both the contact line and the microparticles were pinned. With the depinning contact line, the microparticles moved together spontaneously. Using the software ImageJ, the location of contact lines at different time were acquired and the circle centers and radii of the contact lines were obtained via the least square method. Then the average distance of two neighbor contact lines at a certain time interval was obtained to characterize the motion of the contact line. Fitting the distance-time curve at the depinning contact line stage with polynomials and differentiating the polynomials with time, we obtained the velocity and acceleration of both the contact line and the microparticles located at the line. The velocity and the maximum acceleration were,respectively, of the orders of 1 μm/s and 20-200 nm/s~2, indicating that the motion of the microparticles located at the depinning contact line was quasi-static. Finally, we presented a theoretical model to describe the quasi-static process, which may help in understanding both self-pinning and depinning of microparticles.     

Model for the extreme wetting hysteresis of liquid helium on cesium

Although the liquid- 4He-cesium system is a nearly ideal one for studying wetting phenomena, it can show extreme hysteresis which is profoundly nonideal in behavior. It is suggested that this is due to the roughness of these Cs surfaces. We show that stable micropuddles of liquid 4He can form in shallow cavities on a Cs surface. It is the potential to form micropuddles, as the liquid tries to recede, which pins the contact line due to the large energy needed to create the surface of a micropuddle. This model also accounts for the memory that these surfaces have of being in contact with liquid 4He.