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.     

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.     

Three- and two-dimensional effects in wetting kinetics

Wetting at equilibrium is reviewed in brief, and it is then suggested that a wider class of nonequilibrium problems can exist where an equilibrium-like behaviour is reached simply because the mechanisms for spreading are suppressed.The mechanisms of spreading are reviewed to suggest that experiments of wetting kinetics of liquids with varying volatilities on mica would lead to interesting results. Such experiments were conducted and the results are supportive of the models. It was also observed that when volatility and surface roughness, two important mechanisms of spreading, are removed, the drop motion presumed to be controlled by surface diffusion at the contact line virtually ceases, although scanning electron microscopy results show that they are indeed moving.The role of films of ultra-low thicknesses are examined. It is seen that the dynamics of molecular scale droplets are understandable, and can be modelled in many ways, and the features these moving molecular scale drops exhibit can in some cases affect the movement of microscale drops as well.We are able to identify and define two- and three-dimensional volatilities and mobilities that help one to classify the spreading phenomena, as far as the liquids are concerned. The surfaces can be smooth or rough, a difference that has a strong effect.     

Anisotropy in the wetting of rough surfaces

Surface roughness amplifies the water-repellency of hydrophobic materials. If the roughness geometry is, on average, isotropic then the shape of a sessile drop is almost spherical and the apparent contact angle of the drop on the rough surface is nearly uniform along the contact line. If the roughness geometry is not isotropic, e.g., parallel grooves, then the apparent contact angle is no longer uniform along the contact line. The apparent contact angles observed perpendicular and parallel to the direction of the grooves are different. A better understanding of this problem is critical in designing rough superhydrophobic surfaces. The primary objective of this work is to determine the mechanism of anisotropic wetting and to propose a methodology to quantify the apparent contact angles and the drop shape. We report a theoretical and an experimental study of wetting of surfaces with parallel groove geometry.     

以砂纸为模板制作聚合物超疏水表面

报道了一种聚合物材料超疏水表面的简便制备方法. 以不同型号的金相砂纸为模板, 通过浇注成型或热压成型技术, 在聚合物表面形成不同粗糙度的结构. 接触角实验结果证明, 聚合物表面与水的接触角随着所用砂纸模板粗糙度的增加而加大, 其中粒度号为W7和W5砂纸制作的表面与水的接触角可超过150°, 显示出超疏水性质. 多种聚合物使用砂纸为模均可制备不同粗糙度及超疏水的表面, 本征接触角对复制表面浸润性的影响从Wenzel态到Cassie态而变小. 扫描电镜结果表明, 不规则形状的砂纸磨料颗粒构成了超疏水所需要的微纳米结构的模板.     

Contact line dynamics in drop coalescence and spreading

The dynamics of coalescence of two water sessile drops is investigated and compared with the spreading dynamics of a single drop in partially wetting regime. The composite drop formed due to coalescence relaxes exponentially toward equilibrium with a typical relaxation time that decreases with contact angle. The relaxation time can reach a few tenths of seconds and depends also on the drop size, initial conditions, and surface properties (contact angle, roughness). The relaxation dynamics is larger by 5 to 6 orders of magnitude than the bulk hydrodynamics predicts, due to the high dissipation in the contact line vicinity. The coalescence is initiated at a contact of the drops growing in a condensation chamber or by depositing a small drop at the top of neighboring drops with a syringe, a method also used for the studies of the spreading. The dynamics is systematically faster by an order of magnitude when comparing the syringe deposition with condensation. We explain this faster dynamics by the influence of the unavoidable drop oscillations observed with fast camera filming. Right after the syringe deposition, the drop is vigorously excited by deformation modes, favoring the contact line motion. This excitation is also observed in spreading experiments while it is absent during the condensation-induced coalescence.     

Spreading of Surfactant Solutions over Hydrophobic Substrates

The spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilize the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by our experimental observations. Copyright 2000 Academic Press.     

Theoretical model for the wetting of a rough surface

Many applications would benefit from an understanding of the physical mechanism behind fluid movement on rough surfaces, including the movement of water or contaminants within an unsaturated rock fracture. Presented is a theoretical investigation of the effect of surface roughness on fluid spreading. It is known that surface roughness enhances the effects of hydrophobic or hydrophilic behavior, as well as allowing for faster spreading of a hydrophilic fluid. A model is presented based on the classification of the regimes of spreading that occur when fluid encounters a rough surface: microscopic precursor film, mesoscopic invasion of roughness and macroscopic reaction to external forces. A theoretical relationship is developed for the physical mechanisms that drive mesoscopic invasion, which is used to guide a discussion of the implications of the theory on spreading conditions. Development of the analytical equation is based on a balance between capillary forces and frictional resistive forces. Chemical heterogeneity is ignored. The effect of various methods for estimating viscous dissipation is compared to available data from fluid rise on roughness experiments. Methods that account more accurately for roughness shape better explain the data as they account for more surface friction; the best fit was found for a hydraulic diameter approximation. The analytical solution implies the existence of a critical contact angle that is a function of roughness geometry, below which fluid will spread and above which fluid will resist spreading. The resulting equation predicts movement of a liquid invasion front with a square root of time dependence, mathematically resembling a diffusive process.     

Comparison of contact angle hysteresis of different probe liquids on the same solid surface

Advancing and receding contact angles of water, formamide and diiodomethane were measured on 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on three different solid supports—glass, mica and poly(methyl methacrylate). Up to five statistical monolayers were deposited on the surfaces by spreading DPPC solution. It was found that even on five statistical DPPC monolayers, the hysteresis of a given liquid depends on the kind of solid support. Also on the same solid support the contact angle hysteresis is different for each probe liquid used. The AFM images show that the heights of roughness of the DPPC films cannot be the primary cause of the observed hysteresis because the heights are too small to cause the observed hystereses. It is believed that the hysteresis is due to the liquid film present right behind the three-phase solid surface/liquid drop/gas (vapour) contact line and the presence of Derjaguin pressure. The value of contact angle hysteresis depends on both the solid surface and liquid properties as well as on intermolecular interactions between them.     

Low inertia impact dynamics for nanodrops

Simulations of a droplet impacting a flat solid surface with a small initial speed have been studied using molecular dynamics. Approximating the shape of the drop by a spheroid, spreading radii, and dynamic contact angles are measured. The data reproduce well experimental results from literature. We show that the difference between the equilibrium and the dynamic contact angle cosines, that is, the spontaneous driving force, versus the spreading velocity of the three-phase line varies with impact speed and consists of two distinct regimes which can be described by existing models of moving contact lines.     

On the role of the three-phase contact line in surface deformation

Viscoelastic braking theories developed by Shanahan and de Gennes and by others predict deformation of a solid surface at the solid-liquid-air contact line. This phenomenon has only been observed for soft smooth surfaces and results in a protrusion of the solid surface at the three-phase contact line, in agreement with the theoretical predictions. Despite the large (enough to break chemical bonds) forces associated with it, this deformation was not confirmed experimentally for hard surfaces, especially for hydrophobic ones. In this study we use superhydrophobic surfaces composed of an array of silicon nanostructures whose Young modulus is 4 orders of magnitude higher than that of surfaces in earlier recorded viscoelastic braking experiments. We distinguish between two cases: when a water drop forms an adhesive contact, albeit small, with the apparent contact angle θ < 180° and when the drop-surface adhesion is such that the conditions for placing a resting drop on the surface cannot be reached (i.e., θ = 180°). In the first case we show that there is a surface deformation at the three-phase contact line which is associated with a reduction in the hydrophobicity of the surface. For the second case, however, there cannot be a three-phase contact line associated with a drop in contact with the surface, and indeed, if we force-place a drop on the surface by holding it with a needle, no deformation is detected, nor is there a reduction in the hydrophobic properties of the surface. Yet, if we create a long horizontal three-phase contact line by partially immersing the superhydrophobic substrate in a water bath, we see a localized reduction in the hydrophobic properties of the surface in the region where the three-phase contact line used to be. The SEM scan of that region shows a narrow horizontal stripe where the nanorods are no longer there, and instead there is only a shallow structure that is lower than the nanorods height and resembles fused or removed nanorods. Away from that region, either on the part of the surface which was exposed to bulk water or the part which was exposed to air, no change in the hydrophobic properties of the surface is observed, and the SEM scan confirms that the nanorods seem intact in both regions.     

Mimicking the lotus effect: influence of double roughness structures and slender pillars

Surface roughness is known to amplify hydrophobicity. The apparent contact angle of a drop on a rough surface is often modeled using either Wenzel's or Cassie's formulas. These formulas, along with an appropriate energy analysis, are critical in designing superhydrophobic substrates for applications in microscale devices. In this paper we propose that double (or multiple) roughness structures or slender pillars are appropriate surface geometries to develop "self-cleaning" surfaces. The key motivation behind the double structured roughness is to mimic the microstructure of superhydrophobic leaves (such as lotus). Theoretical analysis similar to that presented in the paper can be used to obtain optimal geometric parameters for the rough surface. The calculation procedure should result in surface geometries with excellent water repellent properties.     

Enhanced hydrophobicity of rough polymer surfaces

Molecular dynamics simulations were used to study the effect of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. Pillars of different lateral dimensions and heights were derived from flat crystalline surfaces, and the results of nanoscale simulations on the structured surfaces were compared with theoretical predictions of the Wenzel and Cassie equations. Hydrophobicity increased on all rough surfaces, but the increase was greater on the structured PE surfaces because of the larger water contact angle on the flat PE surface than the corresponding PVC surface. Equally sized pillar structures on the two polymers resulted in different equilibrium wetting geometries. Composite contacts were observed on rough PE surfaces, and the contact angle increased with decreasing contact area between the solid and the liquid. Opposite results were obtained for rough PVC surfaces; the contact angle increased with the solid-liquid contact area, in agreement with Wenzel's equation. However, the composite contact was observed if the energies of the wetted and composite contacts were almost equal. Good agreement was obtained between the simulated contact angles and equilibrium droplet shapes and the theories but there were also some limitations of the nanoscale simulations.     

Microspreading studies on rough surfaces by scanning electron microscopy

The use of scanning electron microscopy for direct observation of the effects of surface roughness on the spreading of liquids is described, making it possible to view moving liquid drops at distances less than 1 μm from the advancing contact line. Various surfaces were examined including several with simple forms of roughness which can assist in explaining the behavior of more complex surfaces. Spreading is shown to be highly dependent on the orientation and texture of the roughness; in particular, the presence of sharp edges of step height 0.05 μm are shown to influence spreading significantly. These observations reinforce our previously stated doubts of the significance of conventionally measured macroscopic contact angles.     

Effect of oxidation on the wettability of poly(dimethylsiloxane) surfaces

The wetting of amorphous poly(dimethylsiloxane) (PDMS) surfaces by water has been studied using molecular dynamics simulations. PDMS surfaces were generated by compressing a long PDMS chain between two elastic boundaries at atmospheric pressure. Oxidation of the PDMS surface, achieved in real systems by exposure to air plasma or corona discharge, was modeled by replacing methyl groups on the PDMS chain with hydroxyl groups. Three surfaces of varying degrees of oxidation were characterized by measuring the water contact angle and the roughness. The dependence of the microscopic contact angle on drop size was measured from time averaged density profiles. The macroscopic contact angle was measured directly using a cylindrical drop of infinite length with zero contact line curvature. The measured macroscopic contact angle ranged from approximately 125 degrees on the untreated surface to 75 degrees on the most oxidized surface studied. The line tension was found to increase with increasing degree of oxidation, from a negligible value on the untreated surface to approximately 5x10(-11) J m(-1) on the most heavily oxidized surface.     

The dynamics of impacting water droplets on alkanethiol self-assembled monolayers with co-adsorbed CH3 and CO2H terminal groups

The impact of water droplets (diameter 3.6 mm) at a fixed Weber number of 59 on solid surfaces with precisely tailored surface wettabilities was studied experimentally using a high-speed imaging camera at 2500 frames per second. Solid surface wettability was varied using four fractional mixtures of self-assembled monolayers of 1-octadecanethiol and 16-mercaptohexadecanoic acid. The surfaces so obtained are characterized for contact angle and chemical functionality using the axisymmetric drop shape analysis profile (ADSA-P) technique and Fourier transform infrared spectroscopy (FT-IR). Our results correlate the wetting effects of the impacting droplets with the surface energy and contact angle measurements of the tailored surfaces. Literature models for the maximum spreading diameter are employed and compared with those from our experiments. An equation is also proposed for the maximum spreading diameter which makes use of the correct contact angles and results in the least error among the models considered. As a consequence of Young's equation, the correct contact angles to be used for droplet impact dynamics should be the corresponding advancing angles on a smooth substrate of interest. We also conclude that accurate examination of literature models requires careful experimentation on impact dynamic data on well-prepared and characterized surfaces such as those presented here.     

超疏水表面上冷凝液滴发生弹跳的机制与条件分析

使用液滴合并前后的体积和表面自由能守恒作为两个限制条件,确定了合并液滴的初始形状,即为偏离平衡态的亚稳态液滴,具有缩小其底半径而向平衡态液滴转变的推动力.进而分析了液滴变形过程中的推动力和三相线(TPCL)上的滞后阻力,建立了液滴变形的动态方程并进行了差分求解.如果液滴能够变形至底半径为0mm的状态,则根据该状态下液滴重心上移的速度确定液滴的弹跳高度.不同表面上冷凝液滴合并后的变形行为的计算结果表明,光滑表面上的液滴合并后,液滴只能发生有限的变形,一般都在达到平衡态之前就停止了变形,因此冷凝液滴不会发生弹跳;粗糙表面上的Wenzel态液滴的三相线上的滞后阻力更大,因而液滴更难以变形和弹跳;具有微纳二级结构表面上只润湿微米结构,但不润湿纳米结构的部分Wenzel态液滴能够变形至Cassie态,但没有明显的弹跳;只有在纳米或微纳二级结构表面上的较小Cassie态液滴合并后,液滴易于变形至底半径为0mm的状态并发生弹跳.因此,Cassie态合并液滴处于亚稳态,并且其三相线上的移动阻力很小,是导致冷凝液滴弹跳的关键因素.     

Cassie and Wenzel: were they really so wrong?

The properties of superhydrophobic surfaces are often understood by reference to the Cassie-Baxter and Wenzel equations. Recently, in a paper deliberately entitled to be provocative, it has been suggested that these equations are wrong; a suggestion said to be justified using experimental data. In this paper, we review the theoretical basis of the equations. We argue that these models are not so much wrong as have assumptions that define the limitations on their applicability and that with suitable generalization they can be used with surfaces possessing some types of spatially varying defect distributions. We discuss the relationship of the models to the previously published experiments and using minimum energy considerations review the derivations of the equations for surfaces with defect distributions. We argue that this means the roughness parameter and surface area fractions are quantities local to the droplet perimeter and that the published data can be interpreted within the models. We derive versions of the Cassie-Baxter and Wenzel equations involving roughness and Cassie-Baxter solid fraction functions local to the three-phase contact line on the assumption that the droplet retains an average axisymmetry shape. Moreover, we indicate that, for superhydrophobic surfaces, the definition of droplet perimeter does not necessarily coincide with the three-phase contact line. As a consequence, the three-phase contact lines within the contact perimeter beneath the droplet can be important in determining the observed contact angle on superhydrophobic surfaces.     

Condensation on ultrahydrophobic surfaces and its effect on droplet mobility: ultrahydrophobic surfaces are not always water repellant

The condensation of water was studied on topography-based ultrahydrophobic surfaces containing hydrophobized silicon pillars. Optical microscopy showed that water nucleated and grew both on top of and between the pillars. As condensation progressed, water between the pillars became unstable and was forced upward to the surface. Macroscopic water droplets on top of the pillars coalesced with condensed water that remained between the pillars, pinning the droplets at their three-phase contact line. Dynamic contact angle measurements on ultrahydrophobic surfaces wet with condensation revealed a dramatic increase in hysteresis compared to that on dry surfaces, leading to a corresponding decrease in water drop mobility.