The Effect of Drop (Bubble) Size on Contact Angle at Solid Surfaces

Examples of experimental contact angle data for varying drop and bubble volumes on different solids whose surfaces are smooth and homogeneous, rough and homogeneous, smooth and heterogeneous, and covered with unstable organic films are presented. The ideas and theoretical models as proposed in the literature for the interpretation of contact angle/drop (bubble) size relationships are critically reviewed. It is shown that major factors affecting the contact angle variation with drop (bubble) size such as surface heterogeneity, roughness, and stability, have been identified in the literature. However, there is still a need for experimental work with well-defined and well-characterized solid surfaces. Theoretical models that have been proposed in the literature are still inadequate. Advanced modeling of liquid behavior at heterogeneous and rough surfaces is required to understand further, and to predict, the contact angle/drop (bubble) size relationships at imperfect surfaces.     

Electrowetting on dielectrics on lubricating fluid-infused smooth/rough surfaces with negligible hysteresis

Low-voltage electrowetting on dielectrics on substrates with a thin layer of lubricating fluid to reduce contact angle hysteresis is reported here. On smooth and homogeneous solid surfaces, it is extremely difficult to reduce contact angle hysteresis (contact angle difference between advancing and receding drop volume cycle) and the electrowetting hysteresis (contact angle difference between increasing and decreasing voltage cycle) below 10°. On the other hand, electrowetting hysteresis on rough surfaces can be relatively large (~30°); therefore, they are not useful for most of the fluidic devices. In the present report, we demonstrate that using a thin layer of dielectric lubricating fluid on top of the solid dielectric surface reduces the contact angle hysteresis as well as electrowetting hysteresis below 2° on smooth as well as rough surfaces. Electrowetting on lubricating fluid-coated surfaces also show a threshold behavior and the threshold voltage depends on the viscosity of the lubricating fluid. Modified Lippmann equation is used to explain the electrowetting on lubricant-coated surfaces quantitatively. The experimental system can be modeled as two series capacitor, one each for dielectric lubricating fluid and solid dielectric, which jointly govern the electrowetting behavior, whereas the lubricating fluid also minimizes the contact angle hysteresis     

Preparation of a coal surface for contact angle measurements

Coal specimens of different ranks were polished using silicon carbide abrasive papers (with a grit from #60 to #1200) and alumina powder of varying size (from 5 to 0.05 μm). The coal surface roughness and contamination (by alumina powder) were examined with both scanning electron microscopy and atomic force microscopy. The water advancing and receding contact angles were measured on such surfaces by varying the bubble size, using the captive-bubble technique. It was found that silicon carbide paper abraded all components of the coal surface, i.e. both organic and inorganic matter, to a similar depth. The roughness of the coal surface due to polishing with silicon carbide abrasive papers affected the contact angle hysteresis and the contact angle vs. bubble size relationship. Polishing of coal specimens with alumina powder reduced the microroughness of the coal surface but produced rough features at the macro level and caused mineral inclusions rising above the smooth organic matter. This phenomenon results from the heterogeneity of coal specimens consisting of minerals and macerals with different hardness values. The roughness at the macro level was easily distinguishable and had a significant impact on the measured contact angles when the coal surface was polished with coarse alumina powders, 5 and 1 μm in diameter. The effect of surface roughness on the advancing and receding water contact angles was significantly reduced (if not completely eliminated) when the coal surface was polished with a fibrous cloth (CHEMOMET) in the final step, after having been polished with 0.05 (0.06) μm alumina powder. Microscopic observation of the coal surfaces revealed that an appropriate ultrasonic treatment (8-10 min in an ultrasonic bath filled with water) and mechanical cleaning (polishing with a CHEMOMET cloth) of coal samples were required to remove the alumina particles left on the surface due to the previous polishing procedure. An improved methodology for coal surface preparation, prior to contact angle measurements, as proposed in this paper, includes polishing with a series of abrasive papers and 0.05 (0.06) μm alumina powder, polishing and cleaning with a fibrous cloth (e.g. CHEMOMET), and, finally, an extended cleaning in an ultrasonic bath filled with water.     

A generalized Young’s equation for contact angles of droplets on homogeneous and rough substrates

Using Gibbs’ method of dividing surfaces, the contact angle of a drop on a flat homogeneous rough non-deformable solid substrate is investigated. For this system, a new generalized Young’s equation for the contact angle, including the influences of line tension and which valid for any dividing surface between liquid phase and vapor phase is derived. Under some assumptions, this generalized Young’s equation reduces to the Wenzel’s equation or Rosanov’s equation valid for the surface of tension.     

Microsphere tensiometry to measure advancing and receding contact angles on individual particles

In this paper, a method to measure the advancing and receding contact angles on individual colloidal spheres is described. For this purpose, the microspheres were attached to atomic force microscope cantilevers. Then the distance to which the microsphere jumps into its equilibrium position at the air-liquid interface of a drop or an air bubble was measured. From these distances the contact angles were calculated. To test the method, experiments were done with silanized silica spheres (4.1 μm in diameter). From the experiments with drops, an advancing contact angle of 101 ± 4° was determined. A receding contact angle of 101 ± 2° was calculated from the jump-in distance into a bubble. Both experimental techniques gave the same contact angle. In contrast, on similarly prepared planar silica surfaces, a clear hysteresis was measured with the sessile drop method; contact angles of 104.5 ± 1° and 93.8 ± 1° were determined for the advancing and receding contact angles, respectively.     

Low-rate Dynamic Contact Angles on Poly(methyl methacrylate/n-butyl methacrylate) and the Determination of Solid Surface Tensions

Low-rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/n-butyl methacrylate) P(MMA/nBMA) copolymer are measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). It is found that 6 liquids yield non-constant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining 6 liquids, it is found that the liquid- vapour surface tension times the cosine of the contact angle changes smoothly with the liquid-vapour surface tension, i.e., γ_iv cos θ depends only on γ_iv for a given solid surface (or solid surface tension). This contact angle pattern is in harmony with those from other inert and noninert (polar and non-polar) surfaces [34-42, 51 -53]. The solid-vapour surface tension calculated from the equation-of-state approach for solid -liquid interfacial tensions [14] is found to be 34.4 mJ/m², with a 95% confidence limit of \pm 0.8mJ/m², from the experimental contact angles of the 6 liquids.     

The effects of nanostructure and composition on the hydrophobic properties of solid surfaces

The effects of nanoroughness and chemical composition on the contact and sliding angles on hydrophobic surfaces were studied theoretically and experimentally. A theoretical model based on forces developed at the contact area between a liquid drop and hydrophobic smooth or nanoroughened surface was developed and compared with the existing models, which are based on forces developed at the periphery between the drop and the solid surface. The contact area based model gives rise to an interfacial adhesion strength parameter that better describes the drop-sliding phenomenon. Consequently, relationships were derived describing the dependence between the interfacial adhesion strength of the liquid drop to the surface of a given composition, the mass of the drop, the measured contact angles and the sliding angle. For a given surface chemistry, the sliding angle on a nanometric roughened surface can be predicted based on measurements of contact angles and the sliding angle on the respective smooth surface. Various hydrophobic coatings having different surface nanoroughnesses were prepared and, subsequently, contact angles and sliding angles on them as a function of drop volume were measured. The validity of the proposed model was investigated and compared with the existing models and the proposed model demonstrated good agreement with experimental results.     

Instability of the three-phase contact region and its effect on contact angle relaxation

Contact angle relaxation was measured for captive air bubbles placed on solid surfaces of varying degrees of heterogeneity, roughness, and stability, in water. The experimental results indicate that both advancing and receding contact angles undergo slow relaxation in these water-air-solid systems, due to instabilities of the three-phase contact line region. It is shown that the advancing contact angle decreases and the receding contact angle increases for many systems over a period of a few hours. Also, examples of reverse progressions are reported. Additionally, in extreme cases, the contact angle oscillates down and up, over and over again, preventing the system from stabilization/equilibration. Four different mechanisms are proposed to explain the contact angle relaxation. These include (i) pinning of the three-phase contact line and its slow evolution; (ii) the formation of microdroplets on the solid surface and their coalescence with the base of the gas bubble, which causes dynamic behavior of the three-phase contact line; (iii) deformation of the solid surface and its effect on the apparent contact angle; and (iv) chemical instability of the solid.     

Factors affecting the wettability of polymer surfaces

The inconsistencies in contact angle data presented in the literature can be attributed to a number of factors. The awareness of these factors would allow novice researchers to make meaningful contact angle measurements and interpretations. In this survey the effects of surface roughness and heterogeneity, surface preparation and the presence of contaminants, the vapor environment, pressure and temperature, drop size, electrical charge, and heat transfer on the wettability of polymer surfaces were examined.     

The effect of polymer surface on the wetting and adhesion of liquid systems

Young's equation describes the wetting phenomenon in terms of the contact angle between a liquid and a solid surface. However, the contact angle is not the only parameter that defines liquid–solid interactions, an additional parameter related to the adhesion between the liquid drop and the solid surface is also of importance in cases where liquid sliding is involved. It is postulated that wetting which is related to the contact angle, and interfacial adhesion, which is related to the sliding angle, are interdependent phenomena and have to be considered simultaneously. A variety of models that relate the sliding angle to the forces developed along the contact periphery between a liquid drop and a solid surface have been proposed in the literature. Here, a modified model is proposed that quantifies the drop-sliding phenomenon, based also on the interfacial adhesion that develops across the contact area of the liquid/solid interface. Consequently, an interfacial adhesion strength parameter can be defined depending on the mass of the drop, the contact angle and the sliding angle. To verify the proposed approach the adhesion strength parameter has been calculated, based on experimental results, for a number of polymer surfaces and has been correlated with their composition and structure. The interaction strength parameter can be calculated for any smooth surface from measurements of the contact and the sliding angles.     

引入液固界面效应的滴状冷凝传热模型

针对液固界面相互作用对滴状冷凝传热的影响,以Rose滴状冷凝传热模型为基础,考虑接触角、脱落直径对冷凝传热的影响,对滴状冷凝过程中液滴空间序列上的构象,作时间序列上的重构,建立了包含液固界面效应的滴状冷凝传热模型.模型计算结果表明液固表面自由能差越大、接触角滞后越小则越有利于冷凝传热.为滴状冷凝文献数据间存在差异的原因提供了一个新的解释,即液固界面效应的影响.模型可计算得到在不同界面条件下的不同传热结果,模型计算结果与Rose实验值以及本文滴状冷凝传热实验较为吻合.     

粗糙固体平面上液滴的接触角滞后的简单流体静力学模型

The phenomenon of hysteresis of contact angle is an important topic subject to a long time of argument.A simple hydrostatic model of sessile drops under the gravity in combination with an ideal surface roughness model is used to interpret the process of drop volume increase or decrease of a planar sessile drop and to shed light on the contact angle hysteresis and its relationship with the solid surface roughness. With this model, the advancing and receding contact angles are conceptually explained in terms of equilibrium contact angle and surface roughness only,without invoking the thermodynamic multiplicity. The model is found to be qualitatively consistent to experimental observations on contact angle hysteresis and it suggests a possible way to approach the hysteresis of three-dimensional sessile drops.     

Contact Ratio: A New Precise Measurement for Wettability

According to Young's equation, the contact angle “Θ” is considered as the measurable wettability parameter. The rate of change in the contact angle has been commonly used as the relevant parameter of spreading dynamics notwithstanding the difficulties associated with contact angle measurements that are well recognized in the literature. Considering that the velocity of the contact line is the pertinent quantity, it is, therefore, reasonable to regard the change in the contact area as the flux of the process. In this study, we have introduced a new measuring parameter for wettability based on the liquid/solid contact area. The term “contact ratio” has been coined to account for this new measurable parameter. The contact ratio is defined as the ratio between the spreading contact area of liquid over solid surface and the surface area of the spherical drop before spreading. The measurements of contact areas and low‐rate dynamic contact angles for various liquid/solid systems were conducted independently using the ADSA‐P technique. The theoretical relation between the contact ratio and the contact angle is derived based on spherical cap approximation. The results show that there is a good correlation between the theoretical relation and the experimental values. Since the contact angle of a specific system is a unique parameter of the system, the contact ratio can also be presented as a unique parameter of the system. Nevertheless, contact ratio presents a more precise measure of wettability.     

Comparison of wetting models and geometrical analysis in describing the effect of cavity number,size, and position on apparent contact angle

A critical subject of surface science is whether contact area or the triple-phase contact line (TPCL) directly affects the apparent contact angle (APCA). On this premise, effect of cavity size and position on APCA is studied. Cavities were created using a laser machining process. Optimal conditions for laser patterning were obtained via trial and error. It was impossible to deposit a droplet that could rest on all of the cavities for about 0.16 mm distance between the edge of the patterns and the drop’s perimeter. Neither Wenzel nor Cassie–Baxter models can fully explain the acquired data from static contact angle measurements. Revised Cassie–Baxter equation also fails, while a simple geometrical analysis based on Spherical Cap assumption shows a better agreement with the data as long as the cavities are sufficiently far from TPCL. Based on our results, we believe that theoretical analyses regarding wetting models are not in line with engineering aspects of wetting which should be focused on TPCL.     

The effect of bond formation on the tack of polymers

The tack of polymers to be used as adhesives is measured by a two-stage process of bond formation and bond separation. Bond formation is governed by the contact time, the contact force, the roughness of the surfaces, surface and interfacial tensions, and the mechanical or viscoelastic properties of the adhesive and substrate. This paper presents experimental studies of the contact formation of various model polymers on steel surfaces with well-defined and different degrees of roughness. The tack was measured with an instrument of the probe tack type, which determines the adhesive (interfacial) fracture energy per unit of interface as a measure of the tack and by means of which the most important parameters during bond formation and separation, such as the contact time, contact force, rate of separation, and temperature, can be adjusted and measured over sufficiently wide ranges. In the typical time interval for the contact time, the polymers are found in the plateau range of their viscoelastic spectrum. This means that entanglements strongly affect their bonding behaviour. Good agreement was found between the experimental results presented in this study and a model of contact formation on rough surfaces, published recently by Creton and Leibler [1], especially concerning the dependence of the adhesive fracture energy on the contact force and the contact time for smooth and rough substrate surfaces. The influence of the surface roughness becomes significant at low contact forces, where full contact is not yet developed on a rough substrate surface, and for polymers with comparatively high moduli. The fracture energy increases with the contact time and shows the same time dependence as the reciprocal modulus.     

Hydrodynamics and mechanism of hydrophobic foam column tray: Contact angle hysteresis effect

Interfacial wettability adjustment is a new method for intensifying vapor–liquid mass transfer process. Contact angle effect has been well investigated but not complete due to interfacial wettability consisting of both static behavior (contact angle) and dynamic behavior (contact angle hysteresis). Here, methods of adjusting contact angle hysteresis (CAH) were proposed, and then, the CAH effect on the hydrodynamics was investigated. A multiscale analysis of CAH effect, from interfacial force and wettability to single-bubble and gas–liquid two-phase flow inside the foam to bubble swarm hydrodynamics, was conducted, and thus, the hydrodynamic performance criteria were derived. The interfaces had similar contact angles, whereas a significant difference in the CAH was prepared by using the developed sol dip-coating and spray coating methods. Subsequent experiments revealed that lower CAH can decrease the pressure drop, homogenize the gas distribution, and increase the weeping rate, which are consistent with the derived criteria.     

Fabrication and characterization of hydrophobic thin polytrifluoroethyl methacrylate adhered coating on cotton surface via amicellar polymerization

In this study, fluorine-based methacrylate ester monomers were polymerized on cotton fabric by admicellar polymerization to make the cotton surface highly rough and also highly hydrophobic with a reliable water contact angle value. The rough micro/nano-textured surface morphology, after surface fluorination, results in hydrophobicity. The hydrophobic character was confirmed by a simple drop test and contact angle measurements. Surface composition was evaluated by SEM and FT IR analysis to confirm the fluoropolymeric layer adhered on the cotton surface.     

粗糙表面上的移动接触线和动态接触角

提出一个粗糙表面上移动接触线和动态接触角的数理模型：毛细数较低时表观接触线前缘存在极薄的前驱膜,表观接触线在“湿”固体表面上移动,不同于传统模型中认为表观接触线在“干”固体表面上移动.在Moffatt角区内部流动解的基础上,通过引入接触线特征参数表征表观接触线在前驱膜上的滑移程度,导出动态接触角的速度关系.与不同研究者实验数据对比发现量纲1特征参数反映固体材料特性和表面特性对动态湿润过程的影响,与液相的性质无关.结合前期提出的滞后张力模型,对动态法和静态法测量静接触角产生的差异给出合理解释.