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.     

The Apparent Contact Angle of Liquids on Finely-Grooved Solid Surfaces-A SEM Study

A finely parallel-grooved nitrocellulose surface has been employed as a model to study by scanning electron microscopy the influence of roughness on the spreading equilibrium of liquid drops. The Cassie and Baxter equation for spherical drops on a composite interface was experimentally confirmed with mercury and a similar equation derived for a cylindrical drop has also been shown to be approximately valid for liquid polyphenylether. The observed drop shapes have been explained and the importance of groove edges demonstrated.

Direct measurements of the microscopic contact angle of mercury locally on the grooved surfaces were found to be approximately the same for the smooth ungrooved surface.     

Contact Angle of Ethanol and n‐Propanol Aqueous Solutions on Metal Surfaces

The contact angles of the aqueous solution of ethanol and that of n‐propanol on copper, aluminum, and stainless steel surfaces are reported. The contact angles were measured under atmospheric conditions, and then under vapor‐liquid equilibrium conditions at 1 atm and different temperatures. The results showed the variations of the contact angles with the concentrations of aqueous solutions on different metal material surfaces with different roughness. Some unstable behavior of the wetting ability around the azeotropic point of a binary solution is reported. Influences of concentration, kind of materials, and the surface roughness on the wetting ability are discussed. The model for predicting the contact angle of alcohol aqueous solutions on metal surfaces under atmospheric and vapor‐liquid two‐phase equilibrium conditions at 1 atm is derived from the Young equation.     

Determination of the peripheral contact angle of sessile drops on solids from the rate of evaporation

A method was developed to determine the initial peripheral contact angle of sessile drops on solid surfaces from the rate of drop evaporation for the case where ₁ < 90°. The constant drop contact radius, the initial weight, and the weight decrease with time should be measured at the ambient temperature for this purpose. When water drops are considered, the relative humidity should also be known. The peripheral contact angle so obtained is regarded as the average of all the various contact angles existing along the circumference of the drop. Thus, each determination yields an average result not unduly influenced by irregularities at a given point on the surface. In addition, the error in personal judgment involved in drawing the tangent to the curved drop profile at the point of contact can be eliminated. The application of this method requires the use of the product of the vapor diffusion coefficient with the vapor pressure at the drop surface temperature. This product can be found experimentally by following the evaporation of fully spherical liquid drops.     

New method of determining contact angle between monofilament and liquid

This paper describes a method to obtain contact angle by observing the shape of a liquid drop attached to a monofilament. The relations between contact angle and the dimensions of drops are theoretically obtained. Thus, it is possible to calculate the contact angle if drop shape is measured. Through use of this method, the contact angles of epoxy resin on various kinds of monofilaments were measured. It was found that this method has practical utility for measurement of the contact angle between liquid and monofilament.     

Surface structure,topology, and liquid wetting behavior in oriented polymers

The structure and the properties of oriented polymer surfaces were studied for three series of uniaxially oriented films of polypropylene (PP), polystyrene (PS), and poly(ethylene terephthalate) (PET). The surface structure was characterized in terms of relative crystallinity and molecular orientation along with topology and roughness by using FT-IR-ATR dichroism technique, optical microscopy and surface profilometer. In all three polymers, the surface orientation function increases with draw ratio. The relative surface crystallinity and the trans con-former also increases for PP and PET, respectively. In uniaxially drawn PP, the surface becomes rough with increasing draw ratio and the roughness is anisotropic with peaks and valleys elongated along the draw direction. For drawn PP, the equilibrium contact angles for four different liquids all exhibit anisotropy with higher values in perpendicular direction than that in parallel to the draw direction. In contrast, both drawn PET and PS films show smooth surfaces, and the equilibrium contact angles were all isotropic. When roughness is removed from the drawn PP by polishing without altering the molecular orientation, the anisotropy becomes negligible and the contact angles approach the value for undrawn PP. When surface roughness was created deliberately on undrawn PET and PS films, the contact angle anisotropy was clearly observed. Therefore, the anisotropy in surface topology rather than the molecular orientation seems to play a dominant role in developing anisotropic wetting behavior. The equilibrium contact angles for smooth surfaces have been calculated using the experimentally obtained roughness and anisotropic contact angle data from the rough surface. These values are in reasonable agreement with the measured contact angles for smooth surfaces, suggesting that the observed contact angle anisotropy can be attributed entirely to the roughness anisotropy rather than to the molecular orientation.     

Contact of a spherical particle with a droplet

The collection of particles by liquid drops is profoundly influenced by the contact angle of the particles with the drops and the surface tension of the drops. The present investigation was undertaken to establish an equation with reference to the force which acts on a particle by surface tension after contact of a particle with a drop, and to simplify its solution. Moreover, the approximate equations obtained can be applied as regards the arbitrary contact angle of a particle with a drop and the arbitrary ratio of the radius of the drop to the particle. The agreement between theoretical and experimental values could be verified by this experiment.It is considered from these results that the approximate equations can be utilized when it is necessary to know the behaviour of a particle after contact with a liquid drop.     

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.     

The combined effect of roughness and heterogeneity on contact angles: the case of polymer coating for stone protection

The individual effects of heterogeneity and roughness on contact angles have been repeatedly analysed in the literature, but the application of the accepted models to practical situations is often not correctly performed. In the present paper the combined effects of roughness and heterogeneity on the contact angles of water on stone surfaces protected by a hydrophobic polymer coating are considered. Two different kinds of calcareous stone with different surface roughnesses and porosities were protected against the effect of water absorption by two different polymer coatings. The contact angles of water on the protected stone surfaces were measured by the Wilhelmy and the sessile drop techniques. A comparison of the results obtained shows not only the limits of the static sessile drop technique, but also the combined effect of roughness and heterogeneity. Some considerations are developed on the application of commonly accepted models to surfaces with a combination of roughness and heterogeneity. Some other results obtained with techniques such as roughness measurements, mercury porosimetry, energy dispersive X-ray spectroscopy (EDXS), thermogravimetric analysis (TGA), water absorption by capillarity experiments (WAC), all able to show the structure and properties of the obtained films, are also compared with those obtained from contact angle measurements. It is concluded that the static contact angle is not well correlated with the degree of protection; on the contrary, the receding contact angles are well correlated with the degree of protection actually obtained. An ideal protecting agent should have a receding contact angle greater than 90°.     

Analysis of evaporating thick liquid films on solids

The diffusion-controlled evaporation of small circular volatile liquid films from solid surfaces was monitored by employing video microscopy from a plan view and then applying digital image analysis techniques. The decrease of the liquid-solid contact area of these films during the last stages of the evaporation was found to be linear with time. This paper presents experimental results of four organic liquid films (n-nonane, n-octane, toluene, n-butanol) on three substrates poly(methyl methacrylate), poly(ethylene terephthalate) (Mylar), and glass. The linear decreases of the surface areas of hanging drops from a polypropylene fiber for the same liquids were also monitored using both plan and side view video cameras for comparison. Analyses of optically recorded liquid film and drop shapes were carried out and a diffusion model depending on the presence or absence of the substrate was developed. By combining the experimental area decrease of a spherical drop due to the diffusion-controlled evaporation with that of a small spherical cap shaped liquid film resting on a solid surface, it is possible to calculate the small contact angles (less than 10°) of the wetting thick liquid films on solids. The relationship between film evaporation rate and the solid-liquid interfacial interactions is also discussed.     

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.     

Evaluation of surface energy of solid polymers using different models

In the present work, contact angles formed by drops of diethylene glycol, ethylene glycol, formamide, diiodomethane, water, and mercury on a film of polypropylene (PP), on plates of polystyrene (PS), and on plates of a liquid crystalline polymer (LCP) were measured at 20°C. Then the surface energies of those polymers were evaluated using the following three different methods: harmonic mean equation and geometric mean equation, using the values of the different pairs of contact angles obtained here; and Neumann's equation, using the different values of contact angles obtained here. It was shown that the values of surface energy generated by these three methods depend on the choice of liquids used for contact angle measurements, except when a pair of any liquid with diiodomethane was used. Most likely, this is due to the difference of polarity between diiodomethane and the other liquids at the temperature of 20°C. The critical surface tensions of those polymers were also evaluated at room temperature according to the methods of Zisman and Saito using the values of contact angles obtained here. The values of critical surface tension for each polymer obtained according to the method of Zisman and Saito corroborated the results of surface energy found using the geometric mean and Neumann's equations. The values of surface energy of polystyrene obtained at 20°C were also used to evaluate the surface tension of the same material at higher temperatures and compared to the experimental values obtained with a pendant drop apparatus. The calculated values of surface tension corroborated the experimental ones only if the pair of liquids used to evaluate the surface energy of the polymers at room temperature contained diiodomethane. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1831–1845, 2000     

Dynamic Contact Angles of Viscous Liquids

An empirical model has been developed which can predict the dynamic contact angle of a spreading drop of viscous liquid on a plane wettable surface from the contact area for contact angles between 90° and 0° within a specified drop size. This range of drop size is restricted to those drops having a contact area at a 90° cap condition (A₉₀) between 0.10 cm² and 0.20 cm² The drop profile was found not to be that of a spherical segment and hence could not allow a simple geometric interpretation. The model strengthens the interpretation that contact angle development in this range of drop size is mainly the geometric result of spreading. The model was found to hold over a wide variety of polymer melt temperatures (155-240°C), molecular weights and molecular weight distributions, which combined would greatly influence drop profile. The time dependency of the dynamic contact angle was also evaluated by combining the present empirical model with a previous viscosity dependent model relating contact area with time. The model was successfully applied to the unrelated systems of silicone oil and glycerol at room temperature indicating its general applicability.     

Spreading of Polydimethylsiloxane Drops on Solid Horizontal Surfaces

Effect of the volume of drops, surface energy and roughness of substrate together with temperature and viscosity on the spreading velocity of polydimethylsiloxane (PDMS) drops on solid horizontal surfaces was studied. Spreading velocity was shown to grow with decreasing drop volume, the effect being more pronounced at high viscosities of polymer. The deviation of shape of the spreading drop from that of a spherical segment is more pronounced the higher the surface energy of substrate, the higher the polymer viscosity and the smaller the drop volume. Spreading on a rough surface is slower than on a smooth one owing to the energy barrier created by surface inhomogeneities: the barrier is to be overcome by the spreading liquid. Based on the experimental results a mechanism of spreading of polymer drops is proposed. Changes in potential energy of a drop and in the free surface energy of the system during spreading were compared, allowing a theoretical evaluation of the influence of gravity on the spreading velocity of drops. A theoretical analysis of spreading kinetics of viscous drops is given. The equation proposed agrees well with the experimental results at 90° > θ > 0°.     

STABILITY OF THE LENSLIKE LIQUID THICKENING (THE DROP) ON A SOLID SUBSTRATE

The quasi equilibrium of a liquid lens or a liquid drop on a solid substrate is considered on the basis of the thermodynamics of microscopic thin liquid films. Both contact angles, corresponding to the membrane model and to the finite thickness layer convention of the film, have been derived as a function of the disjoining pressure isotherm. The analytical expressions for the line tension terms have been obtained, and the criterion for the stability of a liquid drop on a solid substrate has been proposed.     

STABILITY OF THE LENSLIKE LIQUID THICKENING (THE DROP) ON A SOLID SUBSTRATE

The quasi equilibrium of a liquid lens or a liquid drop on a solid substrate is considered on the basis of the thermodynamics of microscopic thin liquid films. Both contact angles, corresponding to the membrane model and to the finite thickness layer convention of the film, have been derived as a function of the disjoining pressure isotherm. The analytical expressions for the line tension terms have been obtained, and the criterion for the stability of a liquid drop on a solid substrate has been proposed.     

Theoretical and experimental analysis of droplet evaporation on solid surfaces

The evaporation of sessile drops is central to a number of important processes, including printing, washing and coating. In this paper, the evaporation of water sessile droplets on hydrophobised silicon wafers and Teflon was analysed from theoretical and experimental perspectives. The contact angle, volume and base radius of the water droplets as a function of time were determined using tensiometry. The theoretical analysis showed different evaporative flux phenomena for acute and obtuse contact angles. The non-linear evolution of residual droplet volume, contact angle and base radius are solved and depend on the hydrophobicity of the solid surface and droplet dimension. Good agreement between the theoretical and experimental results was observed during pinning and depinning stages of evaporation. It was shown that the surface roughness, hydrophobicity and the contact angle hysteresis significantly influenced the evaporation of sessile drops and need to be considered when quantifying the evaporation process.     

接触角法在测定固体表面洁净度方面的应用

介绍了接触角法测定固体表面洁净度的基本原理,接触角的测定方法,包括量角法,测高法(小液滴法和平衡液滴法)。影响接触角法测定准确的主要因素为表面粗糙度,此外温度变化及平衡时间对接触角也略有影响。接触角法在生产中的具体应用有水滴法、水膜法和喷雾法,讨论了它们在测定物体洁净度和判断清洗方法优劣方面的应用。     

Studies on slag deposit formation in pulverized coal combustors. 1. Results on the wetting and adherence of synthetic coal ash drops on steel

As part of a study of slag deposit formation in pulverized-coal-fired boilers, apparent contact angles and adhesion strengths of molten mineral drops contacted with cooler oxidized steel substrates have been investigated. High-speed photography indicated that freezing of the interface between the molten drop and metal surface occurred in milliseconds. Adherence occurred between an oxide film on the metal and the drop, adherence was weak on stainless steels, and particles of oxide film were broken away from the substrate when the drops were sheared off. Higher substrate temperatures gave increased adhesion, with a larger area of strong interaction between the oxide and the drop interface and less area of weak interaction. Addition of compounds to lower the liquidus temperature of the drop gave increased adherence. Pyrite drops were converted to mainly pyrrhotite on melting and showed a high degree of wetting and adherence to the oxidized steel even at low temperatures.     

Interpretation of contact angle hysteresis

Hysteresis of the contact angle, i.e. the difference between the advancing and receding contact angles, is discussed in terms of the liquid film presence behind the drop when it has receded. It is shown that values of receding contact angles in many systems result from a well-defined free energy balance in the solid/liquid drop system. If a duplex film is present behind the drop, experimental receding contact angles up to 15° may be considered as lying in the range of the experimental error. In the case of low-energy solids (e.g. Teflon), it is possible to determine graphically the minimum value of the surface tension below which a liquid will leave a duplex film behind the drop when receding.