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.     

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.     

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.     

Analysis of evaporating droplets using ellipsoidal cap geometry

The evaporation of small droplets of volatile liquids from solid surfaces depends on whether the initial contact angle is larger or less than 90°. In the latter case, for much of the evaporation time the contact radius remains constant and the contact angle decreases. At equilibrium, the smaller the drop, the more it is possible to neglect gravity and the more the profile is expected to conform to a spherical cap shape. Recently published work suggests that a singular flow progressively develops within the drop during evaporation. This flow might create a pressure gradient and so result in more flattening of the profile as the drop size reduces, in contradiction to expectations based on equilibrium ideas. In either case, it is important to develop methods to quantify confidence in a deduction of elliptical deviations from optically recorded droplet profiles. This paper discusses such methods and illustrates the difficulties that can arise when the drop size changes, but the absolute resolution of the system is fixed. In particular, the difference between local variables, such as contact angle, cap height, and contact diameter, which depend on the precise location of the supporting surface, and global variables such as radii of curvature and eccentricity, is emphasized. The applicability of the ideas developed is not limited to evaporation experiments, but is also relevant to experiments on contact angle variation with drop volume.     

Evaporation of Ethanol-Water Mixture Drop on Horizontal Substrate

This study investigates the evaporation of sessile drop comprising ethanol and water mixture on horizontal poly methyl methacrylate surface. The contact angle (θ) and contact radius (R) of ethanol-water mixture drop are recorded with time, considering the impacts of presence of ethanol. With excess ethanol, the drop evaporation is principally controlled by a phase in which both the contact angle and contact radius are falling. A diffusional model assuming linear relation between contact radius and time is proposed as θ = eR ^?3 + cR ^?1, where e and c denote fitting coefficients. This model correlates with the experimental data.     

NUSSELT NUMBER FOR DIRECT CONTACT EVAPORATION OF A MOVING ELLIPSOIDAL DROP IN AN IMMISCIBLE LIQUID

Since Sideman et al.^[1] derived an analytical solution of the Nusselt number for a spherical drop in the direct contact evaporation in an immiscible liquid, many researchers have performed theoretical research on this field under different assumptions [2]-[6]. However drops moving in another immiscible liquid do not take a spherical form, but oblate form, which may be well approximated as an ellipsoid. This paper establishes the mathematical model of heat transfer for a moving ellipsoidal drop in an immiscible liquid, and presents results from numerical calculation. The relationship of the Nusselt number with the Weber number and the Peclet number is given, which is suitable for a relatively large range of We and Pe. The theoretical results for the Nusselt number show good agreement with experimental data. Some important conclusions are obtained.     

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.     

Controlled organization of self-assembled rod-coil block copolymer micelles

Spherical micelles of a series of poly(styrene-block-(2,5-bis[4-methoxyphenyl]oxycarbonyl)styrene) (PS-b-PMPCS) rod-coil diblock copolymers in a selective solvent can organize into large mono-layered films with a well-ordered hexagonal packing of the spheres after solvent evaporation. Organized domains in the spherical micelle film were observed by transmission electron microscopy (TEM) and atomic force microscopy (AFM). The core-shell structure of the spherical micelle remained after solvent evaporation. The micelle diameter in the ordered film as observed by TEM and AFM agree. The size of the spherical micelles can be controlled by the length of PMPCS when the length of the PS is fixed. The sphere diameters were varied from several tens of nanometers to more than one hundred nanometers. Solutions of smaller micelle spheres formed less ordered films than those from larger micelle particles. Additionally, monolayer films of cylindrical worm-like micelles were also prepared. Those cylindrical micelles were observed to be end-capped by spherical micelles. The monolayer micelle film from the largest spherical micelles appeared red when observed in optical microscopy in the reflection mode. A broad adsorption peak with a maximum adsorption wavelength of 545 nm was observed via UV-Vis spectroscopy.     

ON THERMODYNAMICS OF THIN FILMS: THE MECHANICAL EQUILIBRIUM CONDITION AND CONTACT ANGLES

A thermodynamic model for plane parallel thin liquid films applicable to solid-liquid-vapor systems was presented using the detailed method. The film was modeled as a bulk phase bound by two dividing surfaces. The thermodynamic thickness of the film was established as well as excess properties such as film tension. The analysis using this model yielded disjoining pressure definition identical to the literature reports. The effect of definition for contact angle on the resulting mechanical equilibrium condition was also demonstrated. It was concluded that from a theoretical perspective it is important to clearly define contact angles as the angle a sessile drop makes with either the solid phase or the thin film. However, on a practical level for most cases, the difference between using either of the two mechanical equilibrium conditions to determine film tension or contact angle will be minimal (ascertained by an order of magnitude analysis). The attempt was also made to bring about clarity concerning some of the questions in the literature regarding the thermodynamic model for thin films presented by Li and Neumann.     

ON THERMODYNAMICS OF THIN FILMS: THE MECHANICAL EQUILIBRIUM CONDITION AND CONTACT ANGLES

A thermodynamic model for plane parallel thin liquid films applicable to solid-liquid-vapor systems was presented using the detailed method. The film was modeled as a bulk phase bound by two dividing surfaces. The thermodynamic thickness of the film was established as well as excess properties such as film tension. The analysis using this model yielded disjoining pressure definition identical to the literature reports. The effect of definition for contact angle on the resulting mechanical equilibrium condition was also demonstrated. It was concluded that from a theoretical perspective it is important to clearly define contact angles as the angle a sessile drop makes with either the solid phase or the thin film. However, on a practical level for most cases, the difference between using either of the two mechanical equilibrium conditions to determine film tension or contact angle will be minimal (ascertained by an order of magnitude analysis). The attempt was also made to bring about clarity concerning some of the questions in the literature regarding the thermodynamic model for thin films presented by Li and Neumann.     

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.     

Simultaneous film evaporation and condensation on a two-directionally inclined surface

A theoretical analysis of the effects of inclination on the heat transfer rate during the simultaneous film evaporation on one side and film condensation on the other side of a solid flat plate is presented.The decrease of the evaporating film thickness due to the two-dimensional nature of the flow is relatively small. Hence, the corresponding increase in the overall transfer coefficient is practically insignificant.For a system in which the evaporating film is sustained by a vertically down-flowing liquid, the main effect of the inclination of the plane from the horizontal is due to the formation of an unwetted area. Some practical conclusions related to a bundle of conduits are suggested.In view of the conclusions, the extension of the flat plane analysis by sectional integration to inclined conduits is not warranted.     

Synthesis,structure and properties of polyimide–silica hybrid composites based on biphenyltetracarboxylic dianhydride

A simple and efficient way of synthesizing nanocomposite films using a dispersion technique is reported, with the resulting films having improved mechanical and thermal properties. Nano‐SiO₂ was used in a biphenyltetracarboxylic dianhydride‐based poly(amic acid) precursor and found to be dispersed up to 7 wt% without any additives. The composites were cast to make 10 µm solid films to establish structure and property relationships between liquid and solid film. The structures of the liquid composite materials were studied using NMR and Fourier transform infrared spectroscopy. Solid film properties such as tensile strength, contact angles and thermal behaviour were evaluated for comparison. The properties of the composite films were found to be enhanced compared to polyimide film itself. Atomic force microscopy and macroscale mechanical measurements showed that composite films with more dipolar bonding interactions have higher elastic moduli and are more deformable. They yield higher adhesion energies, and therefore composite coatings offer greater adhesion. There was a limitation in the film formation beyond 5 wt% of silica. Copyright © 2011 Society of Chemical Industry     

Dynamics of Fast Dewetting on Model Solid Substrates

We describe inertial effects in the dewetting of a low viscosity liquid (like water) deposited on hydrophobic solid substrates. The liquid dewets by nucleation and growth of a dry patch. We expect three regimes depending on the liquid viscosity, the film thickness and the static contact angle: (i) purely inertial (similar to the bursting of soap films); (ii) semi inertial, where dissipation occurs in a hydrodynamic boundary layer; (iii) purely viscous, for small contact angles, or very viscous liquids.     

固体平壁上受热降膜分布模型

在降膜受热流动过程中,由于液膜边缘与膜中央之间存在速度差异,造成液膜横向温度分布不均,由此在液膜横向产生了表面张力梯度, 即引起了自液膜边缘向液膜中央的Marangoni流动,从而使得液膜收缩变形. Marangoni流动引起的收缩效应与液体润湿性及流动压力的扩展效应相互作用, 在液膜边缘形成了凸起区. 根据液膜边缘凸起区内的受力平衡和物料平衡关系,同时考虑温度引起的表面张力梯度对液膜流动的影响,建立了受热降膜收缩模型. 此模型显示, 较低的壁温、较小的固液接触角以及较大的液体流量有利于液膜在加热固体壁面上的扩展. 通过与实验数据的对比显示,该模型较准确地预测了受热液膜下落初始过程中的液膜分布, 能够为传质传热过程及其设备的优化设计提供理论依据.     

Contact Angle Hysteresis on Polymer Surfaces: An Experimental Study

In order to characterize a solid surface, the commonly used approach is to measure the advancing and receding contact angles, i.e., the contact angle hysteresis. However, often an estimate of the average wettability of the solid–liquid system is required, which involves both the dry and wetted states of the surface. In this work, we measured advancing and receding contact angles on six polymer surfaces (polystyrene, poly(ethylene terephthalate), poly(methyl methacrylate), polycarbonate, unplasticized poly(vinyl chloride), and poly(tetrafluoroethylene)) with water, ethylene glycol and formamide using the sessile drop and captive bubble methods. We observed a general disagreement between these two methods in the advancing and receding contact angles values and the average contact angle determined separately by each method, although the contact angle hysteresis range mostly agreed. Surface mobility, swelling or liquid penetration might explain this behaviour. However, we found that the 'cross' averages of the advancing and receding angles coincided. This finding suggests that the cross-averaged angle might be a meaningful contact angle for polymer–liquid systems. Hence, we recommend using both the sessile drop and captive bubble methods.     

Ostwald ripening kinetics of angular grains dispersed in a liquid phase by two-dimensional nucleation and abnormal grain growth

Based on the fact that the angular shape of solid grains dispersed in the liquid matrix indicates a singular interface, the coarsening kinetics of angular grains was formulated based on 2-dimensional (2-D) nucleation and solved numerically. For comparison, diffusion-controlled coarsening of grains with a spherical shape was also solved numerically. The solutions showed that coarsening by 2-D nucleation induced abnormal grain growth whilst diffusion-controlled coarsening did not. This result agrees with the general experimental observation that the abnormal grain growth in liquid phase sintering takes place exclusively in the system with angular grains. The ratio of the largest grain size to the average increased monotonously with time in coarsening by 2-D nucleation whilst it decreased in diffusion-controlled coarsening. The artificially-added large grain (10 times larger than the average) became the abnormal grain in 2-D nucleation controlled coarsening but did not in diffusion-controlled coarsening.     

Estimation of contact angles on fibers

A droplet of liquid placed on a flat high-energy solid surface spreads to give a thin film so that no macroscopic droplet shape exists. On a chemically identical solid surface with only the geometry changed to a cylinder, the same droplet can have an equilibrium conformation. When the equilibrium conformation is of a barrel type, the profile of the droplet changes rapidly in curvature as the three-phase contact line is approached and the direct measurement of the contact angle is difficult. This work considers the theoretical profile for barrel-type droplets on cylinders and discusses how the inflection angle in the profile depends on droplet parameters. Experimental results are reported for poly(dimethylsiloxane) oils on a range of fiber surfaces and these are used to estimate the equilibrium contact angle from the inflection angle. The drop radius and volume dependence of the inflection angle is confirmed.     

Fabrication of conjugated polymer arrays by spinodal dewetting

Ordered arrays of conjugated poly(9,9‐dihexylfluorene) (PF) were prepared by the spinodal dewetting of liquid thin films on mica substrates. The size of the aggregates in the arrays was controlled by the evaporation rate of the solvent. Fast solvent evaporation resulted in smaller aggregates; slower evaporation resulted in larger aggregates. The photoluminescence of the PF arrays showed a smaller red‐shift than that of the unpatterned film when compared to PF solutions, which indicated that the aggregation of PF in the arrays is smaller than that in the unpatterned films. Copyright © 2004 Society of Chemical Industry