Liquid drops on vertical and inclined surfaces; II. A method for approximating drop shapes

In this article, a new method is proposed to approximate the shapes of liquid drops on vertical and inclined surfaces. Based on observations from Part I, the profile of a drop at a given azimuthal angle is approximated by two circles sharing a common tangent at the maximum height. The drop volume is obtained by integrating all profiles over the circumference of the base. The volume is thus described as a function of the contact angles and the three-phase contact line. The new method accurately predicts the volumes of drops tested in Part I and independent measurements from the literature. Simplifying the drop shape to a spherical cap can lead to a 75% error in drop-volume prediction. The proposed method is used to study the effect of drop parameters on volume prediction. The two-circle geometry can also be used to measure contact angles from profile images.     

Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces

A simulation study of liquid drops on inclined surfaces is performed in order to understand the evolution of drop shapes, contact angles, and retention forces with the tilt angle. The simulations are made by means of a method recently developed for dealing with contact angle hysteresis in the public-domain Surface Evolver software. The results of our simulations are highly dependent on the initial contact angle of the drop. For a drop with an initial contact angle equal to the advancing angle, we obtain results similar to those of experiments in which a drop is placed on a horizontal surface that is slowly tilted. For drops with an initial contact angle equal to the mean between the advancing and the receding contact angles, we recover previous results of finite element studies of drops on inclined surfaces. Comparison with experimental results for molten Sn-Ag-Cu on a tilted Cu substrate shows excellent agreement.     

Equilibrium of drops on inclined fibers

Why is it that drops do not slip down inclined thin fibers or spider silks? The possible explanation is based on the existence of fiber size, which causes a sustaining force that pins these drops. Following this explanation, the drop remains in equilibrium until a critical value of the sustaining force is reached. We suggest an alternative analyses, from the point of view of the inclined fiber at which the drop slips down is predicted. This result does not depend explicitly on silk surface roughness, but only on the drop size and surface tensions.     

An experimental study of gas adsorption on fractal surfaces

The validity of the fractal versions of the FHH and BET theories for describing the adsorption of butane and nitrogen on a variety of partially dehydroxylated silica surfaces has been tested. The fractal dimensions obtained from adsorption data have been compared with those obtained completely independently using SAXS. It was found that the fractal dimensions obtained from butane adsorption isotherms, using both the fractal FHH and fractal BET theories, agreed well with the corresponding values obtained from SAXS over overlapping length scales. However, in general, a systematic deviation between the fractal dimension obtained from nitrogen adsorption and that obtained from SAXS was observed. The fractal dimensions obtained from nitrogen adsorption were consistently larger than those obtained from SAXS, which is the opposite of what has often been found in the literature. It has been suggested that the differences in the suitability of the adsorption theories tested to describe butane and nitrogen adsorption is due to the significant difference between the interaction strengths of these two different molecules with silica surfaces. A modified theory that can account for the discrepancy between the fractal dimensions obtained from nitrogen adsorption and SAXS has been proposed. The implications of the new theory for the accuracy of nitrogen adsorption BET surface areas for silicas are discussed.     

An ab initio study of the CH3I photodissociation. I. Potential energy surfaces

The multireference spin-orbit (SO) configuration interaction (CI) method in its Lambda-S contracted SO-CI version is employed to calculate two-dimensional potential energy surfaces for the ground and low-lying excited states of CH3I relevant to the photodissociation process in its A absorption band. The computed equilibrium geometry for the X A1 ground state, as well as vibrational frequencies for the nu2 umbrella and nu3 symmetric stretch modes, are found to be in good agreement with available experimental data. The 3Q0+ state converging to the excited I(2P1/2o) limit is found to possess a shallow minimum of 850 cm(-1) strongly shifted to larger internuclear distances (RC-I approximately 6.5a0) relative to the ground state. This makes a commonly employed single-exponent approximation for analysis of the CH3I fragmentation dynamics unsuitable. The 4E(3A1) state dissociating to the same atomic limit is calculated to lie too high in the Franck-Condon region to have any significant impact on the A-band absorption. The computed vertical excitation energies for the 3Q1, 3Q0+, and 1Q states indicate that the A-band spectrum must lie approximately between 33,000 and 44,300 cm(-1), i.e., between 225 and 300 nm. This result is in very good agreement with the experimental findings. The lowest Rydberg states are computed to lie at >or=49,000 cm(-1) and correspond to the ...a(1)2n3a1(6sI) leading configuration. They are responsible for the vacuum ultraviolet absorption lines found experimentally beyond the A-band spectrum at 201.1 nm (49,722 cm(-1)) and higher.     

Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.     

Contact angles of drops on curved superhydrophobic surfaces

Superhydrophobic surfaces have contact angles that exceed 150 degrees and are known to reduce surface fouling, protect surfaces, and improve liquid-liquid separations. Electrospun sub-micron fiber mats can perform as superhydrophobic surfaces. Superhydrophobic behavior is typically measured on planar surfaces, whereas applications may require curved surfaces. This paper discuses the measurement of water contact angles of fiber mats formed on cylindrical surfaces to create superhydrophobic behavior on curved surfaces. Equations are derived that relate the radius of curvature of spherical and cylindrical surfaces and drop size to the observed contact angle on the curved surfaces. Calculations from the equations agree well with experimental observations on spherical surfaces reported in literature and on cylindrical surfaces created in our lab.     

Three-dimensional equilibrium shapes of drops on hysteretic surfaces

In this paper, we study equilibrium three-dimensional shapes of drops on hysteretic surfaces. We develop a function coupled with the publicly available surface energy minimization code Surface Evolver to handle contact angle hysteresis. The function incorporates a model for the mobility of the triple line into Surface Evolver. The only inputs to the model are the advancing and receding contact angles of the surface. We demonstrate this model’s versatility by studying three problems in which parts of the triple line advance while other parts either recede or remain stationary. The first problem focuses on the three-dimensional shape of a static pendant drop on a vertical surface. We predict the finite drop volume when impending sliding motion is observed. In the second problem, we examine the equilibrium shapes of coalescing sessile drops on hysteretic surfaces. Finally, we study coalescing puddles in which gravity plays a leading role in determining the equilibrium puddle shape along with hysteresis.     

Spectral UV irradiance on vertical surfaces: a case study

The UV spectral irradiance on horizontal and vertically oriented surfaces was measured throughout a cloudless day (18 July 1995) at Izana station, Tenerife, using a Bentham DTM300 spectroradiometer scanning from 290 to 500 nm in steps of 5 nm. Results show that irradiance measured on a horizontal surface is not proportional to irradiance on a vertical surface. The relation between the two depends upon orientation of the vertical surface, zenith angle and wavelength. At short UVB wavelengths surfaces directed toward the solar azimuth received their maximum irradiances much closer to solar noon than the maxima for longer wavelengths. Some vertical surfaces also received significantly more irradiance than the horizontal surface at long wavelengths during all but the central hours of the day, while at short wavelengths all vertical irradiances were less than the horizontal except for the measurements at the extreme ends of the day. Erythemally effective radiation followed the diurnal pattern of irradiations for short UVB wavelengths.     

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.     

An NMR study of the freezing of emulsion-containing drops

Various nuclear magnetic resonance (NMR) techniques were used to monitor the freezing behaviour of suspended 2-mm-diameter drops. The drops were composed of hydrocarbon oils emulsified in either water or water/sucrose mixtures. As such they were good model systems for the study of spray freezing, sharing structural similarities with potential products such as ice cream. In particular, simple 1H NMR spectroscopy was used to monitor and individually quantify the freezing or solidification behaviour of the various constituent species of the drops. In addition, the effect of freezing on the emulsion droplet size distribution (and hence emulsion stability) was also measured based on NMR self-diffusion measurements. The effect of freeze/thaw cycling was also similarly studied. The nucleation temperature of the emulsion droplets was found to depend on the emulsion droplet size distribution: the smaller the droplets, the lower the nucleation temperature. Emulsion droplet sizing indicated that oil-in-sucrose-solution emulsions were more stable, showing minimal coalescence, whereas oil-in-water emulsions showed significant coalescence during freezing and freeze/thaw cycling.     

Comparison of sessile drop and captive bubble methods on rough homogeneous surfaces: a numerical study

Quasi-static experiments using sessile drops and captive bubbles are the most employed methods for measuring advancing and receding contact angles on real surfaces. These observable contact angles are the most easily accessible and reproducible. However, some properties of practical surfaces induce certain phenomena that cause a built-in uncertainty in the estimation of advancing and receding contact angles. These phenomena are well known in surface thermodynamics as stick-slip phenomena. Following the work of Marmur (Marmur, A. Colloids Surf., A 1998, 136, 209-215), where the stick-slip effects were studied with regard to sessile drops and captive bubbles on heterogeneous surfaces, we developed a novel extension of this study by adding the effects of roughness to both methods for contact angle measurement. We found that the symmetry between the surface roughness problem and the chemical heterogeneity problem breaks down for drops and bubbles subjected to stick-slip effects.     

Routine measurement of erythemally effective UV irradiance on inclined surfaces

Measurements of erythemally weighted UV radiation are usually related to a horizontal surface. The radiation is weighted with the sensitivity of the human skin, but the surface of the human body has only few horizontal surfaces. Therefore the UV radiation on inclined surfaces has to be quantified to investigate UV effects on humans. To fulfill this task three fully automatic measuring systems were built to measure the erythemally weighted UV radiation in 27 directions within 2 min. This system measures routinely during the whole day and has now been in operation for nearly three years (in total 2000 measurement days) under any kind of meteorological conditions. The measurements provide the informations needed for further investigations concerning the UV effects on humans. The calibration of the erythemally weighting radiometers was performed in a way to provide reliable UV index measurements for all directions. The results of four exemplary measurement days in summer and winter for clear sky and overcast conditions are presented.     

Liquid phase demixing in ferroelectric/semiconducting polymer blends: An experimental and theoretical study

This article describes a combined experimental and theoretical study on nanophase structure development as a result of liquid phase demixing in solution‐cast blends of the organic semiconductor poly(9,9′‐dioctyl fluorene) (PFO) and the ferroelectric polymer poly(vinylidene fluoride‐co‐trifluoroethylene) (P(VDF‐TrFE)). Blend layers (200 nm) are prepared by spin coating a 1:9 (w/w) PFO:P(VDF‐TrFE) blend solution in a common solvent on a poly(ethylenedioxy thiophene)/poly(styrene sulfonate) substrate. Owing to the pronounced incompatibility between the two polymers, a strong phase‐separated morphology is obtained, characterized by disk‐like nanodomains of PFO embedded in a P(VDF‐TrFE) matrix, as revealed by scanning electron microscopy. By varying the processing conditions, we find the average domain size and standard deviation to increase with spinning time. The considerable increase in domain size suggests the coarsening process not to be impeded by a steep rise in viscosity. This indicates solvent evaporation to be only moderate within the experimental time frame. The evolution of the observed phase morphology is modeled using ternary diffuse interface theory integrated with a modified Flory–Huggins (FH) treatment of the homogeneous (bulk) free energy of mixing, to account for significant molecular differences between the active blend components. Using calculated FH interaction parameters, the model confirms the phase separation to occur via spinodal decomposition of the blend solution during spin coating, as suggested by experimental observations. The simulated phase morphologies as well as the modeled trends in domain growth and standard deviation compare favorably with the experimental data. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1255–1262, 2011     

Studies of the wetting kinetics of liquid drops on solid surfaces

The viscosity _L and the surface tension _L of the liquid as well as the equilibrium contact angle _e are essential parameters governing the wetting kinetics of liquids on solids. By means of a contact angle apparatus with video image digitization, the dynamic contact angle and the radiusr of the contact area of sessile drops on solid surfaces have simultaneously been determined in dependence on time after drop application between about 3·10^–2 s and long times.The measurements were performed with series of liquids: polydimethylsiloxanes with different molecular masses and solutions of polyisobutylene in decalin and polyacrylic acid in water, covering a wide range of concentrations. The liquids in each series have a constant surface tension, but viscosities ranging over about four orders of magnitude, allowing the influence of _L and _L to be studied independently. Solids such as glass, polyethylene and polytetrafluoroethylene were chosen so that the cases of complete wetting (spreading) and partial wetting ( _e) could be studied.The curves of cos andr/R ₀ vs. time for the different liquids of a series can be superimposed to a master curve by plotting them against _L·t _L·R ₀, whereR ₀ is the radius of the original drop. All these master curves coincide at small wetting times, with exception of the data for the polysiloxanes. That means that the early stage of the wetting process is determined only by the properties of the wetting liquid. The influence of the solid surface, characterized by the equilibrium contact angle _e becomes significant only at the end of the wetting process.Dedicated to Professor Dr. H. Willersinn on the occasion of his 65^th birthday