The influence of asymmetry in drop shape on an interfacial tension measurement

A requirement of the drop method for interfacial tension measurement is that the drop must have an axi-symmetry. The drop shape was measured as a function of the angle of the rod from which the drop was hanging. The deviation of the interfacial tension caused by asymmetry was calculated using the selected plane method in the pendant drop technique. A sharp maximum was seen in the interfacial tension vs angle curve when the rod was at the vertical point. The maximum value was concluded as being the true value of the interfacial tension. Both decreases in the pressure difference and in the curvature of the drop associated with an increase in the rod-angle are a counterpart with each other to satisfy the Bashforth and Adams equation. The underestimation of the interfacial tension seems to be caused by the apparent inconsistency between the decreases in the curvature and pressure difference terms. The rigorous mechanical setup demonstrated here is necessary to attain the true axi-symmetric condition, and thus obtain a reliable value for the interfacial tension.     

Improvement of interfacial tension measurement using a captive bubble in conjunction with axisymmetric drop shape analysis (ADSA)

Axisymmetric drop shape analysis (ADSA) is a method to measure surface tension using drop or bubble profiles. Combining ADSA with a captive bubble configuration (ADSA-CB) facilitates pulmonary surfactant related studies. The accuracy of ADSA-CB is crucially dependent on the quality of the bubble profile extracted from the raw image. In the previous version of ADSA-CB, a global thresholding method was used to segment the bubble profile. However, that technique is of limited accuracy for images with noise and/or lack of contrast. In this paper, a new generation of ADSA-CB using the Canny edge detector was developed. To obtain better results, a novel edge smoothing technique, termed axisymmetric liquid fluid interfaces-smoothing (ALFI-S), was introduced and incorporated with the Canny edge detector to extract bubble profiles. The performance of the new version of ADSA-CB was evaluated using captive bubble images under different conditions. The results suggest that the new methodology is capable of producing accurate surface tension values under a variety of circumstances.     

Determination of protein adsorption by comparative drop and bubble profile analysis tensiometry

Proteins adsorb at a liquid interface at very low bulk concentrations which is significantly decreased due to the adsorbed amount. Depending on the surface area A to solution bulk volume V ratio this loss in protein can be significant. Using experimental methods with large differences in the A/V ratio the adsorbed amount can be determined from the measured quantities, for example the surface tension. For beta-casein and bovine and human serum albumin data from literature obtained by the Wilhelmy technique and own data measured by drop profile analysis tensiometry are used. The adsorbed amounts measured directly from ellipsometry agree very well with those determined by the proposed method.     

Characterisation of alkyl amines at the water/air surface with the drop and bubble profile analysis tensiometry

Pendant drop and buoyant bubble methods have been used to study the surface characteristics of alkyl amines at the water/air surface. The investigated alkyl amines, triethylamine and octylamine, showed unusual changes in the surface tension as a function of time: an initially steep drop and a subsequent steady increase in the surface tension until a value close to the one of the pure water/air system was observed. This phenomenon is explained by the evaporation of the alkyl amines, for which several sets of experiments have been conducted with the pendant drop and buoyant bubble methods. Using an appropriate experimental protocol, the equilibrium adsorption behaviour of the two amines can be quantitatively measured.     

CFD evaluation of drop retraction methods for the measurement of interfacial tension of surfactant-laden drops

Drop retraction methods are popular means of measuring the interfacial tension between immiscible polymers. Experiments show that two different drop retraction methods, imbedded fiber retraction (IFR) and deformed drop retraction (DDR), give inconsistent results when a surfactant is present on the surface of the drop. These inconsistencies are deemed to be due to dilution of the surfactant and due to gradients in interfacial concentration of surfactant along the drop surface. This physical picture is quantified for the simple case of a Newtonian drop in a Newtonian matrix, with an insoluble, nondiffusive surfactant at the interface. The drop is deformed in computational fluid dynamics simulations by shearing the matrix, and then allowed to retract. Dilution and interfacial tension gradients effects are found to be especially large at the early stages of retraction, making IFR unsuitable for measuring the interfacial tension of surfactant-laden interfaces. The effects of surfactant dilution and gradients are found to persist even at late stages of retraction, causing the DDR method to underestimate the equilibrium interfacial tension significantly. The largest underestimates occur when the drop viscosity is lower than the matrix viscosity.     

Adsorption kinetics of NIPAM-based polymers at the air-water interface as studied by pendant drop and bubble tensiometry

The adsorption of N-isopropylacrylamide (NIPAM) based thermoresponsive polymers at the air-water interface was investigated by using drop and bubble shape tensiometry. The molecular weight dependence of polymer adsorption rate was studied by using narrowly distributed polymer fractions (polydispersity < 1.2) that were prepared by solvent:nonsolvent fractionation. The time-dependent surface tension profiles were fitted to the Hua-Rosen equation and the t values obtained were applied for interpretation of the kinetic data. It was found that the rate of polymer adsorption increased as the molecular weight of the polymer decreased. The relationship between polymer surface concentration and surface tension was determined by applying the pendant drop as a Langmuir-type film balance. From this relationship, the kinetics of polymer adsorption determined experimentally was compared with the adsorption rates predicted by a diffusion-controlled adsorption model based on the Ward-Tordai equation. The predicted adsorption rates were in good agreement with what was found experimentally. The dependence of the adsorption rate on the molecular weight of polymers can be satisfactorily described within the diffusion-controlled model.     

Sliding/rolling phobic droplets along a fiber: measurement of interfacial forces

Phobic droplet-fiber systems possess complex geometries, which have made full characterization of such systems difficult. This work has used atomic force microscopy (AFM) to measure droplet-fiber forces for oil droplets on oleophobic fibers over a range of fiber diameters. The work adapted a previous method and a theoretical model developed by the authors for philic droplet-fiber systems. A Bayesian statistical model was also used to account for the influence of surface roughness on the droplet-fiber force. In general, it has been found that the force required to move a liquid droplet along an oleophobic filter fiber will be less than that required to move a droplet along an oleophilic fiber. However, because of the effects of pinning and/or wetting behavior, this difference may be less than would otherwise be expected. Droplets with a greater contact angle (~110°) were observed to roll along the fiber, whereas droplets with a lesser contact angle (<90°) would slide.     

Investigation of the dependence of inferred interfacial tension on rotation rate in a spinning drop tensiometer

The spinning drop tensiometer is widely used to study the interfacial properties of many systems. However, there have also been several reported limitations with the spinning drop tensiometer. In this paper, it is shown that there is a relationship between the measured interfacial tension and the rotation rate of the drop. A detailed investigation of this relationship is presented.     

The measurement of dynamic surface tension by the maximum bubble pressure method

The principle of maximum pressure in a bubble for measurements of dynamic surface tension is realized in a fully automatically operating apparatus. The set-up yields data in the time interval from 1 ms up to several seconds and can be temperature controlled from 5° to 80°C. Experimental data obtained for different surfactants and gelatine in water and/or water/glycerine mixtures at different temperatures are discussed. A direct comparison with results from oscillating jet and inclined plate experiments shows excellent agreement.     

The effect of salting out and micellization on interfacial tension

We consider a system consisting of oil and water phases with nonionic surfactant distributed between them and present a model for the effect of salt on the interfacial tension. The model accounts for the salting out of surfactant from water to oil and also for the occurrence of micelles in the aqueous phase. In addition, it is shown that salting out affects micellization in interesting ways, e.g. micelles may form as the salt concentration increases even though none are present initially and then disappear at higher concentrations. The effect of chain length and head group size (and hence of HLB) on the interfacial tension is examined for surfactants of the polyoxyethylene type. The calculated interfacial tension decreases continuously and may become negative under certain condition, indicating that the oil-water interface becomes unstable and a microemulsion forms.     

Effect of surfactant on interfacial gas transfer studied by axisymmetric drop shape analysis-captive bubble (ADSA-CB)

A new method combining axisymmetric drop shape analysis (ADSA) and a captive bubble (CB) is proposed to study the effect of surfactant on interfacial gas transfer. In this method, gas transfer from a static CB to the surrounding quiescent liquid is continuously recorded for a short period (i.e., 5 min). By photographical analysis, ADSA-CB is capable of yielding detailed information pertinent to the surface tension and geometry of the CB, e.g., bubble area, volume, curvature at the apex, and the contact radius and height of the bubble. A steady-state mass transfer model is established to evaluate the mass transfer coefficient on the basis of the output of ADSA-CB. In this way, we are able to develop a working prototype capable of simultaneously measuring dynamic surface tension and interfacial gas transfer. Other advantages of this method are that it allows for the study of very low surface tensions (<5 mJ/m2) and does not require equilibrium of gas transfer. Consequently, reproducible experimental results can be obtained in a relatively short time. As a demonstration, this method was used to study the effect of lung surfactant on oxygen transfer. It was found that the adsorbed lung surfactant film shows a retardation effect on oxygen transfer, similar to the behavior of a pure DPPC film. However, this retardation effect at low surface tensions is less than that of a pure DPPC film.     

Effects of injection angle on the measurement of surface tension coefficient by drop weight method

The drop weight method for surface tension measurement is based on the weight of drops detached from a nozzle. The original idea was based on a postulate introduced by Tate (On the Magnitude of a Drop of Liquid Formed Under Different Circumstances, Philos. Mag. 27, 176–180, 1864), assuming that the weights of an ideal pendant drop and a detached ideal drop are identical, and that this weight is equal to the surface force that holds a drop attached to the nozzle. To consider the real volume of a drop that detaches from a nozzle, the method required a correction factor. Harkins and Brown suggested such correction factors for vertical injection from a nozzle. In this study, a correction factor for injection at different angles is presented and some of the hydrodynamic effects on surface tension measurement based on the drop weight method are studied. In addition, a model is introduced for the detachment time of drops in directions other than the vertical direction     

A simple derivation of Vonnegut's equation for the determination of interfacial tension by the spinning drop technique

A simple derivation of Vonnegut's equation for use in the determination of interfacial tension by the spinning drop technique is described. The derivation involves a cylindrical approximation and calculates the kinetic energy of rotation of the system from a consideration of its moment of inertia.     

The effect of the presence of valinomycin on the interfacial tension of lecithin membrane

The effect of the presence of valinomycin in lecithin membrane on its interfacial tension has been studied. The experiments have been carried out at various forming solution compositions and at various potassium ion concentrations in electrolyte solution. Potassium chloride was used as the electrolyte. A complex was formed between the valinomycin molecule and K+ ion. The following parameters describing the complex were determined: K, the stability constant of the valinomycin-K+ complex and B, partition coefficient. These values are equal to 3.52 x 10(5) m3 mol(-1) and 6.0, respectively.     

Dynamic interfacial tension at the oil/surfactant-water interface

We have used dynamic interfacial tension measurements to understand the structure of the ordered monolayer at the hexadecane/water interface induced by the presence of surfactant molecules. No abrupt changes in the interfacial tension (gamma) are observed during the expansion and contraction cycle below the interfacial ordering temperature (Ti) as observed for alkanes in contact with air. The lack of an abrupt change in gamma and the magnitude of this change during the expansion process indicate that the ordered phase may not be crystalline. The change in the interfacial tension is due to an increase in contact between water and hexadecane molecules and the disordering of the interfacial ordered layer. At low surfactant concentrations, the recovery of the interfacial tension is slower below Ti, suggesting that there is a critical surfactant concentration necessary to nucleate an ordered phase at the interface.     

A rigorous theory of ring tensiometry: Addendum on the wall effect

Summary As a supplement to our theoretical calculations for the ring method of measuring surface and interfacial tensions of liquids, the effect of the finite size of the liquid container on the measurement has been studied employing (i) an exact analysis for the case of an infinite straight cylinder midway between two parallel walls and (ii) an approximate analysis for a ring in a circular container. The parameters which can cause errors are identified, and their magnitude is estimated and compared with the experimental results for surface tension of water in air. It is shown that conditions can be readily adjusted to produce negligrors.Nomenclature a radius of cylinder or ring wire; - C ₂₃ (₂ –₃)g/ ₂₃ D=semi-gap width between parallel walls, or radius of liquid container; - f Harkins-Jordan (1) factor - F, E elliptic integrals of the first and second kind (k = modulus) - F equilibrium capillary force on ring or per unit length of a straight cylinder; - F _D,F maximumF for finiteD andD = - g gravity - r _i,z _i r- andz-coordinates of the inner (i =1) and outer (i = 2) contact line circles on ring; - z _c vertical coordinate of the contact line on cylinder; - Y23, YD interfacial tension (D= ; uncorrected interfacial tension measured in container of radiusD - _i density of thei phase - _i slope angle of the inner (i = 1) and outer (i = 2) menisci on ring - 180° - _c slope angle of cylindrical meniscus at the contact line - ₂ 180° – ₂ - Oo contact angle at container wall - (F _D -F )/F for cylinder; (YD - ₂₃)/Y23 for ring     

A theoretical study on surfactant adsorption kinetics: effect of bubble shape on dynamic surface tension

A planar or spherical fluid-liquid interface was commonly assumed on studying the surfactant adsorption kinetics for a pendant bubble in surfactant solutions. However, the shape of a pendant bubble deviates from a sphere unless the bubble's capillary constant is close to zero. Up to date, the literature has no report about the shape effect on the relaxation of surface tension due to the shape difference between a pendant bubble and a sphere. The dynamic surface tension (DST), based on the actual shape of a pendant bubble with a needle, of the diffusion-controlled process is simulated using a time-dependent finite element method in this work. The shape effect and the existence of a needle on DST are investigated. This numerical simulation resolves also the time-dependent bulk surfactant concentration. The depth of solution needed to satisfy the classical Ward-Tordai infinite-solution assumption was also studied. For a diffusion-controlled adsorption process, bubble shape and needle size are two major factors affecting the DST. The existence of a needle accelerates the bulk diffusion for a small bubble; however, the shape of a large pendant bubble decelerates the bulk diffusion. An example using this method on the DST data of C12E4 is illustrated at the end of this work.     

Characterisation by drop tensiometry and by ellipsometry of the adsorption layer formed at the air/champagne wine interface

A foam ring composed of small bubbles on the surface of a champagne glass is one of its hallmarks. The equilibrium state of that ring is linked with the rate of formation and of disappearance of bubbles. The stability of bubbles is usually ascribed to the occurrence and to the properties of an adsorption layer formed at the gas/liquid interface. Our goal is to characterise such an adsorption layer at the gas/wine interface in order to understand its role in bubble stability. Alcohol in wine lowers the surface tension to 49 mN/m. The adsorption of other molecules may cause a further decrease of 2 mN/m. Such a situation makes the study of adsorption by surface tension measurement inaccurate. To overcome this problem, we have diluted the wine four times with water before its surface tension measurement by pendant drop shape analysis. In these conditions, ethanol lowers the surface tension to 64 mN/m and the adsorption of other molecules of the wine can be monitored over 6-8 mN/m. The usual behaviour of such a diluted wine is a lowering of the surface tension during at least 20 min after drop formation. Since the role of macromolecules on the foaming properties of wine had been previously observed, we have chosen to evaluate the effect of this fraction of the wine molecules on its surface properties. Thus, wines were ultrafiltrated on a membrane with a 10000 molecular mass cut-off. The ultrafiltrate (UF) does not show any decrease of its surface tension over a 20-min period while the ultraconcentrate (UC) has a kinetics similar to that of unfiltered wine. Mixtures of UF and UC have behaviours intermediate between those of these products. A technological treatment of the wine with bentonite, believed to lower the content of macromolecules, yields a wine similar to UF. The effect of ultrafiltration was also analysed by spectroscopic ellipsometry. UF has a spectrum similar to that of a water/alcohol mixture with the same ethanol content and its ellipticity is stable during at least 20 min. On the contrary, wine or UC show spectra with the features of an adsorption layer and those characteristics increase during more than 20 min. Two varieties of vine were compared: 'Chardonnay' and 'Pinot noir'. The former is known to have better foaming properties than the latter. Its surface properties measured in this study are also more pronounced than those of Pinot noir. However, the representation of the dilational modulus against the surface pressure (which, in some instances, may be a mathematical transformation of the state equation) puts all the samples (wines, UF and UC of each) on the same master curve, a fact in favour of a common nature for all the adsorption layers. It can be concluded that surface properties of champagne wines are mostly determined by ethanol and by macromolecules with a molecular mass larger than 10000. Moreover, the adsorption layers seem to have the same nature, irrespective of the vine variety and of the concentration ratio of the wine.     

Influence of drop volume on surface tension evaluated using the pendant drop method

The pendant drop technique is one of the most accurate methods to measure surface tension of liquids. Recently, it has been found that the value of the surface/interfacial tension found using the pendant drop method might be drop-volume dependent. In this work, the surface tension of glycerol at a 25 °C and the surface tension of polypropylene at 240 °C were measured using the pendant drop method for different drop volumes. It was shown that the values of the surface tension depend on the drop size if no calibration to take into account the anisotropy in the optical enlargement is performed. However, when a calibration procedure for optical anisotropy correction is performed, the values of the surface tension obtained do not depend on the volume drop size and they corroborate the values in the literature.     

A robust algorithm for the simultaneous parameter estimation of interfacial tension and contact angle from sessile drop profiles

The pendant and sessile drop profile analysis using the finite element method (PSDA-FEM) is an algorithm which allows simultaneous determination of the interfacial tension (gamma) and contact angle (theta(c)) from sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second-order spherical coordinate form of the Young-Laplace equation. Thus, the boundary conditions at the drop apex and contact position of the drop with the substrate are required to solve for the drop profile coordinates. The boundary condition at the position where the drop contacts the substrate may be specified as a fixed contact line or fixed contact angle. This paper will focus on the fixed contact angle boundary condition for sessile drops on a substrate and how this boundary condition is used in the PSDA-FEM curve-fitting algorithm. The PSDA-FEM algorithm has been tested using simulated drop shapes with and without the addition of random error to the drop profile coordinates. The random error is varied to simulate the effect of camera resolution on the estimates of gamma and theta(c) values obtained from the curve-fitting algorithm. The error in the experimental values for gamma from sessile drops of water on acrylic and Mazola corn oil on acrylic falls within the predicted range of errors obtained for gamma values from simulated sessile drop profiles with randomized errors that are comparable in magnitude to the resolution of the experimental setup.