An improved method of sessile drop for determining the surface tension of liquids

An improved procedure is developed for the processing of images of meridional section of a liquid drop, obtained as a result of realization of the sessile drop method for determining the surface tension of liquid. The procedure provides for the scanning of digital image of droplet, for numerical solution of the Young-Laplace equation, and for the calculation of surface tension, wetting angle, and volume of the drop.     

The determination of surface tension at elevated temperatures by drop image analysis

The advantages of image analysis as applied to surface tension measurements by the sessile drop technique are discussed. It is demonstrated that valuable effective improvements of dimensional resolution are obtained. Errors in surface tension arising from various unavoidable sources such as chemical reactions or optical distortions are shown to be the main difficulties in applying the sessile drop technique at high temperature. This suggests a limiting spatial resolution of the digitizer beyond which no further improvements to the accuracy of the surface tension results are possible.

The technique has been applied to determine the surface tension of liquid Cu, Bi and Ag as well as a series of sodium borosilicate glasses.     

High-throughput screening of protein surface activity via flow injection analysis-pH gradient-dynamic surface tension detection

Using flow injection analysis (FIA), a pH gradient is blended in real time with a protein sample as the pH-dependent protein surface activity is measured by a dynamic surface tension detector (FIA-pH-DSTD). This instrumental system was developed as a high-throughput method for the screening of protein surface activity at the air/liquid interface as a function of pH. This method utilizes the continuous flow, drop-based dynamic surface tension detector in combination with flow injection sample introduction and blending of a steady-state concentration of protein sample with a pH gradient ranging from pH 2.0 to pH 11.5. Dynamic surface tension is measured through the differential pressure across the air/liquid interface of repeatedly growing and detaching drops. Continuous surface tension measurement is achieved for each eluting drop of 2-s length (2 muL), providing insight into both the kinetic and thermodynamic behaviors of molecular orientation processes at the liquid/air interface. Three-dimensional data are obtained, with surface tension first converted to surface pressure, which is collected as a function of elution time versus drop time. In FIA-pH-DSTD, a commercial pH probe is used to measure pH during elution time, enabling surface pressure throughout drop time to be subsequently plotted as a function of eluting pH. An automated DSTD calibration procedure and data analysis method is applied, which allows simultaneous use of two different solvents, permitting real-time dynamic surface tension data to be obtained. The method was applied to the analysis of 14 commercial purified proteins, yielding characteristic features of surface activity as a function of pH. The reproducibility of the measurement and selectivity advantage of the DSTD was shown for the analysis of serum albumins from various mammalian sources. Several applications were also suggested and discussed in order to show the potential of the method for protein and food chemistry studies and in the study of protein-polymer interactions.     

Multidimensional analysis of poly(ethylene glycols) by size exclusion chromatography and dynamic surface tension detection

Substantial improvements in a multidimensional dynamic surface tension detector (DSTD) are presented. Rapid, online calibration and measurement of the dynamic surface tension for high-performance liquid chromatography separations is achieved. Dynamic surface tension is determined by measuring the differential pressure across the liquid-air interface of repeatedly growing and detaching drops. Continuous surface tension measurement throughout the entire drop growth (50 ms to 2 s) is achieved, for each eluting drop, providing insight into the kinetic behavior of molecular orientation processes at the liquid-air interface. Three-dimensional data are obtained, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Two key innovations will be reported. First, a novel calibration procedure is described and implemented. Differential pressure signals from three drops (mobile phase, standard in mobile phase, and analyte in mobile phase) are utilized to make the dynamic surface tension measurement, thereby eliminating the need for optical imaging, and viscosity and hydrostatic pressure corrections, as required by other methods. Only pressure signals from one mobile-phase drop and one standard drop pressure signal are required, while the analyte drop pressure signal is measured along the chromatographic time axis. Second, corrections for drop elongation are not required, because the drops are precisely detached by an air burst actuation method in a regime were the surface tension forces significantly dominate gravitational forces. Drops that would fall with a volume of approximately 10 microL due to gravity are precisely and repeatedly detached earlier at a volume of 2 microL. The sensitivity and unique selectivity of the DSTD opens up new possibilities in the analysis of small molecular weight polymers of varying degrees of surface activity, as illustrated for the size-exclusion chromatography analyses of complex poly(ethylene glycol) (PEG) samples. Using partial least squares for data analysis, polydispersity of complex PEG samples is determined at a relative precision of approximately 1%.     

A quasi-containerless pendant drop method for surface tension measurements on molten metals and alloys

A quasi-containerles pendant drop method for measuring the surface tension of molten metals and alloys is being developed. The technique involves melting the end of a high-purity metal rod by bombardment with an electron beam to form a pendant drop under ultra-high-vacuum conditions to minimize surface contamination. The magnified image of the drop is captured from a high-resolution CCD camera. The digitized image of the drop is then analyzed to compute the surface tension. A computer program has been developed that reads the pixel intensities from a graphics file containing the digital image. The code searches for the edge of the drop along rows and columns of pixels and stores the edge coordinates in an array. It then computes an optimized theoretical drop shape by solving the Young-Lapface differential equation from which the quantity of surface tension is deduced. This technique has been demonstrated with the surface tension measurement of molten zirconium metal.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado, U.S.A.     

Surface Tension Measurements of Liquid Metals by the Quasi-Containerless Pendant Drop Method

The surface tensions of liquid metals, Zr, Ni, Ti, Mo, and Nb, have been measured at their melting points using the quasi-containerless pendant drop method. This method involves melting the end of a high-purity metal rod by bombardment with an electron beam to form a pendant drop under ultrahigh-vacuum conditions to minimize surface contamination. The magnified image of the drop is captured from a high-resolution CCD camera and digitized using a frame-grabber. The digital image is analyzed by reading the pixel intensities from a graphics file. The edge coordinates of the drop along rows and columns of pixels are searched by a computer program and stored in an array. An optimized theoretical drop shape is computed from the edge coordinates by solving the Young–Laplace differential equation to deduce the surface tension. The measured surface tensions are compared with available experimental results and theoretical calculations.     

Dynamic surface tension measurements on a molten metal-oxygen system: The behaviour of the temperature coefficient of the surface tension of molten tin

In order to point out the interactions of oxygen with a liquid metal and to study the influence of the actual operating conditions, dynamic surface tension measurements of a liquid test metal (tin), were performed under vacuum conditions by using the large drop method. This classical method has been improved by applying a new experimental procedure which allowed to obtain reliable surface tension measurements at high temperature as a function of time and varying the oxygen content. Further, complementary information on molten metal-oxygen interactions can be obtained. In particular, in this work, the trend of the surface tension temperature coefficient has been analysed as a function of different operative parameters, highlighting some crucial points such as the dependence of the temperature coefficient on the accuracy of the surface tension experimental data and the influence of the dissolved oxygen. It was demonstrated that the surface tension and its temperature coefficient do not depend on the quantity of dissolved oxygen when this is inside a certain range of values.     

Surface tension of the 60%Bi-24%Cu-16%Sn alloy and the critical temperature of the immiscible liquid phase separation

In order to control the core-shell structure of bimetallic lead-free solder balls, the surface tension and the critical temperature for the phase separation of two immiscible liquid phases are required. In this study, the temperature dependence of the surface tension of the 60%Bi-24%Cu-16%Sn alloy was measured using the constrained drop method. The temperature dependence of the surface tension was changed at the critical temperature due to phase separation and corresponding modification of the atomic structure of the surface layer. This simple and new procedure enables us to determine the surface tension and the critical temperature for the separation of two immiscible liquid phases simultaneously.     

The oscillation spectrum of a compound drop

Under microgravity conditions the equilibrium shape of a compound drop, consisting of two immiscible mutually wetting liquids, is given by a spherical liquid core, encapsulated by the second liquid phase. Due to energy considerations, the outer liquid is the one with the lower (vapour-liquid) surface tension. The oscillation spectrum of such a compound drop corresponds to that of two coupled oscillators, one being driven by the surface tension, while the other is due to the interfacial (liquid-liquid) tension between the two immiscible liquids. Therefore, in principle, the values of both, the surface and the interfacial tension, can be derived from the frequencies of the coupled oscillations. In this paper, an analytic expression is presented, relating the frequency spectrum to the surface and interfacial tension, respectively. In addition, the concept for technical realisation using electromagnetic levitation and copper-cobalt as a model system, is discussed.     

Surfactant Effect on the Average Flow Generation Near Curved Interface

The present work is devoted to the average flow generation near curved interface with a surfactant adsorbed on the surface layer. The investigation was carried out for a liquid drop embedded in a viscous liquid with a different density. The liquid flows inside and outside the drop are generated by small amplitude and high frequency vibrations. Surfactant exchange between the drop surface and the surrounding liquid is limited by the process of adsorption-desorption. It was assumed that the surfactant is soluble in the surrounding liquid, but not soluble in the liquid drop. Surrounding liquid and the liquid in the drop are considered incompressible. Normal and shear viscous stresses balance at the interface is performed under the condition that the film thickness of the adsorbed surfactant is negligible. The problem is solved under assumption that the shape of the drop in the presence of adsorbed surfactant remains spherical symmetry. The effective boundary conditions for the tangential velocity jump and shear stress jump, describing the above generation have been obtained by matched asymptotic expansions method. The conditions under which the drop surface can be considered as a quasi-solid are determined. It is shown that in the case of the significant effect of surfactant on the surface tension, the dominant mechanism for the generation is the Schlichting mechanisms under vibrations.     

应用轮廓吻合法测量Li_2B_4O_7·KNbO_3溶液的表面张力系数

讨论了一种表面张力测量方法一轮廓曲线吻合法．它是一种应用计算机技术,用数 字图像信息处理液滴轮廓的方法．应用数字图像测量和信息处理技术,将置于氮化硼水平平板 上的Ｌｉ２Ｂ４Ｏ７＋ＫＮｂＯ３液滴的轮廓图像记录在录像带上,然后转换成数字图像数据,并与理论 方程的数值解吻合,求得表面张力系数．用这种方法侧得的Ｌｉ２Ｂ４Ｏ７＋ＫＮｂＯ３溶液的表面张力 温度系数和表面张力溶质系数分别为 γΤ（ｍＮ／ｍ）＝２１０＋０．１５（Ｔ－９００℃）, ９００℃≤ Ｔ≤１０００℃; γｃ（ｍＮ／ｍ）＝２２９０．４５（ＣＫＮ－１０ｗｔ％）, １０ｗｔ％≤ ＣＫＮ ≤３０ｗｔ％     

Surface tension of mercury on glass,molybdenum and tungsten substrates

The surface tension of mercury on a glass substrate has been determined by the sessile drop technique. It was found that the uncorrected value of surface tension varied with changes in the drop diameter in the range from 0.60 to 4.10 cm. From the Worthington equation for curvature a corrected surface tension of 456 dyn/cm was obtained for the 4.1 cm diameter drop, a value which is in reasonable agreement with previous investigations. However, application of a curve fitting procedure to the results from the smaller drops gave a corrected surface tension which was approximately independent of diameter but at a smaller average value of 413 dyn/cm. The surface tension of a 1.20 cm diameter drop was also measured on tungsten and molybdenum substrates and, in general, corrected values larger than on glass were derived. It is suggested that the small corrected values obtained for drops ⩽2.06 cm in diameter are due to adsorption of impurity from the glass substrate.     

A novel methodology to study shape and surface tension of drops in Electric Fields

A novel methodology is introduced that can be used to study the behavior of conducting drops in electrostatic fields, when gravity effects are negligible. This methodology, called Axisymmetric Drop Shape Analysis — Electric Field (ADSA-EF), generates numerical drop profiles in the electrostatic field, for a given surface tension. Then, it calculates the true value of the surface tension by matching the theoretical profiles with the shape of the experimental drops, with the surface tension as an adjustable parameter. ADSA-EF can be employed for simulating drop shapes in the electric field, detecting the effect of an electric field on liquid surface tensions, and measuring surface tensions in microgravity, where current drop-shape techniques are not applicable. The predicted drop shapes in the electric field were compared with experimental images, indicating good agreement. Preliminary experiments according to ADSA-EF methodology suggested that the surface tension of water increases by about one percent in the electric field.     

Thermodynamic study on the melting of nanometer-sized gold particles on graphite substrate

Surface tension plays an important role in lowering the melting temperature of nanometer-sized particles, but whether the surface tension determined in macro scale is valid for the nanometer-sized particles is unclear. Moreover, the melting of the nanometer-sized particles formed on solid substrates can be affected by interfacial tension, but no research has been reported on the effect of substrates on the melting temperature. Therefore, in order to predict the melting temperature of nanometer-sized metallic particles on solid substrates, thermodynamic parameters such as surface tension and interfacial tension should be properly estimated. In the present work, thermodynamic assesment is given on the melting temperature of gold particles in nanometer-size placed on a graphite substrate. Surface tension of liquid gold and the contact angle between liquid gold and the graphite substrate are measured by the constrained drop method and the sessile drop method in macro scale, respectively. Then, the effect of the graphite substrate on the melting temperature of nanometer-sized gold particles are examined by thermodynamic calculations minimizing the total Gibbs free energy, the sum of bulk, surface and interface energies. It is found that the graphite substrate has negligible effect on the melting temperature of nanometer-sized gold particles. Thermodynamic assessments provide that the surface tension of solid gold is 1.339 N/m at 1373 K and that the decrease in the surface tension of liquid gold with size will be considerable for the particles smaller than ~5 nm.     

Evaluation on Dorsey Method in Surface Tension Measurement of Solder Liquids Containing Surfactants

With the purpose of developing a feasible approach for measuring the surface tension of solders containing surfactants, the surface tension of Sn–3Ag–0.5Cu–xP solder alloys, with various drop sizes as well as different phosphorus (P) content, was evaluated using the Dorsey method based on the sessile drop test. The results show that the accuracy of the surface tension calculations depends on both of sessile drop size and the liquid metal composition. With a proper drop size, in the range of 4.5 mm to 5.3 mm in equivalent spherical diameters, the deviation of the surface tension calculation can be limited to 1.43 mN·m^?1 and 6.30 mN·m^?1 for SnAgCu and SnAgCu–P, respectively. The surface tension of SnAgCu–xP solder alloys decreases quickly to a minimum value when the P content reaches 0.5 wt% and subsequently increases slowly with the P content further increasing. The formation of a P-enriched surface layer and Sn₄P₃ intermetallic phases is regarded to be responsible for the decreasing and subsequent increasing of surface tension, respectively.     

Passage of a liquid drop through a bifurcation

Numerical simulations of the motion of a viscous liquid drop through a two-dimensional bifurcating channel are conducted using a boundary-element method for Stokes flow. The drop viscosity is assumed to be equal to the ambient fluid viscosity and the drop interface is assumed to exhibit uniform surface tension. The mean fluid pressures are prescribed at the channel inlet and two outlets, and the corresponding flow rates are computed as part of the solution. Preliminary simulations show that the shape of a two-dimensional drop moving through a channel with parallel walls is similar to that of an axisymmetric drop moving along the centerline of a circular tube. The ability of a drop to remain intact as it passes through the bifurcation is determined by the drop size and capillary number expressing the significance of surface tension. For a given drop size and channel inlet and outlet pressures, there is a critical capillary number above which a drop splits into two pieces connected by a thinning bridge. The presence of the drop has a weak effect on the inlet and outlet flow rates throughout its passage. Simulations based on a boundary-element method for a rigid particle with circular or elliptical shape reveal a significantly stronger effect due to the absence of interfacial mobility.     

A new curvature technique calculation for surface tension contribution in PLIC-VOF method

The volume of fluid (VOF) methods have been used for numerous numerical simulations. Among these techniques used to define the moving interface, the piecewise linear interface reconstruction (PLIC-VOF) is one of the most accurate. A study of the superficial tension impact on two-phase flow with free surface is presented. A new method based on direct staggered grid is developped to include surface tension in PLIC-VOF. The new numerical curvature calculation method doesn't need smoothed colour function and leads to less “spurious current”. This technique is applied to the calculus of surface tension force in the case of the rise of air bubble in viscous liquid and the fall of liquid drop in the same liquid on free surface. Droplets, thin layer and capillarity waves are observed after the free surface rupture for different Bond number. The influence of surface tension calculus is then obvioused and when the drop hit the free surface, wavelets propagate toward the virtual boundaries imposed.     

The shape of a liquid surface in a uniformly rotating cylinder in the presence of surface tension

The free-surface shape of a liquid in a uniformly rotating cylinder in the presence of surface tension is determined before and after the onset of dewetting at the bottom of the cylinder. Two scenarios of liquid withdrawal from the bottom are considered, with and without deposition of thin film behind the liquid. The governing non-linear differential equations for the axisymmetric liquid shapes are solved numerically by an iterative procedure similar to that used to determine the equilibrium shape of a liquid drop deposited on a solid substrate. The numerical results presented are for cylinders with comparable radii to the capillary length of liquid in the gravitational or reduced gravitational fields. The capillary effects are particularly pronounced for hydrophobic surfaces, which oppose the rotation-induced lifting of the liquid and intensify dewetting at the bottom surface of the cylinder. The free-surface shape is then analyzed under zero gravity conditions. A closed-form solution is obtained in the rotation range before the onset of dewetting, while an iterative scheme is applied to determine the liquid shape after the onset of dewetting. A variety of shapes, corresponding to different contact angles and speeds of rotation, are calculated and discussed.     

微圆管内R1234ze(E)流动沸腾的环状流特性模拟研究

本文建立了制冷剂R1234ze(E)在微圆管内流动沸腾过程中的环状流模型,对传热和气液两相流动压降进行了模拟研究。综合考虑重力、表面张力及气液界面剪切力的影响,模拟分析了周向液膜不均匀分布特性及该特性对流动与换热的影响,经验证,计算结果与已有实验结果吻合较好。本文还研究了不同因素对环状流区域表面传热系数与压降的影响。模拟结果表明:在流动起始区域,截面液膜厚度的分布受重力作用影响,随着流动沸腾过程的进行,该影响作用开始减弱,且有重力作用时的环状流平均表面传热系数高于无重力作用时的环状流平均表面传热系数,随着重力加速度的增加,环状流的平均表面传热系数不断增大;随着质量流速的增大,表面传热系数与压降均随之增大;随着管径增大,表面传热系数与压降均随之减小。     

Dynamic surface tension and adhesion detection for the rapid analysis of surfactants in flowing aqueous liquids

A multidimensional dynamic surface tension detector (DSTD) for flowing liquid samples is reported. The DSTD is based on measuring the pressure with time of a repeating drop formed by the flow of liquid out the end of a pointed stainless steel capillary. This pressure-based DSTD provides information on dynamic surface tension at the air-liquid interface and adhesion at the solid-liquid interface on the side of the pointed capillary tip for each drop of surfactant solution, resulting in rapid characterization of complex samples. The signal obtained with the pressure-based DSTD is characterized, and a method is developed for extraction of the desired analytical information from the pressure signal. The DSTD was calibrated with 2-propanol over the range of 0-0.30 in relative surface tension lowering, Δγ/γ. The experimentally obtained Δγ/γ was in agreement with a theoretical model and published data for Δγ/γ over this range. A data analysis method was developed to adapt the DSTD to applications such as liquid chromatography and flow injection analysis, where the concentration of surfactant changes as a function of time. The DSTD signal yields a pressure-based Δγ/γ that is due to surface tension alone and a time-based Δγ/γ that is a combination of both surface tension and adhesion, providing essentially a contact angle measurement on a flowing sample. The data analysis method involves plotting the pressure-based and time-based surface tension measurements against each other at the same surfactant concentration for each pair of measurements, yet over a range of concentrations to establish a slope. This is referred to as a dynamic analysis plot and is applied in the characterization of various surfactants such as dodecyl sulfate ion-paired with tetrabutylammonium, industrial surfactant solutions FC-171 and FC-129, and biological surfactants tetradecyl maltoside, benzyldimethyldodecylammonium bromide, and 3-(N-decyl-N,N-dimethylammonio)-1-propanesulfonate. The slopes of the dynamic analysis plots for these surfactants were found to be unique, generally independent of concentration, and useful for understanding the type and degree of operating surface interactions. The FC-171 solution was found to exhibit considerable adhesion at the capillary tip, while dodecyl sulfate was found to have a small adhesion effect. Adhesion for dodecyl sulfate solutions was significantly enhanced by coating the stainless steel capillary tip with a hydrophobic polymer. Thus, there is potential for tuning the extent of the surface tension and adhesion effects for selective chemical analysis. The detection limit for dodecyl sulfate ion-paired with tetrabutylammonium is 0.9 ppm. Application of the DSTD for liquid chromatography is demonstrated, and the multidimensional data are shown to be useful in identifying and characterizing the poly(ethylene glycol)s separated from 2-propanol.