Simulations of gravity-induced trapping of a deformable drop in a three-dimensional constriction

An efficient algorithm is developed to determine the three-dimensional shape of a deformable drop trapped under gravity in a constriction, employing an artificial evolution to a steady state. During the simulation, the drop surface is advanced using a rationally-devised normal "velocity", based on local deviation from the Young-Laplace equation and the adjacent solid shape, to approach the trapped drop shape. The artificial "time-dependent" evolution of the drop to the static, trapped shape requires that the free portions of the drop interface eventually satisfy the Young-Laplace equation, and the drop-solid contact portions of the drop interface conform to the solid surface. The significant advantage of this solution method is that a simple, numerically-efficient "velocity" is used to construct the evolution to the steady state; the coated areas where the drop is in near contact with solid boundaries of the constriction do not have to be specified a priori, but are found in the course of the solution. Alternative methods (e.g., boundary integral) based on realistic time-marching would be much more costly for determining the trapped state. Trapping conditions and drop shapes are studied for gravity-induced settling of a deformable drop into a three-dimensional constriction. For conditions near critical, where the trapped-drop steady state ceases to exist, severe surface-mesh distortions are treated by a combination of 'passive mesh stabilization', mesh relaxation and topological mesh transformations through node reconnections. For Bond numbers above a critical value, the drop is deformable enough to pass through the hole of the constriction, with no trapping. Critical Bond numbers are determined by linearly fitting minima of the root-mean-squared (rms) surface velocities versus corresponding Bond numbers greater than critical, and then extrapolating the Bond number to where the minimum rms velocity is zero (i.e., the drop becomes trapped). For ring and hyperbolic-tube constrictions, with axes parallel to the gravity vector, the results for trapped drops and critical Bond numbers are in close agreement with those obtained by the previous, highly-accurate axisymmetric method [1]. Also, the three-dimensional Young-Laplace and boundary-integral methods show good agreement for the static shape of a drop trapped in a tilted three-sphere constriction. For all constriction types studied, including circular rings, hyperbolic tubes and agglomerates of three and four spheres, the critical Bond number increases nearly linearly with an increase in the drop-to-hole size ratio. In contrast, the constriction type and tilt angle, which is the angle between the gravity vector and the normal to the plane of the constriction hole, have generally a weaker effect on the critical Bond number.     

旋转滴方法研究界面扩张流变性质

采用旋转滴方法, 对2-丙基-4,5-二庚烷基苯磺酸钠(DHPBS)在癸烷-水界面上的扩张流变性质进行了研究, 较为详细地介绍了SVT20N视频旋转滴张力仪的装置和实验方法, 考察了油滴注入体积、基础转速及振荡振幅等实验条件对扩张模量的影响. 研究结果表明, 旋转滴方法是一种研究扩张流变性质的新型手段, 在涉及低界面张力现象的领域具有良好的应用前景.     

Dilational rheology of protein films adsorbed at fluid interfaces

This report aims at (i) presenting a quantitative interpretation of interfacial dilational moduli (|E|) for four proteins at three different interfaces and (ii) identifying the main parameters responsible. The proteins were adsorbed from aqueous solution against air, n-tetradecane and sunflower seed oil, as a function of protein concentration and adsorption time.Experimentally, a dynamic drop tensiometer is a convenient instrument to generate the required sinusoidal oscillations for compression/expansion of interfaces (Benjamins et al., 1996 [1]).Theoretically, a simple two-dimensional solution model with a constant molecular area of the protein described the data only at fairly low pressures. Much better agreement over the entire elastic range was found with a recent extension of the model. This extension accounted for adsorbed proteins adopting smaller molecular areas with increasing surface pressure.Three factors dominated the values of the dilational modulus: (i) rigidity of protein molecules, (ii) degree of interfacial non-ideality and (iii) tension of the clean interface (Benjamins et al., 2006 [2]). The last factor is clearly of great relevance to food emulsions.For each protein at different interfaces, the elasticity increased with the enthalpy parameter (Η^S) of the equation of state. Elasticity and Η^S both increased with the clean-interface tension, γ⁰, i.e., with decreasing polarity of the interface (Benjamins et al., 2006 [2]; Fainerman et al., 2003 [3]). The elasticity of the different proteins also increased with increasing rigidity of the molecules, indicating a lower compressibility of the molecular area at the interface.Pure viscosities were never observed in our experience. However, viscoelastic behaviour was found at high pressures, i.e., in densely packed surfaces. The measured viscous phase angles strongly decreased at still higher pressures, indicating that the active relaxation mechanism slowed down with increasing molecular packing density. Specific kinetic models are yet to be developed for such mechanisms.     

空气/水界面2,5-二丙基-4-十一烷基苯磺酸钠的表面动态扩张流变性质

利用悬挂滴方法研究了2,5-二丙基-4-十一烷基苯磺酸钠(3-11-3)在空气/水界面上的动态扩张粘弹性质, 考察了时间、表面压、工作频率及3-11-3的浓度对扩张模量和相角的影响. 研究结果表明, 低表面压条件下, 表面膜以弹性为主, 分子在表面上的状态决定膜性质；高表面压条件下, 分子在体相和表面间的交换过程决定膜性质, 表面膜以粘性为主.     

A Surface Rheological Study of Silwet L-77 Surfactant at the Air/Water Interface

The dilational viscoelastic properties of Silwet L-77, a trisiloxane surfactant of the general formula (Me₃SiO)₂SiMe(CH₂)₃(OCH₂CH₂)_7.5OH, at the air/water interface were investigated. Aqueous solutions of Silwet L-77 were spread onto a pendant drop and the dynamic surface tensions were measured by means of axisymmetric drop shape analysis. The surface dilatational elasticity, viscosity, and phase angle of the adsorption monolayer were also determined using the oscillating drop technique. The influences of frequency and concentration on the surface dilational properties were expounded. It is shown that the surface dilational modulus and elastic modulus increased with the increase of frequency, the viscous modulus was complex, while the phase angle decreased with the increase of frequency. Surface dilational modulus, elastic modulus, and viscous modulus passed through the maximum with the increase of bulk concentration and the phase angle increased with the increase of concentration.     

A Surface Rheological Study of Polyoxyethylene Alkyl Ether Carboxylic Salts and the Stability of Corresponding Foam

The dynamic dilational viscoelastic properties of polyoxyethylene alkyl ether carboxylic salts at the air-water interface were investigated by drop shape analysis method and their foam stability were measured by Bikerman Method. The influences of time, dilational frequency, and bulk concentration on surface dilational modulus and phase angle were expounded. The results show that the surfactant with the longest straight-chain shows the highest dilational modulus, which in agreement with the best foam stability. However, the foam stability of branched-alkyl chain surfactant cannot be explained in terms of film elasticity alone.     

Effect of Glyphosate Isopropylamine on the Surface Tension and Surface Dilational Rheology Properties of Polyoxyethylene Tallow Amine Surfactant

In order to develop the substitutes for polyoxyethylene tallow amine (POEA), the understanding the interaction of glyphosate isopropylamine and POEA is essential. The surface behaviors of POEA and POEA in the presence of 1 wt% glyphosate isopropylamine have been investigated at the air-water interface by the drop shape analysis method. The influences of surface tension, dilational frequency, and bulk concentration on the surface properties were expounded. The experiment results show that the adsorption films of POEA behave elastic in nature at low bulk concentration. With increasing in bulk concentration, the dilational modulus, dilational elasticity, and dilational viscosity pass through a maximum value, the phase angle increase monotonically. These phenomena can be attributed to the diffusion-exchange process between the bulk and the interface. The addition of 1 wt% glyphosate isopropylamine significantly influences on the POEA surface tension and dilational properties. The dilational modulus, dilational elasticity, and dilational viscosity obvious decrease in general, and the values of phase angle significant change after the addition of 1 wt% glyphosate isopropylamine. Glyphosate isopropylamine and POEA form a new complex in the solution and the surface activity and surface dilational properties of complex is different from POEA.     

疏水改性聚丙烯酰胺对原油组分界面扩张流变性质的影响

利用悬挂滴方法研究了疏水改性聚丙烯酰胺(HMPAM)对胜利采油厂高温高盐油藏采出原油中酸性活性组分和沥青质界面膜扩张流变性质的影响,考察了不同活性组分浓度条件下的界面扩张流变行为.实验结果表明:1750mg·L-1HMPAM能够在界面上形成网络结构,界面扩张模量数值高达100mN·m-1左右;油相中的酸性组分随着老化时间增加吸附到界面上,与HMPAM分子的疏水改性部分形成聚集结构,一方面通过快速的扩散交换过程大大降低扩张模量,另一方面通过与疏水改性部分的相互作用加强HMPAM分子间的缔合强度,增强网络结构的弹性.沥青质分子尺寸相对较大,分子间存在氢键等较强的相互作用,造成沥青质界面聚集体和HMPAM形成的网络结构共同决定界面膜性质,混合膜的扩张模量较单独HMPAM体系仅略有降低.     

Effect of pH on the adsorption kinetics of egg yolk at the triacylglycerol–water interface and viscoelastic properties of interfacial egg yolk films: a dynamic drop tensiometry study

Interfacial properties of normal egg yolk (EY), as well as stabilized, i.e. enzymatically modified with phospholipase A2, egg yolk (SEY) at the triacylglyceride (TAG) oil–water interface have been investigated with the use of the dynamic drop tensiometry (DDT) technique in the wide interval of pH values of aqueous EY solutions. We found that for both EY and SEY pH values of their aqueous solutions affect absolute values of interfacial tension at the TAG oil–water interface. In the presence of EY this effect was more pronounced, with minimum of interfacial tension values at pH nearly equal to the isoelectric point of EY proteins. For SEY solutions no clear trend was noticed, although a reduction of interfacial tension near pH 6 was also observed. Moreover, the pH-dependence of nearly steady values of interfacial tension in the presence of EY was substantially less pronounced than it has been reported previously. It was also found that there is a difference in the interfacial viscoelasticity of SEY and EY films formed at the TAG oil–water interface. Although the dependence of dilational modulus, ∣ε∣, versus surface pressure for SEY solutions goes through a maximum, absolute values of ∣ε∣ increase for EY solutions in a wide pH range. At the same time, no visible effect of pH on the viscoelasticity of EY and SEY interfacial films was noticed. It became clear from the dilational modulus versus surface pressure curves for both EY and SEY that adsorption of their surface-active components at the TAG oil–water interface occurs in a step-wise manner. We found also that the phase angle values for the adsorbed EY layers were lower that those observed in the presence of SEY, indicating an increasing viscous contribution to the dilational modulus in the SEY-containing system.     

不同结构芳香侧链酰基牛磺酸钠的表面扩张性质

利用悬挂滴方法研究了N-(α-苯氧基)十四酸牛磺酸钠(12+B-T)和N-(α-对乙基苯氧基)十四酸牛磺酸钠(12+2B-T)在空气/水表面上的动态扩张粘弹性质, 考察了时间、扩张频率及摩尔浓度对扩张模量和相角的影响, 测定了不同摩尔浓度条件下的泡沫性能. 研究发现: 低浓度条件下, 表面分子间相互作用决定表面活性剂吸附膜的性质, 膜以弹性为主; 高浓度条件下, 扩散交换过程起主导作用, 吸附膜表现出粘弹特性. 表面活性剂芳环支链上增加一个乙基, 分子间相互作用增强, 扩张模量增大, 泡沫更加稳定.     

Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

原油活性组分油水界面膜扩张粘弹性研究

研究了用超临界萃取分馏法（SFEF）从伊朗重质原油中分离的两个具有不同平均分子量的原油界面活性组分在正癸烷/水界面的扩张粘弹性行为以及温度对体系扩张粘弹性的影响.研究发现平均分子量大的样品能在油水界面形成更为牢固的界面膜.从扩张模量幅度对扩张频率的双对数曲线和扩张模量相角的频率依赖关系可以推断所有实验体系界面膜的主要的弛豫过程不是扩散弛豫,而可能主要是通过吸脱附势垒的弛豫过程.温度对两个样品的扩张粘弹性参数都有强烈的影响.升高温度可以降低膜的强度和粘度,并且改变相角的频率响应.     

界面张力弛豫法研究不同结构破乳剂油水界面扩张粘弹性

采用界面张力弛豫法研究了支链破乳剂AE121和直链破乳剂SP169在正癸烷-水界面上的扩张粘弹性质，并与小幅周期振荡法获得的结果进行了比较.阐述了两种破乳剂的扩张模量随扩张频率和破乳剂浓度的变化规律.研究发现，在低频率处，两种破乳剂的扩张模量均接近于零；在中间频率范围内，扩张模量随扩张频率的增加而增大；在高频率处，扩张模量的幅度接近于极限扩张弹性.在中间频率范围内，扩张模量随破乳剂浓度增大，在接近临界胶束浓度处出现一个极大值；同时还发现，界面上和界面附近的微观弛豫过程的数目随破乳剂浓度增加而增大，其贡献也呈规律性变化.     

不同结构破乳剂油水界面扩张粘弹性研究

研究了支链破乳剂AE121和直链破乳剂SP169在正癸烷-水界面上的扩张粘弹性质,阐述了两种破乳剂扩张模量随扩张频率和破乳剂浓度的变化规律,考察了两种破乳剂对原油活性组分界面扩张性质的影响,测定了两种破乳剂的水溶液与正癸烷的动态界面张力,并与界面扩张流变性质进行了关联.研究结果表明,两种破乳剂的加入均会大大降低原油活性组分界面膜的扩张模量.较低浓度下直链破乳剂SP169由于吸附能力稍强,降低扩张模量效果较好；而一定浓度以上支链破乳剂AE121由于顶替能力较强,具有一定优势.由于破乳剂本身具有一定的扩张模量,在降低界面扩张模量的效果上,破乳剂的用量并非越大越好.     

Determining the mechanical response of particle-laden fluid interfaces using surface pressure isotherms and bulk pressure measurements of droplets

The mechanical response of particle-laden fluid interfaces is determined by measuring the internal pressures of particle-coated drops as a function of the drop volume. The particle monolayers undergoing compression-expansion cycles exhibit three distinct states: fluid state, jammed state, and buckled state. The P-V curves are compared to the surface pressure isotherms Pi-A that are measured using a Langmuir trough and a Wilhelmy plate on a flat water-decane interface covered with the same particles. We find that in the fluid and jammed states, the water drop in decane can be described by the Young-Laplace equation. Therefore in these relatively low compression states, the bulk pressure measurements can be used to deduce the interfacial tension of the droplets and yield similar surface pressure isotherms to the ones measured with the Wilhelmy plate. In the buckled state, the internal pressure of the drop yields a zero value, which is consistent with the zero interfacial tension measured with the Wilhelmy plate. Moreover we find that the compressibility in the jammed state does not depend on the particle size.     

Viscoelastic Properties of Crude Oil Components at Oil‐Water Interfaces. 2: Comparison of 30 Oils

The dilational properties of diluted (0.7 vol/vol in toluene) and undiluted crude oil‐water interfaces have been studied using the oscillation drop method with the objective of understanding the properties contributing to the overall stability of crude oil emulsions. The importance of working with undiluted crude oils instead of model systems when dilational properties of real oil‐water systems are going to be reproduced in the laboratory setting has been discussed. For such studies, molecular exchange mechanisms and the aggregation state of asphaltenes are too dependent on concentration to justify the use of model compounds, i.e. fractionated asphaltenes diluted in a solvent. As expected in the low frequency range (0.01–1 Hz), molecular exchange from the bulk oil phase strongly affected the measured dilational parameters. For the diluted crude oils, the frequency dependence of the dilational modulus increased with its magnitude. The systems that exhibited particularly low magnitude of the dilational modulus were of the heaviest crude oils in the sample set, whereas the systems with greatest dilational modulus were among the lightest crude oils. The overall characteristic time of relaxation of the crude oil‐water interfaces was in the range below 10 seconds. The undiluted crude oil‐water interfaces had similar interfacial properties as the diluted samples except for slightly reduced magnitude of the dilational modulus. The crude oil‐water interfaces appeared to be soluble, but some observations pointed to intrinsic rheological properties of the interfaces. Intrinsic elasticity and viscosity of the films should be studied outside the frequency range used here at low (ω～0 Hz) and high (ω→500 Hz), respectively.     

Effect of Molecular Weight on the Interfacial Dilational Viscoelasticity of Anionic Polyelectrolyte/Surfactant Systems

In this article, the effect of molecular weight on the interfacial tension and interfacial dilational viscoelasticity of polystyrene sulfonate/surfactant adsorption films at the water-octane interface have been studied by spinning drop method and oscillating barriers method respectively. The experimental results show that different interfacial behaviors can be observed in different type of polyelectrolyte/surfactant systems. PSS/cationic surfactant CTAB systems show the classical behavior of oppositely charged polyelectrolyte/surfactant systems and can be well explained by electrostatic interaction. Molecular weight of PSS plays a crucial role in the nature of adsorption film. The complex formed by CTAB and higher molecular weight PSS, which has larger dimension and stronger interaction, results in higher dilational modulus at lower surfactant bulk concentration. In the case of PSS/anionic surfactant SDS systems, the co-adsorption of PSS at interface through hydrophobic interaction with alkyl chain of SDS leads to the increase of interfacial tension and the decrease of dilational modulus at lower surfactant bulk concentration. For PSS/nonionic surfactant T × 100 systems, PSS may form a sublayer contiguous to the aqueous phase, which has little effect on interfacial tension but slightly decreases dilational modulus.     

Communication: Identical temperature dependence of the time scales of several linear-response functions of two glass-forming liquids

The frequency-dependent dielectric constant, shear and adiabatic bulk moduli, longitudinal thermal expansion coefficient, and longitudinal specific heat have been measured for two van der Waals glass-forming liquids, tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl-4-ether. Within the experimental uncertainties the loss-peak frequencies of the measured response functions have identical temperature dependence over a range of temperatures, for which the Maxwell relaxation time varies more than nine orders of magnitude. The time scales are ordered from fastest to slowest as follows: Shear modulus, adiabatic bulk modulus, dielectric constant, longitudinal thermal expansion coefficient, and longitudinal specific heat. The ordering is discussed in light of the recent conjecture that van der Waals liquids are strongly correlating, i.e., approximate single-parameter liquids.