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.     

A study on interfacial tension between flexible polymer and liquid crystal

The interfacial property in polymer-liquid crystal systems is quite different from flexible polymer-polymer mixtures due to the anisotropic properties of liquid crystals. The apparent interfacial tension between a liquid crystal and a flexible polymer was measured by deformed droplet retraction method. The deformation and recovery of a single liquid crystal droplet dispersed in a poly(dimethylsiloxane) matrix were realized by a transient shear flow and observed by polarized optical microscope. The apparent interfacial tension of polymer-liquid crystal system was found to be greatly dependent on the temperature, initial droplet deformation and liquid crystal droplet size.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

小角躺滴法测定低界面张力

在测定界面张力,特别是测定低界面张力的各种方法中,躺滴法占有相当重要的位置。但一般的躺滴法都要求获得赤道半径(图1中的x_e)数据.故躺滴与基底之间的接触角必须大于90°.这在低界面张力体系中常常难以实现,致使躺滴法的应用受到限制。本文提出一种新的躺滴法,它不依赖于接触角的大小,只需测定躺滴轮廓线上两个相关点的坐标,根据所给数值表即可计算出界面张力,从而为躺滴法应用于低界面张力,特别是     

Contact line dynamics in drop coalescence and spreading

The dynamics of coalescence of two water sessile drops is investigated and compared with the spreading dynamics of a single drop in partially wetting regime. The composite drop formed due to coalescence relaxes exponentially toward equilibrium with a typical relaxation time that decreases with contact angle. The relaxation time can reach a few tenths of seconds and depends also on the drop size, initial conditions, and surface properties (contact angle, roughness). The relaxation dynamics is larger by 5 to 6 orders of magnitude than the bulk hydrodynamics predicts, due to the high dissipation in the contact line vicinity. The coalescence is initiated at a contact of the drops growing in a condensation chamber or by depositing a small drop at the top of neighboring drops with a syringe, a method also used for the studies of the spreading. The dynamics is systematically faster by an order of magnitude when comparing the syringe deposition with condensation. We explain this faster dynamics by the influence of the unavoidable drop oscillations observed with fast camera filming. Right after the syringe deposition, the drop is vigorously excited by deformation modes, favoring the contact line motion. This excitation is also observed in spreading experiments while it is absent during the condensation-induced coalescence.     

Spreading of a fluid phase on a spherical surface

The adsorption between a liquid drop and a micro-particle in an air or an air bubble and a micro-particle in water is dominated by liquid-solid or air-solid interfacial tension and wetting area of the liquid or air on the particle surface. The wetting area is determined by the spreading of the liquid drop or the bubble on the micro-particle. To explore this spreading, a wetting model of a fluid phase on a spherical particle was built. According to the theoretical results, the contact angle is constant when a fluid phase spreads on a spherical solid surface; the micro-particle can not submerge under a fluid when only interfacial tensions are involved and the wetting is not a complete wetting. The corresponding experiments were performed to confirm the theoretical results.     

生物基表面活性剂七叶皂素的界面行为

以天然三萜皂苷七叶皂素为研究对象, 分别采用吊片法、 悬滴法和高速摄像机动态拍摄法探究了七叶皂素分子在气-液、 液-液、 固-液界面的界面行为. 考察了以七叶皂素为乳化剂制备乳液的性质, 以及七叶皂素对液滴在疏水固体表面润湿铺展行为的调控规律, 并从分子层次角度分析了作用机理. 结果表明, 七叶皂素能在气-液界面发生吸附, 将水的表面张力降低至42.1 mN/m, 临界胶束浓度为5×10^?4 mol/L. 七叶皂素还可以在油-水界面吸附, 将亲油端插入油相, 亲水端插入水相, 形成稳定的界面膜, 降低界面张力. 以七叶皂素为乳化剂所制备的乳液, 随着浓度增大可以达到较小的粒径和较大的Zeta电势, 短时间内表现出较好的稳定性. 高浓度的七叶皂素可以很好地抑制液滴在疏水固体表面的弹跳和回缩, 达到很好的铺展效果, 有利于拓展其在诸多领域的应用.     

Wetting and spreading of nanofluids on solid surfaces driven by the structural disjoining pressure: statics analysis and experiments

The wetting and spreading of nanofluids composed of liquid suspensions of nanoparticles have significant technological applications. Recent studies have revealed that, compared to the spreading of base liquids without nanoparticles, the spreading of wetting nanofluids on solid surfaces is enhanced by the structural disjoining pressure. Here, we present our experimental observations and the results of the statics analysis based on the augmented Laplace equation (which takes into account the contribution of the structural disjoining pressure) on the effects of the nanoparticle concentration, nanoparticle size, contact angle, and drop size (i.e., the capillary and hydrostatic pressure); we examined the effects on the displacement of the drop-meniscus profile and spontaneous spreading of a nanofluid as a film on a solid surface. Our analyses indicate that a suitable combination of the nanoparticle concentration, nanoparticle size, contact angle, and capillary pressure can result not only in the displacement of the three-phase contact line but also in the spontaneous spreading of the nanofluid as a film on a solid surface. We show here, for the first time, that the complete wetting and spontaneous spreading of the nanofluid as a film driven by the structural disjoining pressure gradient (arising due to the nanoparticle ordering in the confined wedge film) is possible by decreasing the nanoparticle size and the interfacial tension, even at a nonzero equilibrium contact angle. Experiments were conducted on the spreading of a nanofluid composed of 5, 10, 12.5, and 20 vol % silica suspensions of 20 nm (geometric diameter) particles. A drop of canola oil was placed underneath the glass surface surrounded by the nanofluid, and the spreading of the nanofluid was monitored using an advanced optical technique. The effect of an electrolyte, such as sodium chloride, on the nanofluid spreading phenomena was also explored. On the basis of the experimental results, we can conclude that a nanofluid with an effective particle size (including the electrical double layer) of about 40 nm, a low equilibrium contact angle (<3°), and a high effective volume concentration (>30 vol %) is desirable for the dynamic spreading of a nanofluid system with an interfacial tension of 0.5 mN/m. Our experimental observations also validate the major predications of our theoretical analysis.     

Measurement of the kinetic rate constants for the adsorption of superspreading trisiloxanes to an air/aqueous interface and the relevance of these measurements to the mechanism of superspreading

Super-spreading trisiloxane surfactants are a class of amphiphiles which consist of nonpolar trisiloxane headgroups ((CH3)3-Si-O)2-Si(CH3)(CH2)3-) and polar parts composed of between four and eight ethylene oxides (ethoxylates, -OCH2CH2-). Millimeter-sized aqueous drops of trisiloxane solutions at concentrations well above the critical aggregate concentration spread rapidly on very hydrophobic surfaces, completely wetting out at equilibrium. The wetting out can be understood as a consequence of the ability of the trisiloxanes at the advancing perimeter of the drop to adsorb at the air/aqueous and aqueous/hydrophobic solid interfaces and to reduce considerably the tensions of these interfaces, creating a positive spreading coefficient. The rapid spreading can be due to maintaining a positive spreading coefficient at the perimeter as the drop spreads. However, the air/aqueous and solid/aqueous interfaces at the perimeter are depleted of surfactant by interfacial expansion as the drop spreads. The spreading coefficient can remain positive if the rate of surfactant adsorption onto the solid and fluid surfaces from the spreading aqueous film at the perimeter exceeds the diluting effect due to the area expansion. This task is made more difficult by the fact that the reservoir of surfactant in the film is continually depleted by adsorption to the expanding interfaces. If the adsorption cannot keep pace with the area expansion at the perimeter, and the surface concentrations become reduced at the contact line, a negative spreading coefficient which retards the drop movement can develop. In this case, however, a Marangoni mechanism can account for the rapid spreading if the surface concentrations at the drop apex are assumed to remain high compared to the perimeter so that the drop is pulled out by the higher tension at the perimeter than at the apex. To maintain a high apex concentration, surfactant adsorption must exceed the rate of interfacial dilation at the apex due to the outward flow. This is conceivable because, unlike that at the contact line, the surfactant reservoir in the liquid at the drop center is not continually depleted by adsorption onto an expanding solid surface. In an effort to understand the rapid spreading, we measure the kinetic rate constants for adsorption of unaggregated trisiloxane surfactant from the sublayer to the air/aqueous surface. The kinetic rate of adsorption, computed assuming the bulk concentration of monomer to be uniform and undepleted, represents the fastest that surfactant monomer can adsorb onto the air/aqueous surface in the absence of direct adsorption of aggregates. The kinetic constants are obtained by measuring the dynamic tension relaxation as trisiloxanes adsorb onto a clean pendant bubble interface. We find that the rate of kinetic adsorption is only of the same order as the area expansion rates observed in superspreading, and therefore the unaggregated flux cannot maintain very high surface concentrations at the air/aqueous interface, either at the apex or at the perimeter. Hence in order to maintain either a positive spreading coefficient or a Marangoni gradient, the surfactant adsorptive flux needs to be augmented, and the direct adsorption of aggregates (which in the case of the trisiloxanes are bilayers and vesicles) is suggested as one possibility.     

A Growing Drop Technique for Measuring Dynamic Interfacial Tension

A novel, growing drop technique is described for measuring dynamic interfacial tension due to sorption of surface-active solutes. The proposed method relates the instantaneous pressure and size of expanding liquid drops to the interfacial tension and is useful for measuring both liquid/gas and liquid/liquid tensions over a wide range of time scales, currently from 10 ms to several hours. Growing drop measurements on surfactant-free water/ air and water/octanol interfaces yield constant tensions equal to their known literature values. For surfactant-laden, liquid drops, the growing drop technique captures the actual transient tension evolution of a single interface, rather than interval times as with the classic maximum-drop-pressure and drop-volume tension measurements. Dynamic tensions measured for 0.25 mM aqueous 1-decanol solution/air and 0.02 kg/m³ aqueous Triton X-100 solution/dodecane interfaces show nonmonotonic behavior, indicating slow surfactant transport relative to the imposed rates of interfacial dilatation. The dynamic tension of a purified and fresh 6 mM aqueous sodium dodecyl sulfate (SDS) solution/air interface shows only a monotonic decrease, indicating rapid surfactant transport relative to the imposed rates of dilatation. Conversely, an aged SDS solution, naturally containing trace dodecanol impurities, exhibits dynamic tensions which reflect a superposition of the rapidly equilibrating SDS and the slowly adsorbing dodecanol.     

The relative role of coalescence and interfacial tension in controlling dispersed phase size reduction during the compatibilization of polyethylene terephthalate/polypropylene blends

The breaking thread and the sessile drop methods have been used to evaluate the interfacial tension between a polypropylene (PP) and a polyethylene-terephthalate (PET). An excellent correlation was found between the two. The breaking thread technique was then used to evaluate the interfacial tension of these blends at various levels of a styrene-ethylene butylene-styrene grafted with maleic anhydride (SEBS-g-MA) compatibilizer. In order to evaluate the relative roles of coalescence and interfacial tension in controlling dispersed phase size reduction during compatibilization, the morphology of PP/PET 1/99 and 10/90 blends compatibilized by a SEBS-g-MA were studied and compared. The samples were prepared in a Brabender mixer. For the 10/90 blend, the addition of the compatibilizer leads to a typical emulsification curve, and a decrease in dispersed phase size of 3.4 times is observed. For the 1/99 blend, a 1.7 times reduction in particle size is observed. In the latter case, this decrease can only be attributed to the decrease of the interfacial tension. It is evident from these results that the drop in particle size for the 10/90 PP/PET blend after compatibilization is almost equally due to diminished coalescence and interfacial tension reduction. These results were corroborated with the interfacial tension data in the presence of the copolymer. A direct relationship between the drop in dispersed phase size for the 1/99 PP/PET blend and the interfacial tension reduction was found for this predominantly shear mixing device. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2271–2280, 1997     

The role of a compatibilizer to saturate interfacial tension and to emulsify a polymer blend

A linear drop of the interfacial tension between polyamide 6 (PA6) and poly(propylene) (PP) upon increasing concentration of the reactive compatibilizer and a leveling-off at higher compatibilizer contents were found in this study. The reduction of the interfacial tension is compared with the reduction of the dispersed phase size of the corresponding blends. As a result, the domain size is not directly proportional to the interfacial tension under the condition that other factors are equal.     

用耗散粒子动力学方法研究高分子链取向对形变液滴回缩法测定界面张力值的影响

在利用形变液滴回缩法(DDRM)测量了分子共混体系界面张力的过程中, 要求椭球液滴内高分子链应力松弛速度远快于椭球的回缩速度. 我们建立高分子链取向模型, 用耗散粒子动力学研究高分子链的取向及应力松弛对界面张力测量值的影响. 结果表明, 当高分子链沿着流场方向取向时, 应力是否完全松弛对界面张力测量值的影响较大, 当高分子链取向方向垂直于流场方向时, 应力是否松弛对测量值影响较小.     

The influence of electric field-induced orientation on the retraction of a liquid crystal droplet immersed in a flexible polymer matrix

We measured the apparent interfacial tension between a liquid crystal and a flexible polymer by deformed droplet retraction method. An external electric field is applied to change the director orientation in liquid crystal droplet. The deformation and recovery of a single liquid crystal droplet dispersed in a polydimethylsiloxane (PDMS) matrix were realized by a transient shear flow and observed by polarized optical microscope. In order to control the director orientation in LC droplet, the electric field is applied perpendicular and parallel to the flow field, respectively. The different orientation induced by electric field in liquid crystal droplet has different behavior during droplet retraction and affect the apparent interfacial tension between liquid crystal and flexible polymer.     

Surface tension of some liquid crystals in the cyanobiphenyl series

The temperature dependence of the surface tension was measured by the pendant drop method for four compounds from the homologous series of alkylcyanobiphenyls (nCB), in the nematic liquid crystal and isotropic phases. For 8CB (octylcyanobiphenyl) the temperature dependence was also measured in the smectic range. Not very close to the isotropic transition temperature, and with the exception of 8CB, the surface tension decreases with increase in temperature in the nematic range. A downward jump at the transition temperature was observed for all liquid crystals studied. The shape of the drop in the smectic A phase of 8CB gives indications of stratification in a system of terraces.     

Interfacial tension and spreading coefficient for thin films

We present a modified mathematical expression for the interfacial tension of very thin films. At large thicknesses the modified expression converges to the classic mathematical expression. We use this modified expression to derive an equation for the spreading coefficient as a function of film thickness. The spreading coefficient equation is then used to calculate the equilibrium thickness of a wetting liquid film for a "pancake drop". Our predictions agree with experimental data. The study is subjected to systems with van der Waals interactions only.     

Microfluidic approach for rapid interfacial tension measurement

A novel microfluidic approach to measure interfacial tension of immiscible fluids rapidly is reported. This method rests upon quantitative force balance analysis of drop formation dynamics in a coaxial microfluidic device. The values of interfacial tension for several two liquids without/with surfactants are measured. These measurements compare well with those measured by the commercial interfacial tensiometry. The viscosity of water phase fluid can also be accurately measured in the same microfluidic device. Several model systems with interfacial tension from 1.0 to 10.0 mN/m and water phase viscosity from 1.0 to 10.0 mPa.s are tested in this work.     

Interfacial tension measurements at the interface between two highly immiscible electrolyte solutions: the trapped air bubble method

A dynamic method for the measurement of interfacial tension at a liquid–liquid interface under controlled interfacial potential difference is described. The interface was formed as a drop suspended at the tip of a liquid filled glass micro-syringe into which a trapped air bubble of known volume had been introduced. Changes in volume of the air bubble allow changes in the surface tension to be calculated. Application to measurement of the variation in interfacial tension with cyclic variation in interfacial potential difference (‘cyclic volttensiometry’) is demonstrated.     

Surface tension of some liquid crystals in the cyanobiphenyl series

The temperature dependence of the surface tension was measured by the pendant drop method for four compounds from the homologous series of alkylcyanobiphenyls (nCB), in the nematic liquid crystal and isotropic phases. For 8CB (octylcyanobiphenyl) the temperature dependence was also measured in the smectic range. Not very close to the isotropic transition temperature, and with the exception of 8CB, the surface tension decreases with increase in temperature in the nematic range. A downward jump at the transition temperature was observed for all liquid crystals studied. The shape of the drop in the smectic A phase of 8CB gives indications of stratification in a system of terraces.     

Microdrops on atomic force microscope cantilevers: evaporation of water and spring constant calibration

The evaporation of water drops with radii approximately 20 microm was investigated experimentally by depositing them onto atomic force microscope (AFM) cantilevers and measuring the deflection versus time. Because of the surface tension of the liquid, the Laplace pressure inside the drop, and the change of interfacial stress at the solid-liquid interface, the cantilever is deflected by typically a few hundred nanometers. The experimental results are in accordance with an analytic theory developed. The evaporation process could be monitored with high accuracy even at the last stage of evaporation because (1) cantilever deflections can be measured with nanometer resolution and (2) the time resolution, given by the inverse of the resonance frequency of the cantilever of approximately 0.3 ms, is much faster than the typical evaporation time of 1 s. Experimental results indicate that evaporation of the last thin layer of water is significantly slower than the rest of the drop, which can be due to surface forces. This drop-on-cantilever system can also be used to analyze the drop impact dynamics on a surface and to determine the spring constant of cantilevers.