Effect of interfacial tension on linear viscoelastic behavior of immiscible polymer blends

When interfacial tension is increased from zero to infinity, the storage dynamic modulus predicted by Palierne's model varies in a nearly Gaussian fashion with almost equal asymptotic values at the limits of low and high interfacial tension. We report a simple physical discussion of such an effect. Received: 13 January 1999 Accepted: 22 March 1999     

钢纤维增强砂浆的轴拉损伤力学模型

基于Li Fa Ming的平行棒模型,对短钢纤维增强砂浆的平板试件,在直接拉伸条件下的破坏行为进行了分析,假设试件由N根相互平行的复合棒组成,每根复合棒又由一根纤维棒和S根砂浆棒组成,考虑纤维在基体中分布的方向因子和长度因子.砂浆的损伤可按连续损伤力学进行处理,将Loland模型和Mazars模型加以改进来描述.依据多根纤维的拉拨模型,假定纤维与基体间界面的损伤由纤维脱粘长度与纤维插入长度的比值来描述,复合材料的损伤包括基体的损伤和纤维的损伤,借助已有的试验数据和文献资料来确定本构模型中的各种参数,成功建立了短钢纤维增强砂浆直接拉伸应力一应变全曲线模型.所建模型与试件在直接拉伸试验下的应力-应变全曲线进行了对比,结果较为吻合.     

Elastic recovery of immiscible blends 1. Analysis after steady state shear flow

Due to the interfacial tension, immiscible blends can show an elastic recovery that is substantially larger than that of their pure components. Here it is attempted to relate the elastic recovery after steady shear flow to the underlying morphology. On the one hand, the predictions of the Palierne and the Doi-Ohta models are calculated for the flow conditions during recoil. On the other hand, systematic recoil experiments after steady state shearing have been performed on a model blend. As the component polymers hardly show any recoil under the stresses applied in these tests, the measured recovery can be attributed completely to the action of the interface. Comparison of the model predictions with the experimental results shows that the recoverable strain can be derived quantitatively from the linear Palierne theory. Although the droplet deformation remained limited during the preshear, the retardation time predicted by this model has to be multiplied by the aspect ratio of the droplet phase to the power 2/3 to describe the experiments. For conditions in which the material does not show an intrinsic length scale, particular scaling relations as derived from the Doi-Ohta theory are found to apply also to recoil. Received: 5 August 1998 Accepted: 17 November 1998     

The modified imbedded disc retraction method for measurement of interfacial tension in polymer melts

The imbedded disc retraction method is used to estimate interfacial tension in LLDPE/PS system with PS as the imbedded disc. Shape evolution of a disc of one material (PS) imbedded into the matrix of another material is observed (LLDPE). Three to five repetitions at three different temperature levels are observed. The Newtonian model of Rundqvist et al. (1996) for the imbedded disc retraction is modified to include elastic effects. The modified model is derived assuming uniaxial extension, starting with the lower convected Maxwell model. Both the original model and modified imbedded disc retraction model are used in data analysis. The mean values of interfacial tension at 190 °C, 200 °C, and 210 °C are 6.8 ± 0.7 mN/m, 3.9 ± 0.3 mN/m, and 3.7 ± 0.2 mN/m, respectively. A method of estimating whether elastic effects will significantly affect the estimated interfacial tension value during retraction for the given polymer pair is provided. Received: 6 August 1999 Accepted: 2 January 2001     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Interfacial tension reduction in PBT/PE/clay nanocomposite

We investigated the effect of organically modified nanoclay (organoclay) on immiscible polymer blends [polybutylene terephthalate (PBT)/polyethylene (PE)] with a special focus on the role of clay as a compatibilizer. When organoclay (Nanofil 919; Sud-Chemie, Inc.) is added to the blend, the clay first locates at the interface and then selectively locates in the PBT phase due to its affinity with PBT. This results in effective size reduction and narrowed size distribution of the dispersed phase. However, with a small amount of organoclay, it is observed that the clay locates at the interface regardless of its affinity for a specific component to minimize the chemical potential. The interfacial tension change of the blend with the addition of organoclay was quantitatively predicted from extensional force measurement. When the blend is subjected to an extension, the interfacial tension functions as a resistance against drop deformation. When we added organoclay to the blend, the extensional force was significantly reduced, which means that the contribution of the interfacial tension to the total force is reduced. For a 10/90 PBT/PE blend, the interfacial tension was reduced from 5.76 to 0.14 cN m⁻¹ when 1 wt% of organoclay was added. This interfacial tension reduction arises from the localization of the organoclay at the interface and its nonhomogeneous distribution along the interface, suppressing the coalescence between the droplets, which is a role of a compatibilizer. Conclusively, the immiscible polymer blends can be compatibilized with organoclay. The organoclay changes the blend morphology by interfacial tension reduction due to the localization of the organoclay at the interface and by the viscosity ratio change due to the selective localization by its affinity to a specific component in the blend.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

Determination of interfacial tension by the retraction method of highly deformed drop

The traditional retraction of the deformed drop method (DDRM) to determine the interfacial tension is reformulated to relax the limit the small deformation assumption. The kernel of the new formalism is the calculation of the velocity gradient on the vertex of the ellipsoidal drop. Two models were used for such calculations: the Jackson and Tucker model [J Rheol 47:659–682] and the Yu and Bousmina model [J Rheol 47:1011–1039]. The method can be used either in the retraction of shear deformed drop, or in the retraction of elongated drops produced by the breakup of a long thread. Comparison with experimental results of the literature showed that conversely to the classical DDRM, good accuracy is obtained when the new modeling for the determination of interfacial tension is used both under small and large deformations.     

Stress dependence of cross slip energy barrier for face-centered cubic nickel

The energy barrier for the cross slip of screw dislocations in face-centered cubic (FCC) nickel as a function of multiple stress components is predicted by both continuum line tension and discrete atomistic models. Contrary to Escaig's claim that the Schmid stress component has a negligible effect on the energy barrier, we find that the line tension model, when solved numerically, predicts comparable effects from the Schmid stress and the Escaig stress on the cross slip plane. When the line tension model is compared against an atomistic model for FCC nickel, a good agreement is found for the effect of the Escaig stress on the glide plane. However, the atomistic model predicts a stronger effect than the line tension model for the two stress components on the cross slip plane. This discrepancy is larger at higher stresses and is also more severe for the Escaig stress component than for the Schmid stress component.     

The imbedded disk retraction method for measurement of interfacial tension between polymer melts

A method for measuring interfacial tension of high viscosity polymer melts at elevated temperatures is described. The method involves the tracking of the shape evolution of a disk of one material imbedded in a second one. This makes it possible to determine the interfacial tension over a relatively short time period. The technique of preparing the samples makes it possible to measure on practically any combination of polymer melts without restrictions on viscosities and melting temperature, as long as one of the materials is transparent in the molten state.The retraction of the disk is observed by using a microscope with a high resolution video camera. The camera is connected to a video frame grabber in a personal computer which is programmed to collect images with preselected time intervals. Data of the retraction is acquired by using an image analysis software, measuring the average radius of the disk.The driving force for the shape evolution is interfacial tension and it is balanced by viscous forces. The analysis of the retraction process is done analytically with a simplified one-dimensional model. The model has been compared to experiments with the system PS/PMMA at 210 °C, covering viscosity ratios over a range of six decades and five different molecular weight values of PS. It is shown that interfacial tension can be determined over the whole range and a value of 1.1±0.2 mN/m was obtained for all samples.     

Understanding droplet coalescence and its use to estimate interfacial tension

The study of coalescence of polymer droplets is presented in the viscosity ratio range (p) going from 0.1 to 10. It is shown that the determination of the characteristic time of coalescence is a good way to estimate the interfacial tension. Polydimethylsiloxane (PDMS) is mixed with polyisobutylene (PIB) and the temperature change provides a way to modify the interfacial tension of the PDMS/PIB system significantly, as measured using a pendant drop apparatus. We obtain a dependence of the reduced coalescence time as a function of p^-1/2 which gives access to the interfacial tension. This technique can be an interesting choice for estimating interfacial tension without requiring sophisticated techniques. In a further attempt to correlate these observations with a theoretical model (Verdier C (2001) Polymer 42), the flow field inside and outside the droplets is investigated. PIV measurements are carried out where the evidence of elongational regimes is demonstrated. Such experiments are also interesting for future comparisons with numerical results.     

Droplet retraction in the presence of nanoparticles with different surface modifications

We studied the influence of nanoparticles with different surface modifications on the interfacial tension and relaxation of model polymer blend after cessation of different strains. The droplet retraction experiments were carried out on a model system composed of polydimethylsiloxane (PDMS) as the suspending fluid and polyisobutylene (PIB) as droplet at room temperature in the presence of hydrophobic and hydrophilic nanosilica. Different weight fractions of particles were dispersed in the PIB droplet before forming a dispersed droplet by using a microsyringe in shear cell. We found that applied strain, nanoparticle concentration and their thermodynamically preferred localization affect both nominal interfacial tension and droplet retraction process. By addition of nanoparticles at a concentration as low as 0.2%wt, the nominal interfacial tension decreases from 3.12?±?0.15 mN/m for neat PIB-PDMS interface depending on the surface characteristics of nanosilica. Hydrophilic nanosilica has the most effect on nominal interfacial tension and decreases it as low as 0.2?±?0.21 mN/m at 1 wt.% loading under a strain of 7. The results show that the retraction process in this system is mainly controlled by interfacial phenomena rather than bulk rheological properties. Additionally, the shape evolution of droplets changes and the retraction rate slows down in the presence of nanoparticles.     

Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability

Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor (RT) instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao’s result if we only consider the viscous effect and with Xia’s result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White’s experimental data.     

Multiphase flow with a simplified model for oil entrapment

A computationally simple procedure is described to model effects of oil entrapment on three-phase permeability-saturation-capillary pressure relations. The model requires knowledge of airwater saturation-capillary pressure relations, which are assumed to be nonhysteretic and are characterized by Van Genuchten's parametric model; scaling factors equal to the ratio of water surface tension to oil surface tension and to oil-water interfacial tension; and the maximum oil (also referred to as nonwetting liquid in a three-phase medium) saturation which would occur following water flooding of oil saturated soil. Trapped nonwetting liquid saturation is predicted as a function of present oil-water and air-oil capillary pressures and minimum historical water saturation since the occurrence of oil at a given location using an empirically-based algorithm. Oil relative permeability is predicted as a simple function of apparent water saturation (sum of actual water saturation and trapped oil saturation) and free oil saturation (difference between total oil and trapped oil saturation), and water relative permeability is treated as a unique function of actual water saturation. The proposed method was implemented in a two-dimensional finite-element simulator for three-phase flow and component transport, MOFAT. The fluid entrapment model requires minimal additional computational effort and computer storage and is numerically robust. The applicability of the model is illustrated by a number of hypothetical one- and two-dimensional simulations involving infiltration and redistribution with changes in water-table elevations. Results of the simulations indicate that the fraction of a hydrocarbon spill that becomes trapped under given boundary conditions increases as a nonlinear function of the maximum trapped nonwetting liquid saturation. Dense organic liquid plumes may exhibit more pronounced effects of entrapment due to the more dynamic nature of flow, even under static water table conditions. Disregarding nonwetting fluid entrapment may lead to significant errors in predictions of immiscible plume migration.     

1D Simulations for Microbial Enhanced Oil Recovery with Metabolite Partitioning

We have developed a mathematical model describing the process of microbial enhanced oil recovery (MEOR). The one-dimensional isothermal model comprises displacement of oil by water containing bacteria and substrate for their feeding. The bacterial products are both bacteria and metabolites. In the context of MEOR modeling, a novel approach is partitioning of metabolites between the oil and the water phases. The partitioning is determined by a distribution coefficient. The transfer part of the metabolite to oil phase is equivalent to its ”disappearance,” so that the total effect from of metabolite in the water phase is reduced. The metabolite produced is surfactant reducing oil–water interfacial tension, which results in oil mobilization. The reduction of interfacial tension is implemented through relative permeability curve modifications primarily by lowering residual oil saturation. The characteristics for the water phase saturation profiles and the oil recovery curves are elucidated. However, the effect from the surfactant is not necessarily restricted to influence only interfacial tension, but it can also be an approach for changing, e.g., wettability. The distribution coefficient determines the time lag, until residual oil mobilization is initialized. It has also been found that the final recovery depends on the distance from the inlet before the surfactant effect takes place. The surfactant effect position is sensitive to changes in maximum growth rate, and injection concentrations of bacteria and substrate, thus determining the final recovery. Different methods for incorporating surfactant-induced reduction of interfacial tension into models are investigated. We have suggested one method, where several parameters can be estimated in order to obtain a better fit with experimental data. For all the methods, the incremental recovery is very similar, only coming from small differences in water phase saturation profiles. Overall, a significant incremental oil recovery can be achieved, when the sensitive parameters in the context of MEOR are carefully dealt with.     

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

A weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.     

Adhesion between elastic cylinders based on the double-Hertz model

A cohesive zone model for two-dimensional adhesive contact between elastic cylinders is developed by extending the double-Hertz model of Greenwood and Johnson (1998). In this model, the adhesive force within the cohesive zone is described by the difference between two Hertzian pressure distributions of different contact widths. Closed-form analytical solutions are obtained for the interfacial traction, deformation field and the equilibrium relation among applied load, contact half-width and the size of cohesive zone. Based on these results, a complete transition between the JKR and the Hertz type contact models is captured by defining a dimensionless transition parameter μ, which governs the range of applicability of different models. The proposed model and the corresponding analytical results can serve as an alternative cohesive zone solution to the two-dimensional adhesive cylindrical contact.     

Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys

A crystal-inelasticity-based constitutive model for martensitic reorientation and detwinning in shape-memory alloys (SMAs) has been developed from basic thermodynamics principles. The model has been implemented in a finite-element program by writing a user-material subroutine. We perform two sets of finite-element simulations to model the behavior of polycrystalline SMAs: (1) The full finite-element model where each finite element represents a collection of martensitic microstructures which originated from within an austenite single crystal, chosen from a set of crystal orientations that approximates the initial austentic crystallographic texture. The macroscopic stress-strain responses are calculated as volume averages over the entire aggregate: (2) The Taylor model (J. Inst. Metals 62 (1938) 32) where an integration point in a finite element represents a material point which consist of sets of martensitic microstructures which originated from within respective austenite single-crystals. Here the macroscopic stress-strain responses are calculated through a homogenization scheme.Experiments in tension and compression were conducted on textured polycrystalline Ti-Ni rod initially in the martensitic phase by Xie et al (Acta Mater. 46 (1998) 1989). The material parameters for the constitutive model were calibrated by fitting the tensile stress-strain response from a full finite-element calculation of a polycrystalline aggregate to the simple tension experiment. With the material parameters calibrated the predicted stress-strain curve for simple compression is in very good accord with the corresponding experiment. By comparing the simulated stress-strain response in simple tension and simple compression it is shown that the constitutive model is able to predict the observed tension-compression asymmetry exhibited by polycrystalline Ti-Ni to good accuracy. Furthermore, our calculations also show that the macroscopic stress-strain response depends strongly on the initial martensitic microstructure and crystallographic texture of the material.We also show that the Taylor model predicts the macroscopic stress-strain curves in simple tension and simple compression reasonably well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.     

蜂窝夹芯试件破坏行为分析

通过平面拉伸试验和双悬臂梁试验研究了蜂窝夹芯试件的破坏行为. 在平面拉伸试验中, 发现的破坏模式不是预期的面芯界面脱胶破坏而是面板层间分层破坏;在双悬臂梁试验中, 发现了一种与以往文献报导中不同的破坏模式(面板层间分层,预制裂纹偏转和面板分层扩 展依次出现). 针对试验中所发现的新的破坏模式,结合粘结模型,建立了基于 蔡-希尔破坏准则和能量准则的计算模型. 模拟结果与试验结果对比发现,所建立 的计算模型能够很好地模拟所发现的破坏行为.