二元工质Marangoni对流的实验研究与数值模拟

用实验和数值模拟方法研究了正值表面张力温度系数的二元醇类特殊水溶液Marangoni对流流动. 首先通过实验测量确定正戊醇水溶液表面张力在特定的浓度分布和温度区间内具有明显随温度升高而增加的变化区域, 然后利用特定浓度配比的正戊醇水溶液,采用PIV方法实验观测了矩形液池中二元工质液层在水平温差驱动下的Marangoni对流, 发现了不同于常规的反向热毛细对流流动, 测量的表面速度分布与相同工况的数值模拟结果进行了比较, 发现二者变化趋势一致. 实验观测和理论结果的比较进一步验证了表面张力温度系数为正值时二元工质液层的热毛细流动输运特性.      

表面张力驱动对流的实验研究

液桥的表面张力驱动对流问题,是目前国际上最受重视的空间科学研究课题之一。本文回顾了该问题的起因及实验研究的进展状况,综述了现有的实验结果,指出了一些存在的问题。      

基于移动粒子半隐式法的表面张力模拟

采用移动粒子半隐式法(MPS)模拟了受表面张力影响的自由面流动。表面张力的计算采取了一种较适合于MPS方法的表面自由能模型。方形液滴振荡和射流断裂的模拟结果分别与理论分析和试验结果一致,同时进行了三维射流注水模拟,从而验证了MPS方法结合该表面张力模型可以有效、方便地进行自由面流动中表面张力现象的模拟。     

饱和下降液膜的稳定性研究

通过简化表面张力、蒸汽压力和液膜波动之间的关系,用线性理论分析了饱和液膜在等温竖壁上的流动稳定性,讨论了雷诺数、波数、壁面和液膜温差及流体物性变化的影响。     

表面张力、黏性和驱动对非传播表面孤立波的影响

从理论上研究了表面张力、黏性和驱动对非传播表面孤立波的影响。指出表面张力使孤波高度增大、宽度减小．作出了孤波的等波响应曲线（ｅｑｕａｌ－ｗａｖｅ－ｒｅｓｐｏｎｓｅ－ｃｕｒｖｅｓ）并与实验结果进行了比较。     

三维液体非线性晃动及其复杂现象

主要讨论三维液体非线性晃动问题 。将ALE（任意的拉格朗日-欧拉）运动学描述引人到Navier-Stokes方程的分步有限元计算格式中;在时间域上采用分步离散方法中的速度修正格式,利用Galerkin加权余量方法得到了系统的有限元离散方程;推导了考虑表面张力效应时有限元边界条件的弱积分形式;模拟了三维液体的非线性晃动问题,得到了一系列三维液体非线性晃动的复杂现象.进一步模拟了考虑表面张力效应以及在微重力环境下三维液体的非线性晃动,揭示了考虑表面张力效应以及在微重力环境下液体非线性晃动的重要特征.井将所得结论与现有的实验结果进行了比较.从而证实了该方法的有效性与正确性.     

非传播孤立波和表面张力

本文讨论了关于表面张力的实验与理论分析之间的矛盾把表面张力的能量当作高阶小量、导出了非传播孤立波的基本方程，得到的解与实验结果相符。     

微注射成形中表面张力效应的数值模拟

微注射成形过程是一个喂料射入膜腔挤出腔内空气的过程。在这一过程中,存在喂料和空气的移动界面。由于喂料和气体物质特性差异很大,喂料分子对界面上的分子引力明显大于气体分子的引力,故界面上的分子会受到方向指向喂料内部的合力,即表面张力。为了研究表面张力效应对粘性流微注射模拟结果的影响,在矢量化显式算法的有限元模拟软件中,实现了表面张力计算和模拟功能,并在有限元方法中以系统化方法确定了离散变量场的拉普拉斯算子值。应用植入该功能的软件,模拟了一个典型的注射填充过程的算例,探讨了表面张力作用项对粘性流体填充过程的影响。通过对不同尺寸构件的模拟结果比较,证实表面张力作用项对粘性流注射填充过程模拟结果影响不大,除了毫米级以下构件,在一般情况下可以忽略。     

α铁晶界熵及表面张力的分子动力学模拟

晶界也是一种界面。表面张力是晶界的一个重要的热力学量。本文采用计算机分子动力学模拟(CMD)方法计算 α-Fe,∑=9 的晶界在不同温度和压力下的表面张力,结果与实验值的比较是满意的。发现熵对晶界的表面张力的贡献是很小的,通常可以忽略不计。     

微重环境中三维液体非线性晃动的数值模拟

将ALE（任意的拉格朗日-欧拉）运动学描述关系引入到Navier-Stokes方程中,在时间域上采用分步离散方法中的速度修正格式,利用Galerkin加权余量方法推导了系统的有限元数值离散方程;推导了考虑表面张力效应时有限元边界件的弱积分形式。模拟了考虑表面张力情况下圆筒形贮腔中液体的非线性晃动,揭示了考虑表面张力效应时液体非线性晃动的重要特征。     

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.     

Modeling of complex interfaces for pendant drop experiments

Interfaces of fluid-fluid systems play an important role in the stability of foams and emulsions in chemistry, biology, consumer products, and foods. For most applications, surface active agents are added and adsorbed onto the interface to enhance stability, making the rheological behavior of the interface more complex. To understand the phenomena of these complex interfaces, various techniques are used to determine the interfacial properties. One of the most popular methods is the pendant drop technique. From the equilibrium state of the pendant drop, the interfacial tension of a system can be obtained quite easily in the absence of surface active agents. But when complex viscoelastic interfacial characteristics are considered, in particular in oscillatory measurements, interfacial constitutive relations need to be defined. Interfaces containing proteins, particles or Langmuir monolayers formed by insoluble low weight surfactants appear to act like viscoelastic solid membranes. In this work, a two-dimensional axisymmetric finite element model is designed to study the behavior of complex interfaces in pendant drop experiments. The bulk fluid consists of a Newtonian fluid, while the interface behaves according to the Kelvin-Voigt model as elastic interfacial forces dominate. To be able to capture large deformations, the Kelvin-Voigt constitutive model is made quasi-linear by using a combination of two non-linear strain tensors. A parameter study is performed to investigate the influence of the five model parameters of the quasi-linear Kelvin-Voigt equation. To demonstrate the applicability of the numerical model, a small amplitude oscillatory measurement is simulated.     

Rheology of oil-in-water emulsions

The effect of interfacial tension on the steady-flow and dynamic viscoelastic behavior of emulsions are studied experimentally. At very low inter-facial tensions and low volume fractions, the viscosity decreases with increasing shear rate and becomes constant at high shear rates. The high-shear-rate Newtonian viscosity is not affected by interfacial tension, but the transition from pseudoplastic to Newtonian flow shifts to lower shear rates as the interfacial tension decreases. At an interfacial tension of 5 × 10^–3 Nm^–1, the viscosity decreases, passes through a minimum, and then increases as the shear rate is increased. The dilatant behavior may be attributed to elastic responses of interfaces during collision of drops. At high volume fractions, the emulsions show remarkable elasticity resulting from the interfacial energy associated with deformation of liquid films. The modulus and viscosity are proportional to interfacial tension and inversely proportional to drop size.     

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.     

Transient two‐layer thin‐film flow

The transient two‐layer thin‐film planar flow is investigated theoretically in this study. The interplay among inertia, viscous and surface/interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, velocity and film thickness ratios at inception, and the surface‐to‐interfacial tension ratio. The nonlinear stability of the steady state reveals the formation of a solitary wave after flow inception, which propagates in the form of a convective instability, with the steady state recovered only in the tail (upstream) region of the wave. In the presence of surface/interfacial tension, surface modulation appears, which grows in wavelength and amplitude with position. The flow is found to be particularly stable for higher viscosity of the lower film layer. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

ATOMIZATION OF A LIQUID DROP BY PULSATION

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An integrated smoothed particle hydrodynamics model for complex interfacial flows with large density ratios

In this paper, an integrated smoothed particle hydrodynamics (SPH) model for complex interfacial flows with large density ratios is developed. The discrete continuity equation and acceleration equation are obtained by considering the time derivative of the volume of particle and Eckart's continuum Lagrangian equation. A continuum surface force model is used to meet the fact that surface force may not be distributed uniformly on each side of the interface. An improved boundary condition is imposed to model wall free-slip and no-slip condition for interfacial flows with large density ratios. Particle shifting algorithm (PSA) is added for interfacial flows by imposing the normal correction near the interface, called as Interface-PSA. Then four representative numerical examples, including droplet deformation, Rayleigh-Taylor instability, dam breaking, and bubble rising, are presented and compared well with reference data. It is demonstrated that inherent interfacial flow physics can be well captured, including surface tension and the dynamic evolution of the complex interfaces.     

Measurement of the surface concentration (liquid) of an evaporating multicomponent droplet using pendant droplet method

The surface concentration on the liquid side of the interface of an evaporating multicomponent droplet could be different from the bulk concentration. In this work, surface tension is used as a means to measure surface concentration of an evaporating multicomponent droplet. Surface tension is measured using pendant droplet method that relies on the best fit between theoretical and experimental drop profiles. Surface tension is a surface property, and it exhibits a dependence on concentration. Hence, it is an ideal candidate to track the variation of surface concentration during the evaporation of a multicomponent droplet. This method is used to study the evaporation of ethanol–water and methanol–water droplets. The correctness and applicability of this technique are critically assessed, and important observations are made for single droplet evaporation for these binary mixtures.     

Experimental evaluation of Marangoni stress and surfactant concentration at interface of contaminated single spherical drop using spatiotemporal filter velocimetry

Spatiotemporal filter velocimetry (SFV) was extended to Lagrangian measurements with boundary-fitted measurement areas, and was applied to flows about single spherical drops of glycerol-water solution falling in stagnant silicon oil under clean and contaminated conditions to examine its applicability to the estimation of the Marangoni stress and surfactant concentration at a moving interface. Effects of bulk concentration of surfactant on the velocity field, the Marangoni stress and the surface concentration of surfactant were discussed from the measured data. As a result, we confirmed that accurate velocity distribution in the vicinity of the interface measured by SFV enables us to evaluate interfacial velocity and interfacial shear stresses and to estimate the Marangoni stress, interfacial tension and surfactant concentration at the interface with the assumption of negligible surface viscosity. The flow inside the drop and the interfacial velocity become weak due to the Marangoni stress caused by the gradient of surfactant concentration at the interface as the bulk concentration of surfactant increases. These results demonstrate that SFV is of great use in experimental analysis of adsorption and desorption kinetics at a moving interface.