Self-propelled droplets

Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own ‘exhausts’ allows to additionally study collective phenomena.     

Modeling and simulation of thermocapillary flows using lattice Boltzmann method

To understand how thermocapillary forces manipulate droplet motion in microfluidic channels, we develop a lattice Boltzmann (LB) multiphase model to simulate thermocapillary flows. The complex hydrodynamic interactions are described by an improved color-fluid LB model, in which the interfacial tension forces and the Marangoni stresses are modeled in a consistent manner using the concept of a continuum surface force. An additional convection–diffusion equation is solved in the LB framework to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. A stress-free boundary condition is also introduced to treat outflow boundary, which can conserve the total mass of an incompressible system, thus improving the numerical stability for creeping flows.The model is firstly validated against the analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of three-dimensional deformable droplet at various Marangoni numbers, and its accuracy is once again verified against the theoretical prediction in the limit of zero Marangoni number. Finally, we numerically investigate how the localized heating from a laser can block the microfluidic droplet motion through the induced thermocapillary forces. The droplet motion can be completely blocked provided that the intensity of laser exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and constant velocity. When the droplet motion is completely blocked, four steady vortices are clearly visible, and the droplet is fully filled by two internal vortices. The external vortices diminish when the intensity of laser increases.     

Numerical simulation of filler metal droplets spreading in laser brazing

A finite element model was constructed using a commercial software Fidap to analyze the Cu-base filler metal droplet spreading process in laser brazing, in which the temperature distribution, droplet geometry,and fluid flow velocity were calculated. Marangoni and buoyancy convection and gravity force were considered, and the effects of laser power and spot size on the spreading process were evaluated. Special attention was focused on the free surface of the droplet, which determines the profile of the brazing spot.The simulated results indicate that surface tension is the dominant flow driving force and laser spot size determines the droplet spreading domain.     

液态三元Fe-Sn-Si/Ge偏晶合金相分离过程的实验和模拟研究

本文采用自由落体实验技术和格子玻尔兹曼计算方法研究了低重力条件下液态Fe-Sn-Si/Ge合金的相分离过程. 实验发现, 二种合金液滴在自由下落过程中均发生显著的液相分离, 形成了壳核和弥散组织. 当Fe-Sn-Si合金中的Si元素被等量的Ge元素替换后, 壳核组织中富Fe区和富Sn区的分布次序会发生反转. 计算表明, 在液相分离过程中冷却速率、Marangoni对流和表面偏析对壳核构型的选择和弥散组织的形成起决定性作用.     

Dissipative hydrodynamic oscillators

Summary The oscillatory motion of a liquid-liquid interface induced by the Marangoni effect,i.e. the variation of surface tension with the concentration of a surfactant, is described as the harmonic oscillation of the surfactant concentration at the interface. Then, at vanishing damping, threshold values and parameter regions for sustainedlongitudinal (Marangoni-Lucassen) waves are given in terms of the transport coefficients of the two liquids. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

边界耦合的Marangoni对流边界层问题的近似解析解

研究了由温度梯度引起的Marangoni对流边界层问题.由于动量方程和能量方程的边界条件耦合,利用相似变换将偏微分方程组转化为常微分方程非线性边界值问题.通过巧妙引入摄动小参数对速度和温度边界层方程同时渐近展开求解,得到了问题的近似解析解,并对相应的动量、能量传递特性进行了讨论. 关键词： Marangoni对流 近似解析解 渐近展开     

添加剂对LiBr溶液吸收蒸汽过程中的强化机理

利用吊板法测量了加有正辛醇和异辛醇这两种添加剂的溴化锂溶液的表面张力 ,利用激光照相的可视化方法研究了在静池吸收过程中添加剂对溴化锂溶液吸收水蒸汽的强化影响 .实验结果显示液体添加剂和蒸汽添加剂都能显著地降低溴化锂溶液的表面张力 ;蒸汽添加剂不仅和液体添加剂一样可以在吸收表面引起马拉戈尼对流 ,而且对吸收具有更好的强化效果 .根据对实验现象的分析 ,得出了添加剂对吸收的强化机理 :由于溶液表面层对液体添加剂或蒸汽添加剂的表面吸附作用 ,造成吸收界面处表面张力分布不均匀 ,从而在吸收界面引起马拉戈尼对流现象 ,强化了吸收过程中的传热、传质性能     

基于范德瓦尔斯表面张力模式液滴撞击疏水壁面过程的研究

液滴撞击疏水壁面过程的研究在介观流体力学和微流体作用材料科学的研究中具有重要的理论意义和工程价值. 论文在SPH方法中引入范德瓦尔斯状态方程处理液滴表面张力, 考虑流体粒子之间远程吸引, 近程排斥的内部作用力, 提出了流体粒子与疏水壁面粒子间势能函数与表面张力相结合的作用模式. 通过模拟真空条件下两个静止的等体积液滴相互融合的过程, 验证了计算模式在模拟液滴的表面张力中的有效性. 采用该模式模拟的液滴撞击疏水壁面过程, 不仅能够有效地模拟液滴撞击壁面后的变形过程, 而且清晰地模拟出液滴的回弹、腾空以及二次撞壁现象的完整过程. 模拟结果与液滴撞击疏水壁面的实验结果以及VOF模拟结果符合较好, 表明本文所提出的表面张力和疏水壁面作用力处理模式对模拟液滴撞壁过程具有实际应用价值.     

A coupled arbitrary Lagrangian–Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants

A finite element scheme to compute the dynamics of insoluble surfactant on a deforming free surface is presented. The free surface is tracked by the arbitrary Lagrangian–Eulerian (ALE) approach, whereas the surfactant concentration transport equation is approximated in a Lagrangian manner. Since boundary resolved moving meshes are used in the ALE approach, the surface tension, which may be a linear or nonlinear function of surfactant concentration (equation of state), and the Marangoni forces can be incorporated directly into the numerical scheme. Further, the Laplace–Beltrami operator technique, which reduces one order of differentiation associated with the curvature, is used to handle the curvature approximation. A number of 3D-axisymmetric computations are performed to validate the proposed numerical scheme. An excellent surfactant mass conservation without any additional mass correction scheme is obtained. The differences in using a linear and a nonlinear equation of state, respectively, on the flow dynamics of a freely oscillating droplet are demonstrated.     

倾斜粗糙壁面上含不溶性活性剂溶液的动力学特性

针对倾斜随机粗糙壁面上含不溶性活性剂溶液的流动过程, 采用润滑理论建立了液膜厚度和浓度的时空演化模型, 通过PDECOL程序数值求解得到了液膜流/液滴铺展的动力学特性及壁面结构参数的影响. 研究表明: 在重力分量和Marangoni效应共同作用下, 液膜流/液滴铺展速度加快, 液膜边缘和液滴中心出现毛细隆起, 液膜/液滴底部出现凹陷, 同时受粗糙壁面影响, 液膜表面变形更显著. 增加壁面倾角θ具有使重力分量和Marangoni效应增强, 导致隆起和凹陷程度均有所增加的作用. 增大壁面高度D可使液膜流/液滴铺展速度加快, 表面变形放大. 而壁面波数k₀则使液膜流/液滴铺展过程减缓, 抑制隆起和凹陷产生. 与液膜流相比, D和k₀对液滴铺展速度的影响相对较小. 关键词： 随机粗糙壁面 液膜 Marangoni效应 倾斜流动     

Preliminary study of two immiscible liquid layers subjected to a horizontal temperature gradient

Marangoni convection, driven by interfacial instability due to a surface tension gradient, presents a significant problem in the crystal growth process. To achieve better materials processing, it is necessary to suppress and control this convection, especially in crystal growth using Liquid Encapsulated Czochralski techniques in which the melt is encapsulated in an immiscible medium. Marangoni convection can occur at the liquid-liquid interface and at the gas-liquid free surface. Buoyancy driven convection can also affect and complicate the flow. The present report studied Marangoni convection in a two-liquid layer system in an open and enclosed cavity. Flow in the cavity was subjected to a horizontal temperature gradient. Interactive flow near the liquid-liquid interface was measured by the Particle Image Velocimetry (PIV) technique. The measured flow field is in good agreement with numerical predictions.     

分离结晶过程中熔体热毛细对流的转变

为了了解微重力条件下新型分离结晶生长过程中熔体热毛细对流的基本特征,利用有限差分法进行了数值模拟,熔体深径比A取1和2,自由界面无因次宽度B分别取0.05、0.075和0.1.当熔体上表面为自由表面时,得到了分离结晶Bridgman生长过程中熔体热毛细对流的流函数和温度分布.计算结果表明:当Ma数较小时,在上下两个自由表面的表面张力的驱动下,熔体内部产生了两个流动方向相反的流胞,流动为稳态流动,随着Ma数的增加,上下自由表面速度增大,温度分布的非线性增加;当Ma数超过某一临界值后,流动将转化为非稳态流动;与熔体上表面为固壁时相比,A=1时的临界Ma数减小,而A=2时的临界Ma数增大;流动失稳的物理机制是流速的变化和阻力的变化之间存在滞后.     

Numerical simulation of natural convection in a sessile liquid droplet

Heat transfer in a sessile liquid droplet was studied with numerical methods. A computer code was developed for solving the problem of convection in an axisymmetric hemispherical droplet and in a spherical layer as well. The problem of establishing an equilibrium state in a droplet was solved using several variables: temperature, stream function, and vorticity. Simulation was performed for droplets of water, ethyl alcohol, and model liquids. Variable parameters: intensity of heat transfer from droplet surface, Rayleigh and Marangoni dimensionless criteria, and the characteristic temperature difference. It was revealed that the curve of convective flow intensity versus heat transfer intensity at droplet surface has a maximum. A dual-vortex structure was obtained in a stationary hemispherical profile of liquid droplet for the case of close values for thermocapillary and thermogravitational forces. Either thermocapillary or thermogravitational vortex might be dominating phenomena in the flow structure.     

表面弹性对含可溶性活性剂垂直液膜排液的影响

针对含可溶性活性剂的垂直液膜排液过程,在考虑表面弹性作用的基础上,采用润滑理论建立了液膜厚度、表面速度、表面和内部活性剂浓度的演化方程组,通过数值计算分析了表面弹性和活性剂溶解度耦合作用下的液膜演化特征.结果表明：表面弹性是影响可溶性活性剂垂直液膜排液过程中必不可少的因素.排液初期,随表面弹性增加,液膜初始厚度增大,表面更趋于刚性化.随排液进行,弹性不同的液膜呈现不同的典型排液特征：当弹性较小时,液膜上部表面张力高,下部表面张力低,产生正向的马兰戈尼效应,与重力作用相抗衡.当弹性较大时,膜上部表面张力低,下部表面张力高,产生逆向的马兰戈尼效应,促使液膜排液加速,更易发生失稳.活性剂溶解度通过控制液膜表面的活性剂分子吸附量,进而影响表面弹性：当活性剂溶解度较大时,液膜厚度较小,很快发生破断;随溶解度降低,液膜稳定性增加,初始表面弹性也随之增大,并随液膜变薄逐渐接近极限膨胀弹性值.     

水平温差对环形浅液池内Marangoni-热毛细对流的影响

双向温差驱动下的Marangoni-热毛细对流在许多工程技术领域具有重要作用, 但是, 已有的大部分研究集中于单向温差作用下的流动. 因此, 采用数值模拟的方法研究了水平温差对双向温差驱动下的环形浅液池内Marangoni-热毛细对流的影响. 在一个给定的顶部换热条件下, 确定了不同水平温差作用下流动由轴对称稳态流动向三维非稳态流动转变的临界底部热流密度. 结果表明, 水平温差使得Marangoni-热毛细对流不稳定; 随着水平温差的持续增强, 稳态流动转变为一种规律的振荡流动, 最终变得混乱; 发现两种新的状态演化过程; 确定了水平温差和垂直温差在共同驱动流体运动时各自发挥的作用; 随着水平温差的增强, 最初出现在中间区域的最高表面温度不断向热壁移动, 在此过程中, 内壁附近的流动增强, 而外壁附近的流动减弱.     

Marangoni instability of a liquid layer with insoluble surfactant under heat flux modulation

We investigate the parametric excitation of Marangoni convection by a periodic flux modulation in a liquid layer with insoluble surfactant absorbed on the nondeformable free surface. The stability analysis of the convective system is performed for arbitrary wave numbers of the disturbances. An interesting feature of the onset of convection is the existence of bifurcating neutral curves with double minima, one of which corresponds to a quasi-periodic solution, and the other one corresponds to a subharmonic solution. The evolution of the subharmonic instability region depending on the amplitude of the external heat flux modulation and the frequency of the modulation is studied. The quasi-periodic neutral curve is close to the oscillatory neutral curve of the nonmodulated problem.     

不同液膜体系中Marangoni效应对活性剂液滴铺展的影响

针对含可溶性表面活性剂的液滴在预置液膜上的铺展过程,应用润滑理论建立液滴厚度、活性剂表面浓度及内部浓度演化过程的控制方程组,采用PDECOL程序模拟液滴的演化特征,探讨不同液膜体系下Marangoni效应的作用机理,并基于瞬态增长法分析负体系下液滴演化的不稳定性.研究表明,正体系下Marangoni效应可促进活性剂分子扩散,有利于活性剂液滴的稳定铺展;负体系下Marangoni效应则抑制液滴铺展,使液滴在中心区域产生振荡现象,呈现不稳定性特征,且该特征随负效应增强而愈加明显.在正负两种体系下,Marangoni作用力均是促使液滴横向演化的主要驱动力.     

Tension gradients and Marangoni flows in nematic interfaces

This brief report (i) presents equations that govern the balance of tangential forces in interfaces between isotropic viscous fluids and nematic liquid crystals, and (ii) establishes the physical origin of nematic Marangoni flows. It is shown that surface gradients in the orientation dependent surface free energy gives rise to tangential nematic Marangoni forces. Tangential nematic Marangoni forces are caused by surface gradients of the nematic tensor order parameter, and the kinetic coefficient characterizing this interfacial phenomenon is proportional to nematic elastic storage. Expressions of the Marangoni forces using a classical constitutive equation for the surface free energy are given for general and uniaxial nematic ordering states. Nematic Marangoni flows or nematocapillarity augments the class of Marangoni flows present in electrocapillarity, diffusocapillarity, and thermocapillarity.     

润湿性梯度驱动液滴运动的格子Boltzmann模拟

运用考虑了固体与液体间分子作用力的格子Boltzmann方法,数值研究了由于固液界面上表面张力梯度引起的Marangoni效应驱动的液滴运动.当表面张力梯度较小时,计算结果和前人的理论预测符合较好.而表面张力梯度较大时,由于液滴不变形和准平衡态等假设不再满足,理论预测的液滴运动速度高于数值模拟的结果.计算结果显示,在向亲水端运动过程中液滴内部出现旋涡结构,当润湿性梯度较大时,其前进速度和接触角随时间变化出现振荡.     

润湿性梯度驱动液滴运动的格子Boltzmann模拟

运用考虑了固体与液体间分子作用力的格子Boltzmann方法,数值研究了由于固液界面上表面张力梯度引起的Marangoni效应驱动的液滴运动.当表面张力梯度较小时,计算结果和前人的理论预测符合较好.而表面张力梯度较大时,由于液滴不变形和准平衡态等假设不再满足,理论预测的液滴运动速度高于数值模拟的结果.计算结果显示,在向亲水端运动过程中液滴内部出现旋涡结构,当润湿性梯度较大时,其前进速度和接触角随时间变化出现振荡. 关键词： 润湿性 格子Boltzmann方法 Marangoni效应 液滴