凹槽基底上含不溶性活性剂液膜的流动特性

针对凹槽基底上含不溶性活性剂液膜的流动过程,采用润滑理论建立液膜厚度和浓度演化模型,通过数值模拟得到液膜的流动特性及相关参数的影响规律.研究表明:含不溶性活性剂液膜在凹槽基底上流动时,重力和活性剂浓度梯度引起的Marangoni力对液膜的流动起促进作用,表面活性剂通过引起表层液体流动进而牵引内部液体运动,但其作用力相对重力较弱,重力起主导作用;与基底尺寸有关的粘性力则起阻碍作用;提高邦德数G和减小毛细力数C具有减弱液膜变形的作用;增大凹槽高度或减小凹槽斜度,均使Marangoni力增加,促使液膜变形加大.     

Threshold onset of Marangoni convection in narrow channels

There are several experimental studies where the Marangoni convection begins only at a certain difference in the surface tension, i.e. in a threshold way. This effect contradicts a traditional point of view according to which the surface flow in Newtonian fluids should begin at an arbitrary small difference in surface tension. To explore this phenomenon in detail we investigated the initiation of the Marangoni convection at a free liquid surface caused by injection of a droplet of surfactant. It was found that the surface motion occurs in a threshold manner, i.e. when a surfactant concentration in the droplet approaches a certain critical value. The described phenomenon is more important in narrow channels and essentially depends both on the purity of the basic liquid and on the surfactant used. Based on the experimental results, a hypothesis about an important role of residual impurities contained in basic liquids which can thoroughly change a surface rheology was suggested. The theoretical model taking into account special rheological properties in the free surface is considered. The results of the numerical simulation are in a good agreement with the experimental observations.     

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.     

Oscillation of the convective flow around an air bubble in a vertically stratified surfactant solution

The appearance of oscillatory modes of the concentration convection around an air bubble in an aqueous solution with a vertical gradient of surfactant concentration was revealed experimentally. The solution filled a thin vertical layer containing an air bubble in the form of a short horizontal cylinder with a free lateral surface. Due to a small layer thickness, two-dimensional flows and concentration distributions were generated in the liquid. Their evolution was investigated using an interferometric technique. It was found that the flow oscillation was caused by a specific interaction between the diffusion and two solutal (capillary and gravitational) mechanisms of convective mass transfer, which had quite different characteristic times. The time variation of the oscillation period was analyzed in relation to the surfactant concentration gradient, the average solution concentration, and the concentration Marangoni number. It was shown that the ratio of the dimensionless oscillation frequency to the Marangoni number is time independent and is the same for different liquids and various orientations of the concentration gradient. Published in Russian in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 130, No. 2, pp. 363–370. The text was translated by the authors.     

含表面活性剂液膜去湿过程的数值模拟

对存在壁面滑移的含非溶性表面活性剂薄液膜在固体表面的去湿过程,采用PDECOL程序对描述其演化过程的液膜厚度和表面活性剂浓度方程组进行数值求解.基于液膜表面扰动波形的变化,分析各参数对去湿特性及液膜稳定性的影响规律.研究指出:Marangoni数M较小时其效应使液膜失稳区缩短,而M较大时液膜失稳区间无限延伸,稳定性降低;毛细力数减小使液膜失稳区间缩短,减至一定程度后可有效抑制去湿现象的发生;滑移效应对演化过程的影响与M有关,M较小时滑移使液膜失稳区间缩减,使扰动增长率增大,M较大时这一影响并不显著;随平衡液膜厚度增大,液膜表面的扰动程度减小,但扰动区间显著增大.相对于外源性表面活性剂而言,内源性情形的失稳区间更小,液膜稳定性更强.     

Formation of thermocapillary structures in a heated liquid film

The conditions of formation of a three-dimensional thermocapillary structure on the surface of a liquid film flowing along a heater with the constant temperature were studied numerically based on the derived system of equations. Formation of the thermocapillary structure was modeled by periodic perturbations in the transverse direction superimposed on the two-dimensional flow. It is shown in calculations that transversal perturbations can develop into periodic rivulet structures on the film surface if the Marangoni number exceeds some threshold value. It is revealed that the rivulet structure develops when the period belongs to a certain range, which is determined by the value of Marangoni number. The results of calculations are in a good agreement with experimental data.     

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.     

垂直排液过程不稳定性的数值模拟

为分析线框排液实验中液膜表面出现的不稳定现象及其成因,针对含有不溶性活性剂的线框液膜排液过程,模拟液膜底部的不稳定现象,分析Marangoni效应、膨胀黏性和扰动波数因素的影响。结果表明：底部扰动在排液开始比较剧烈,而后快速减弱,到排液后期又逐渐增强。排液开始的扰动是由初始扰动引起,而排液后期的扰动与活性剂分布有关。较弱的Marangoni效应可增强表面扰动,而较强的Marangoni效应则减弱底部扰动,使液膜呈刚性,发生表面逆流现象;较高的膨胀黏性减慢液膜排液进程,降低表面速度,且能抑制Marangoni效应引起的逆流现象;波数较大的扰动使液膜在排液初期的扰动变强,但对排液后期的稳定性不产生影响。     

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.     

活性剂浓度分布对液膜排液过程的影响

针对含不溶性活性剂的垂直液膜排液过程,考虑分离压和表面黏度的作用,应用润滑理论建立液膜厚度、活性剂浓度和表面速度的控制方程组,分析初始活性剂浓度及梯度对排液过程的影响.结果表明：当液膜表面不含活性剂时,其排液历程很短,很快发生破断.当液膜表面添加活性剂时,可以延长液膜存续时间.而当液膜表面活性剂浓度较低时,其诱发的Marangoni效应不足以克服重力的排液作用,其形成的"黑膜"不能稳定存在.随活性剂浓度增大,液膜表面流动速度减小,液膜表面更加"坚固",所形成的"黑膜"非常稳定.当考虑初始活性剂浓度梯度时,其影响主要体现在减缓排液初期的表面速度.     

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     

非平整基底上受热液膜流动稳定性研究

本文研究了二维黏性流体薄膜沿非平整不均匀加热基底流动时非线性表面波的演化及其流动稳定性.利用长波摄动法推导出非平整线性加热基底上非线性表面波的零阶和一阶演化方程,基于所得演化方程,绘制出正弦波纹基底上液膜的表面波形图,并研究液膜流动的线性稳定性,分析了各无量纲参数对液膜线性稳定性的影响.分析结果表明:在正弦波纹基底上,液膜自由表面随同壁面作相同频率的正弦型波动,且液膜厚度沿流动方向逐渐变小;Marangoni数为稳定影响因素,随Marangoni数的增大,液膜稳定区域增大;Peclet数和倾角θ均为不稳定影响因素,随Peclet数和倾角θ的增大,液膜稳定区域减小;在非平整基底的波峰和波谷处,Peclet数、Marangoni数和倾角θ对稳定性的影响趋势一致,但基底波谷处的液膜稳定区域小于波峰处区域,流动更易失稳.     

Estimating surfactant surface coverage and decomposing its effect on drop deformation

A novel method is introduced to estimate surface coverage and the equation of state of insoluble surfactant on droplets, involving measurement of interfacial tension on a single parent drop and progressively subdivided generations of daughter drops. This has enabled quantitative decomposition of the dilution, tip-stretching, and Marangoni effects of surfactants on drop deformation. For a small viscosity ratio of 0.09, the Marangoni effect dominates, increasing first and then decreasing with surface coverage, the dilution effect is significant at high, and tip-stretching only at low surface coverage. For a viscosity ratio of 2.3, the dilution effect dominates, and neither Marangoni nor tip-stretching effects play an important role.     

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids,and the Marangoni boundary layer flow with heat generation is investigated.Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered.The governing partial differential equations are simplified by dimensionless variables and similarity transformations,and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique.It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.     

A fixture for interfacial dilatational rheometry using a rotational rheometer

In characterizing complex fluid-fluid interfaces, interfacial rheometry has become an important tool to indirectly probe the interfacial microstructure and molecular interactions. It can also be useful to obtain the constitutive properties of an interface for calculating the interfacial flows of complex fluid-fluid interfaces. A number of devices for measuring interfacial shear rheology have been designed and have been thoroughly validated. However, although a range of devices for measuring interfacial dilatational rheology exist, they do not always allow for a proper separation of the effects of dynamic surface tension, curvature elasticity, Marangoni stresses, bulk flow effects and the desired dilatational rheological material functions. In the present work it is investigated if a fixture for a standard rotational rheometer can be designed which probes the dilatational viscoelastic properties of a planar complex fluid-fluid interface. A modification of the double wall ring geometry for shear rheometry is proposed, which creates a mixed but analyzable flow field. The use of a mixed flow field inherently limits the sensitivity for the dilatational properties, but some advantages over existing techniques are presented, in particular for insoluble monolayers. More importantly, the analysis illustrate some generic aspects on the use of mixed interfacial flow fields for measuring the surface rheological properties.     

波纹基底上含不溶性活性剂液滴的铺展稳定性

针对波纹基底上含不溶性活性剂液滴的铺展历程, 采用润滑理论建立了液滴铺展数理模型, 推导出基态和扰动态下液膜厚度和活性剂浓度的演化方程组, 基于非模态稳定性理论分析了液滴铺展的稳定性及参数的影响规律. 研究表明: 扰动量在液滴中心及铺展前沿处很小, 在液膜最薄处达到最大值且活性剂浓度的负扰动现象比较明显; 扰动波数可增强液滴铺展稳定性, 但随扰动波数增加, 该稳定性逐渐下降甚至转变为不稳定. 增加 Marangoni数将导致液滴铺展不稳定性加剧; 增大基底高度具有增强液滴铺展稳定的作用, Peclet数和基底波数取适中值时有利于液滴铺展的稳定性. 关键词： 活性剂液滴 非平整基底 铺展 非模态稳定性     

Arbitrary Lagrangian–Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian–Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier–Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant.     

Influence of the Si(111)-7×7 surface reconstruction on the diffusion of strontium atoms

The diffusion of strontium atoms on the Si(111) surface at room temperature has been investigated using scanning tunnel microscopy and simulation carried out in terms of the density functional theory and the Monte Carlo method. It has been found that the reconstruction of a clean silicon surface with a 7 × 7 structure has a profound effect on the diffusion process. The average velocity of motion of a strontium atom in a unit cell of the 7 × 7 structure has been calculated. The main diffusion paths of a strontium atom and the corresponding activation energies have been determined. It has been demonstrated that the formation of scanning tunnel microscope images of the Si(111)-7 × 7 surface with adsorbed strontium atoms is significantly affected by the shift of the electron density from the strontium atom to the nearest neighbor silicon adatoms in the 7 × 7 structure.     

A Two-Layer Model for Superposed Electrified Maxwell Fluids in Presence of Heat Transfer

Based on a modified-Darcy-Maxwell model, two-dimensional, incompressible and heat transfer flow of two bounded layers, through electrified Maxwell fluids in porous media is performed. The driving force for the instability under an electric field, is an electrostatic force exerted on the free charges accumulated at the dividing interface. Normal mode analysis is considered to study the linear stability of the disturbances layers. The solutions of thelinearized equations of motion with the boundary conditions lead to an implicit dispersion relation between the growth rate and wave number. These equations are parameterized by Weber number, Reynolds number, Marangoni number, dimensionless conductivities, and dimensionless electric potentials. The case of long waves interfacial stability has been studied. The stability criteria are performed theoretically in which stability diagrams are obtained. Inthe limiting cases, some previously published results can be considered as particular cases of our results. It is found that the Reynolds number plays a destabilizing role in the stability criteria, while the damping influence is observed for the increasing of Marangoni number and Maxwell relaxation time.     

Terrestrial simulation of drop saturation by a surfactant under microgravity conditions

The paper presents the results of experimental study of mass transfer in a drop of weakly soluble fluid during its saturation with a surfactant from its water solution forming a thin (∼ 1 mm) horizontal layer. The use of the interferometer allowed us to visualize the concentration fields and to define the structure of flows under the conditions of maximum suppression of the buoyancy convection. It has been found that despite the small layer thickness, in the case of initially homogeneous solution penetration of the surfactant into the drop leads to the formation of the local density inhomogeneities at both sides of the interface and to the development of a slow gravitational flow. An increase in the initial concentration of the surfactant in the solution causes a small-scale non-stationary solutocapillary motion at the drop surface. On the other hand, solubility of the drop in water also increases which leads to the formation of a counter-diffusion flux and eventually to the disappearance of the interface. In the case of initially inhomogeneous distribution of the surfactant, a competition between the gravitational and capillary mechanisms of convection gives rise to a large-scale oscillatory flow around the drop.