Points singuliers d'une ligne de contact mobile

It is proposed to represent the dynamics of a moving contact line by an Onsager like mobility relation between the contact angle and the speed of the moving line, including an Arrhenius factor small enough in many physical situations to be the limiting factor for the motion. The liquid-vapor interface is then in quasiequilibrium, which allows one to analyse a dynamical wetting transition. This approach predicts well the formation of angular points on the rear edge of droplets sliding on a tilted plane.     

Fingering patterns on an expanding miscible drop in a rotating Hele‐Shaw cell

We perform a detailed numerical study for the evolution of an expanding miscible drop in a rotating Hele‐Shaw cell. Two mathematical formulations applied to model the coating layer expansion during practical spin‐coating process, such as thinning of the layer by cell pressing and drop spreading outward due to injection, are investigated. Including miscible interfacial stresses, we focus on the investigation of dynamical and morphological influences of two different stabilizing parameters: the gap width parameter for the pressing cell and the injecting strength. In the case of a pressing cell, the fingering features of the expanding miscible drop, such as the critical radius, are distinct from those ones in the experiments of spin coating due to the different distributions of the inherent radial velocity. On the other hand, the global interfacial evolutions of an expanding drop with an additional injection bear remarkable resemblances to their immiscible counterparts. The better agreement for an injecting model suggests its appropriateness when we simulate the emerging fingering instabilities in the spin‐coating process. Moreover, we investigate the effects of Coriolis force at higher miscible Bond numbers. Coriolis force affects significantly the onset of fingering instability and the tilting angles of fingers. These stable effects are in line with the results from the previous studies for miscible and immiscible flow fields. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrodynamics of contact of a falling drop with a liquid free surface

A fine structure of the flows developing during primary contact of freely falling drops with a deep quiescent fluid is studied using the macrophotography and high-speed video filming methods. Water drops falling in water, alcohol, and oil, as well as drops of oil, petroleum, and aqueous solutions of salt or alcohol falling in water are investigated. The work is focused on the visualization of the finespray scattering from the primary contact area. The collisions of small droplets with the surface of the submerging drop are first recorded. The direction of the spray and streamer scattering is determined by the surface tension coefficients of the coalescing liquids. The conditions under which the spray droplets collide with the drop surface are determined.     

Flows with a moving contact line

The problem of a two-dimensional viscous fluid drop which steadily moves along a horizontal rigid surface is considered. Such motion arises if the rigid surface wettability is nonuniform. A sequence of solutions for the velocity field and the free surface shape with the successively increasing applicability region near the moving contact lines is obtained for small capillary numbers Ca. The solution of the problem is found in the case when the distortion of the free surface of the drop during motion can be neglected. The problem is then reformulated using functions of a complex variable and expanded variables are introduced. In the new variables a more accurate solution of the same problem is found, with a much more narrow inapplicability region near the moving contact lines. In the solution obtained the free surface approaches the receding contact line at an angle of 180° and the advancing line at a zero angle. The solution is applicable up to the receding contact line and here approaches the known asymptotics. Near the advancing contact line the solution is applicable until the angle between the free surface and the rigid substrate becomes of the order of Ca^1/3.     

On the deformation of two droplets in a quasisteady stokes flow

A theoretical method is given for the determination of the shape of two drops (bubbles) moving with constant velocities parallel to their line of centres in a quiescent viscous fluid. The Reynolds numbers for the motions within the fluids are assumed to be sufficiently small that the equations governing these motions are quasisteady Stokes' equations. It is also assumed that the maximum deviation of the interfaces from spherical form is small when compared with the radius of the “equivalent” spherical drop. The paper deduces the first-order pressure distribution exterior and interior to the droplets. Effects of fluid viscosities, capillary numbers and distances between the droplets are taken into account. Special attention is paid to the influence of a solid plane or solid sphere on the shape of a drop (bubble) approaching or receding away from the solid boundary. The obtained solutions may serve as a first iteration of an iterative procedure for determining more accurate flow fields, taking into account the deviation from sphericity of the deformed particles.     

Direct simulation of multiphase flows with modeling of dynamic interface contact angle

We describe a modeling technique for dynamic contact angle between a phase interface and a solid wall using a generalized Navier boundary condition in the context of a front-tracking-based multiphase method. The contact line motion is determined by the generalized Navier slip boundary condition in order to eliminate the infinite shear stress at the contact line. Applying this slip boundary condition only to the interface movement with various slip ratios shows good agreement with experimental results compared to allowing full fluid slip along the solid surface. The interface slip model performs well on grid convergence tests using both the slip ratio and slip length models. A detailed energy analysis was performed to identify changes in kinetic, surface, and potential energies as well as viscous and contact line dissipation with time. A friction coefficient for contact line dissipation was obtained based on the other computed energy terms. Each energy term and the friction coefficient were compared for different grid resolutions. The effect of varying the slip ratio as well as the contact angle distribution versus contact line speed was analyzed. The behavior of drop impact on a solid wall with different advancing and receding angles was investigated. Finally, the proposed dynamic contact model was extended to three dimensions for large-scale parallel calculations. The impact of a droplet on a solid cylinder was simulated to demonstrate the capabilities of the proposing formulation on general solid structures. Widely different contact angles were tested and showed distinctive characteristic behavior clearly.     

镓铟锡液滴撞击泡沫金属表面的运动学特性研究

常温下为液态的镓铟锡合金以其优异的导热性能在具有特殊要求的传热领域有着重要的应用价值,与传统流动介质相比较大的表面张力使得其产生的流动现象必有所区别.本文研究镓铟锡所形成的液滴撞击泡沫金属表面后所产生的铺展、回缩及回弹现象.采用高速相机拍摄液滴投影轮廓随液滴运动的变化过程,并通过图像处理获得不同撞击速度、底板表面孔径下的液滴铺展系数、中心位置轮廓高度以及液滴回弹后在空中的振动特性.研究结果表明:具有较高表面张力的镓铟锡液滴的铺展系数随无量纲时间的变化在铺展初始阶段仍满足常规流体的1/2次幂关系,只在铺展后期与底板的无量纲孔径有关系;液滴的最大铺展系数在较小无量纲孔径底板大于在光滑镍板,且随底板无量纲孔径增大而逐渐减小;在回弹过程,由于底板孔隙结构的存在使得液滴回弹后在空中的振动呈现3种形态:规则的横向和纵向振动、带旋转的横向和纵向振动以及旋转振动;最后,通过对振动频率的拟合和分析,进一步拓展了传统振动频率理论公式在非规则振动过程预测中的应用.      

Strength-optimal running surface contour for track links

The various stresses resulting from weight, driving and tracking forces are transmitted over the contact point between track roller and track link running surface which is, compared with the dimensions of a track-type undercarriage, very small. The design of this contact point and hence the running surface profile of a track link, therefore, is particularly important. References were analyzed with the aim of discussing theoretical diversions on contact problems between plain and curved bodies to get the basis for an optimized design of the running surface profile of track-type undercarriages. Therefore stresses at point and line contact, i.e. for curved and plane running surfaces, are compared by Hertz' theory. In the case of line contact, the maximum Hertzian stress and thus also the maximum effective stresses strongly depend on the actual tilted position of the track roller to the track link running surface. The lowest stress is applied in the case of ideal line contact which is only theoretically interesting. Already at small angles of misalignment, the stresses for line contact are higher than for point contact. In field operation, at constantly changing angles of misalignment, the edge stresses cause the formation of curved running surfaces due to plastic deformation. If track links are already designed with such a running surface contour, the result will be constant stresses over the whole service life which are largely independent of the angle of misalignment avoiding excessive stresses caused by roller misalignments.     

Theoretical and experimental studies on the contact line motion of second-order fluid

In this study, we studied the contact line motion of second-order fluids theoretically and experimentally. The theoretical study showed that the positive first normal stress difference (N ₁) increases the contact line velocity while the second normal stress difference (N ₂) does not affect the contact line motion. The increased contact line velocity is caused by the hoop stress acting on the curved stream lines near the contact line. The hoop stress increases the liquid pressure near the contact line, and the increased pressure changes the surface profile to have the smaller curvature and smaller dynamic contact angle. The contribution of N ₁is 1 order of magnitude smaller than the contribution from the viscous component when the Deborah number remains O(1). For experiments, silicone oils of different kinematic viscosities (1,000–200,000 mm ²/s) were used while eliminating the drying problem and shear-thinning effect near the contact line. The silicone oils were well fitted to the second-order fluid model with the positive first normal stress difference. The spreading rate of a silicone oil drop on a solid surface was faster than the spreading rate predicted by the theory for Newtonian fluids. As the theory predicts that N ₁increases the contact line velocity and the experimental result confirms the theoretical prediction, the effect of N ₁is established.     

Lattice Boltzmann simulation of multiple droplets impingement and coalescence in an inkjet-printed line patterning process

Three-dimensional computations on the basis of the index-function lattice Boltzmann method are performed to simulate the process of multiple droplets impinging and coalescing into a line pattern on a solid substrate. The employed calculation model is validated by theoretical calculated values and experimental data from the literature. The influences of the equilibrium contact angle, droplet spacing and impinging velocity on the droplets impingement and coalescence behaviours are investigated. Numerical results demonstrate the width of the formed line depends significantly on the equilibrium contact angle and droplet spacing. The droplet spacing plays a significant role in controlling the coalescence moment of multiple droplets. The resolution of the printed pattern can be slightly increased with increase in impinging velocity.     

Preliminary drop-tower experiments on liquid-interface geometry in partially filled containers at zero gravity

Plexiglass containers with rounded trapezoidal cross sections were designed and built to test the validity of Concus and Finn's existence theorem (1974, 1983) for a bounded free liquid surface at zero gravity. Experiments were carried out at the NASA Lewis two-second drop tower. Dyed ethanol-water solutions and three immiscible liquid pairs, with one liquid dyed, were tested. High-speed movies were used to record the liquid motion. Liquid rose to the top of the smaller end of the containers when the contact angle was small enough, in agreement with the theory. Liquid interface motion demonstrated a strong dependence on physical properties, including surface roughness and contamination.     

基于新型广义位移的箱形梁扭转单元及应用

为了改进变截面连续箱梁桥的扭转分析理论,将截面总扭转角分解为自由翘曲扭转角和约束剪切扭转角,选取自由翘曲转角扭率作为广义位移,提出一个2节点8自由度的扭转梁段单元。从约束扭转控制微分方程出发,推导单元刚度矩阵及等效节点荷载列阵。引入应力增大系数,以反映约束扭转对初等梁应力的增大效应。数值算例验证了本文梁段单元的可靠性。最后对一个三跨变截面连续箱梁桥进行分析,结果表明,双力矩影响线与弯矩影响线较为类似,按双力矩影响线进行最不利荷载加载时最大应力值偏小;应力增大系数在集中荷载作用截面出现极值,均发生在腹板与顶板交点处;利用偏载放大系数来考虑扭转附加效应时,不宜考虑弯曲正应力较小及翘曲正应力出现极值的梁段区域。     

Modelling the wetting of a solid occlusion by a liquid film

We investigate in this work how the presence of an occlusion affects the dynamics of the wetting front of a liquid film draining down a vertical surface. This numerical study is developed in the context of the lubrication approximation. Through a parametric study, we show that depending on the asymptotic film thickness and the fluid properties, there exists a critical substrate contact angle below which separation of the contact line from the occlusion wall is observed which results in the appearance of a dry zone in the wake of the occlusion. In analogy with external aerodynamics, we also show that a sharp corner in the occlusion can induce this contact line separation. Our numerical results also highlight the importance of the occlusion wettability on the morphology of the wetting front suggesting a possible mechanism to control and mitigate the often undesirable fingering instability.     

微量第二润滑介质辅助的增强水润滑研究

研究了一种微量第二润滑介质辅助的增强水润滑方案. 在水润滑环境下,测量了丁腈橡胶块-不锈钢环接触入口区短时(10 s)注入微量乳化油(100 μL)时的摩擦力特性. 结果表明:在试验工况下短时注入微量乳化油降低了橡胶块磨损. 低速时,摩擦副处于混合润滑状态,短时注入的乳化油减摩效果明显;速度升高时,短时注入的乳化油使轴承特性系数增加,会引起摩擦力增加. 此外,在水环境下利用线接触光干涉技术揭示了乳化油以离水展着的方式形成承载润滑膜. 研究工作为应对短时恶劣工况下的水润滑失效提供新的思路,为水环境下微量乳化油的辅助润滑调控提供数据支持.      

A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

A method of potentially wide application is developed for deriving analytical expressions of the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The cross line composed of the interface and the crack is mapped into a line, and then the complex potentials are educed. The Muskhelishvili method is extended by creating a Plemelj function that matches the singularity of the real crack tips, and eliminates the pseudo tips’ singularity induced by the conformal mapping. The stress field is obtained after solving the Riemann–Hilbert boundary value problem. Based on the stress field expressions, crack tip stress intensity factors, dislocation dipole image forces and image torque are formulated. Numerical curves show that both the translation and rotation must be considered in the static equilibrium of the dipole system. The crack tip stress intensity factor induced by the dipole may rise or drop and the crack may attract or reject the dipole. These trends depend not only on the crack length, but also on the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the center of the dislocation dipole is much smaller than the vertical one. Whether the dipole subjected to clockwise torque or anticlockwise torque is determined by whether the Burgers vector of the crack-nearby dislocation of the dipole is positive or negative. A concentrated load induces no singularity to crack tip stress fields as the load is located at the crack line. However, as the concentrated force is not located on the crack line but approaches the crack tip, the nearby crack tip stress intensity factor K_IIIu increases steeply to infinity.     

梯度润湿表面上液滴定向迁移及合并行为的格子Boltzmann模拟

采用改进的格子Boltzmann方法,对梯度润湿性表面上液滴的定向迁移及合并行为进行了数值模拟,该模型在精度和稳定性上都有很大改善,同时,研究了梯度润湿性表面上液滴定向迁移和合并的动力学特性,并对液滴尺寸及润湿梯度对液滴动力学特性的影响规律进行了分析。数值结果表明,液滴在梯度润湿性表面运动时会发生形变,且动态接触角逐渐减小。润湿梯度对液滴定向迁移行为有显著影响,润湿梯度越大,液滴左右侧接触线位移越大,润湿长度增加越快。但是液滴尺寸对接触线位移影响较小。润湿梯度对液桥宽度基本无影响,但对液滴初始合并时间有显著影响。     

Adhesion of oriented nematic droplets

We propose and analyze a two-dimensional model for the equilibrium of oriented droplets of nematic liquid crystals that may adhere to a rigid substrate, while surrounded by an isotropic environment. We obtain the contact condition at the edge where the liquid crystal, the substrate, and the environment come together. We further develop a fairly general method to arrive at the equilibrium shapes of a drop, which is then applied to the case where the surface tension at the liquid crystal interface is given by Rapini and Papoular's expression. In this case, we also predict the existence of concave equilibrium shapes. Here is indeed the main difference between this method and Wulff's construction, which always yields convex equilibrium shapes for a drop free from adhesion. Received February 22, 2000     

Speckle technique for dynamic drop profile measurement on rough surfaces

A technique has been developed for measuring three-dimensional instantaneous drop profiles on rough surfaces. The surface is illuminated using a laser and images are captured of the resulting speckle pattern with and without the drop in place. The analysis consists of finding the contact line, measuring the deformation of the speckle field caused by refraction of light at the drop surface, then reconstructing the drop using simulated annealing optimization to find the drop shape whose shift vector field best matches the one measured. An error analysis of the technique was performed using a Monte Carlo technique and comparisons to sideview drop images for a large sample of drops. Mean contact angle measurement error was found to be −1.6° with a 1 − σ error bound of −6.9°, +2.0°.     

Influence of yield stress on the fluid droplet impact control

The impact and the spreading of a drop of the yield stress fluid on a solid surface have been experimentally investigated. A yield stress fluid chosen as a model fluid can shed some light on the manner in which it is possible to control the impacted drop's profile. Several gels based on polymer concentration were prepared to obtain different levels of yield stress. Their shear rheological behaviours were characterized and their flow behaviours were modeled using Herschell–Bulkley equation. Droplets were impacted in a wide range of velocities upon a dry and smooth polymethylmetacrylate substrate. Their dynamics on the impacted surface were captured using a high-speed camera. The spreading and recoil of drops are studied and their behaviour was compared to that of a Newtonian fluid at each impact velocity.Influence of the yield stress level and intensity of inertia on the transient and final stages of drops impact were studied. It was shown how the increasing yield stress dictates the drop formation and also led to an emphasis of the inhibition of spreading and the weakening of retraction in the case of high inertial impacts. It was also noticed that the magnitude of the gravitational subsidence observed for the low impact velocities, is governed by the initial non-spherical shape of droplets. Dimensionless numbers were defined in the case of yield stress fluids, allowing us to compare the effects of forces present in the process and better understand the phenomena observed. Wall slip of gels on the PMMA substrate was characterized. Its influence on the drop spreading has been discussed.     

Elastocapillary Coiling of an Elastic Rod Inside a Drop

Capillary forces acting at the surface of a liquid drop can be strong enough to deform small objects and recent studies have provided several examples of elastic instabilities induced by surface tension. We present such an example where a liquid drop sits on a straight fiber, and we show that the liquid attracts the fiber which thereby coils inside the drop. We derive the equilibrium equations for the system, compute bifurcation curves, and show the packed fiber may adopt several possible configurations inside the drop. We use the energy of the system to discriminate between the different configurations and find a intermittent regime between two-dimensional and three-dimensional solutions as more and more fiber is driven inside the drop.