关于沿内角的自发毛细流动现象回顾

文章从静力和动力学的角度简要回顾了关于沿内角的自发毛细流动研究的最近进展.作为一个通用几何形状,内角在地面微观尺度下或处于失重状态的航天飞行器系统内大尺度下为液体提供有效的输运通道.当一定的几何条件得到满足并且当毛细力远远大于体力比如重力的时候,沿着内角会发生自发毛细力驱动流动现象.从静力学的角度来说,本文讨论的自发毛细驱动流动和当特定的边界条件发生突然变化,比如重力作用突然消失时带有内角的容器内部单值有限高度的平衡自由面的非存在性有关系. Concus-Finn方法可以用来确定这样的平衡自由面在一个横截面处处一致的柱形容器内的非存在性.用这个方法可以推导出在失重状态下一个内角为2α的通常柱形容器里,当接触角小于π/2-α时,平衡曲面不存在.通常来说,沿内角的自发毛细驱动流动属于层流.利用尺度分析和摄动法,成功分析了该流动的动力学特性,并且推导出对设计有用的封闭形式的解析解.一个典型的结果是在黏性流的范畴里毛细面端点的移动和t1/2成正比      

小孔流速实验中的排水时间和流量系数的研究

本文以水作为理想流体,考虑到水头损失和孔口缩流效应,对小孔流速实验涉及的容器排水问题进行了系统的理论和实验研究.从理论上推导得出了圆柱形容器排水时间的解析解,分析了排水时间和自由液面速度、流量系数之间的规律,提出了排水时间的等效性.实验上,加工了底部开有不同小孔的大型圆柱形容器,测量了容器排水时间随液面高度的变化关系,借助实验结果计算了流量系数值,验证了容器排水时间的等效性关系,实验结果与理论计算符合较好.     

微重力条件下与容器连通的毛细管中的毛细流动研究

利用落塔的短时微重力条件, 实验研究了与容器连通的毛细管中的流体在微重力条件下的毛细流动过程, 并通过理论分析建立了相应的毛细管中弯月液面高度随时间变化的微分方程. 结果表明, 对于不同的接触角和不同的容器/毛细管参数, 由建立的理论公式得到的数值解结果都与实验结果在定量上较为一致. 此外, 实验中发现, 改变乙醇和去离子水混合液的比例可以明显地改变接触角参数, 但对毛细流动的影响很小, 建立的理论公式也对这一现象给出了合理的解释. 该研究对于预测和分析微流道及空间微重力条件下的毛细流动行为具有明显的应用价值.     

微重力环境下无限长柱体内角毛细流动解析近似解研究

应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度.     

纳米尺度下毛细流动的分子动力学模拟

采用分子动力学模拟研究纳米尺度下壁面润湿性对毛细流动的影响,主要考虑纳米通道两侧壁面润湿性相同与不同两种情况。研究表明：两侧壁面润湿性相同条件下,毛细流动随着壁面润湿性增强而加快, 毛细高度随时间的变化早期偏离Lucas-Washburn理论,但后期与其预测符合。在纳米通道两侧壁面润湿性不同的情况下,液面会发生振荡,两侧壁面毛细高度也不相等,且液面振荡的幅度和两侧壁面毛细高度差都随着两侧壁面润湿性差异的增大而增大。基于能量转化分析,提出两侧壁面湿润性不同情况下纳米通道中毛细流动发生的条件以及毛细流动快慢的判别依据。研究结果加深了对纳米尺度下毛细流动机理的认识,并为相关工程应用提供理论参考。     

容器内角处流体界面特性与Surface Evolver程序适用性的研究

微重力条件下内角处液体行为的研究对于认识表面张力主导的液体行为, 预测和控制空间微重力条件下的液体位置、瞬时状态, 以及对空间流体进行有效的管理等方面都非常重要. 通过分析接触角与流体界面在容器内角处的接触线方向之间的关系, 并与Concus-Finn理论进行比较, 提出了内角处接触线、接触角和几何形状之间相互关联的机理, 并探讨了Concus和Finn等 的相关理论结果的物理内涵. 在此基础上, 进一步将内角处的相关理论结果与Surface Evolver程序得出的数值结果进行了比较, 指出当容器中的内角小于180°时, Surface Evolver程序通过自动划分网格即可比较准确地预言内角处的接触线和液面行为, 但是当内角大于180°时, 自动划分网格得到的数值结果有较大的误差, 需要通过手动划分网格减少网格奇异才能减小误差. 因此, 对于具有复杂几何形状的容器, 需注意网格的奇异性, 并对内角处的液面进行定量的验证, 才能有效判断Surface Evolver程序结果的正确性. 本工作对于深入认识内角处的液面特性和机理, 理解Surface Evolver程序的适用条件, 以及分析微重力条件下容器内角处的液体行为等方面都具有明显意义.     

关于变摆长的单摆运动与相关的铅直运动的耦合

研究了一个变摆长单摆运动的例子,在平面极坐标系下给出了描述该运动的二阶微分方程组.采用微分方程高精度数值解法得到了随时间变化的摆角、摆长、摆长变化率以及运动轨迹的数值精确解.在小摆角近似下,采用迭代方法推导出摆角、摆角变化率的一级近似解析表达式和摆长、摆长变化率的二级近似解析表达式.由解析表达式得到的数值结果与数值精确解相比较,二者在前几个摆动周期内相吻合.     

基于孔口出流模型的实验研究及理论分析

基于孔口出流模型对底部有小孔的圆柱体容器中液体液面高度随时间的变化规律进行了实验研究,并通过计入液体表面张力引起的孔口收缩和流体黏滞力导致的能量损失对实验结果进行了理论分析,与实验结果一致.     

毛细管探针法测定液体的表面张力系数

在毛细管法测定液体表面张力系数的实验中,利用被测液体导电的性质,在螺旋测微计的测微螺杆上沿轴线方向加装一根金属探针,通过电学方法探测毛细管内液面及容器内液面的位置,实现液体在毛细管内上升高度的测量.利用探针法分别测量了蒸馏水在几个不同温度下的毛细上升高度,利用瑞利公式计算表面张力系数.实验结果表明,探针法测量毛细上升高度的重复性好,所测得蒸馏水的表面张力系数与其公认值的百分误差约小于0.12%.     

微重力下圆管毛细流动解析近似解研究

应用同伦分析法研究微重力环境下圆管毛细流动解析近似解问题, 给出了级数解的表达公式. 不同于其他解析近似方法, 该方法从根本上克服了摄动理论对小参数的过分依赖, 其有效性与所研究的非线性问题是否含有小参数无关, 适用范围广. 同伦分析法提供了选取基函数的自由, 可以选取较好的基函数, 更有效地逼近问题的解, 通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度, 同伦分析法为圆管毛细流动问题的解析近似求解开辟了一个全新的途径. 通过具体算例, 将同伦分析法与四阶龙格库塔方法数值解做了比较, 结果表明, 该方法具有很高的计算精度. 关键词： 圆管 微重力 毛细流动 同伦分析法     

EHD sprayings induced by the pulsed voltage superimposed to a bias voltage

Effects of pulsed voltage superimposed on dc bias voltage and meniscus height on electrohydrodynamic (EHD) spraying were investigated. Results show that greater pulsed voltages were associated with jet formation while a dripping mode was apt to appear with a lower pulsed voltage. This is because that with increasing pulsed voltages the energy gain per unit area of the liquid and the tangential electric stress at the meniscus lateral were increased more quickly than the normal electric stress at the apex of the meniscus. Additionally, the increment of meniscus height led to an unchanged tangential electric stress at the meniscus lateral, but a more quickly increased energy gain per unit area of the liquid than the normal electric stress at the apex of the meniscus. For the same pulsed voltage, spraying in Dripping I mode was produced from menisci of smaller heights due to the intensive normal electric stress. A much greater meniscus height, on the other hand, led to spraying in Dripping II mode when the pulsed voltage was insufficiently great. These various modes were determined by contributions of the tangential electric stress, the normal electric stress and the meniscus height.     

Theoretical Study on the Capillary Force between an Atomic Force Microscope Tip and a Nanoparticle

Considering that capillary force is one of the most important forces between nanoparticles and atomic force microscope （AFM） tips in ambient atmosphere, we develop an analytic approach on the capillary force between an AFM tip and a nanoparticle. The results show that the capillary forces are considerably affected by the geometry of the AFM tip, the humidity of the environment, the vertical distance between the AFM tip and the nanoparticle, as well as the contact angles of the meniscus with an AFM tip and a nanoparticle. It is found that the sharper the AFM tip, the smaller the capillary force. The analyses and results are expected to be helpful for the quantitative imaging and manipulating of nanoparticles by AFMs.     

An asymptotic outer solution applied to the Keller box method

The Keller box method (“Numerical Solutions of Partial Differential Equations, Vol. 2” (B. Hubbard Ed.), pp. 327–350, Academic Press, New York, 1970) was applied to incompressible flow past a flat plate to demonstrate that the basic computation region must extend outward from the wall until the outer boundary conditions are effectively obtained. The Keller box method was modified to include an asymptotic outer solution for the case of the self-similar solution for compressible flow in a boundary layer. Initial application of the basic and modified Keller box methods to incompressible flow past a flat plate showed similar rates of convergence but smaller RMS error for the same basic range of the independent variable when the asymptotic outer solution is applied. Furthermore, extension of the solution beyond the range of the independent variable for the numerical solution using the resulting asymptotic solution produced RMS error at least as small as the RMS error on the range of the numerical solution. Also, when the asymptotic solution was applied, a smaller range of independent variables could be used in the numerical solution to obtain the same RMS error. Numerical results for compressible flow were qualitatively the same as for the case with the incompressible velocity profile except the rate of iterative convergence was slightly slower. Application of asymptotic outer solution for incompressible flow at a two dimensional stagnation point produced similar results with smaller relative improvements. For compressible flow with smaller favorable pressure gradients than the stagnation point and with adverse pressure gradients, significant improvements were again obtained. Examination of the errors associated with the asymptotic solution reveals that greatest success is obtained for flows with thicker boundary layers and shows that the boundary layer at a two dimensional stagnation point is too thin for small error in the asymptotic solution. Despite relatively large errors in the asymptotic solutions for boundary layer in strong favorable pressure gradients where the boundary layer is thin, the boundary layer solutions generally showed improvement in error and reduction in computation times.     

Micro-PIV measurements of capillary underfill flows and effect of bump pitch on filling process

Abstract  

This study is devoted to investigate the effects of the bump pitch on the capillary underfill flow. A micro particle image velocimetry (μPIV) system was used to visualize the flows and the shape of meniscus. Transparent flip chip specimens with quadrilateral bump arrangements were fabricated by etching silicon on glass wafer. Six bump pitches from 60 to 160 μm were tested and glycerin was dispensed to fill into the flip chip specimens. From the present experiments, it is shown that the overall filling speed becomes faster at larger bump pitch and changes abruptly when the bump pitch is twice the bump diameter. The detailed meniscus movement also has different behavior if the bump pitch gets smaller and larger than twice the bump diameter. The variation of dynamic contact angle is synchronized with that of the meniscus velocity throughout the whole process. During the interaction with the flip chip bumps, the contact line of the meniscus becomes concave or convex. The curvature of the concave and convex lines is larger at the smaller bump pitch.     

Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

A local domain-free discretization-immersed boundary method (DFD-IBM) is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form. Like the conventional immersed boundary method (IBM), the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object. The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points. To be specific, the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity. As compared to the conventional IBM, the present approach accurately implements the non-slip boundary condition. As a result, there is no flow penetration, which is often appeared in the conventional IBM results. The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder. The obtained numerical results agree very well with the data in the literature.     

用拉普拉斯变换差分法求解试井分析中的一维渗流问题

结合拉普拉斯变换和有限差分法给出求解试井分析中一维渗流问题的拉普拉斯变换差分法:首先对渗流方程采用拉普拉斯变换消去时间变量得到拉普拉斯空间数学模型,采用有限差分法求解拉普拉斯空间数学模型,最后通过拉普拉斯反演算法得到井底压力或产量.通过与有限差分法结果和解析解对比,拉普拉斯变换差分法比有限差分法计算误差小.虽然单步计算耗时长,但计算任意时刻结果时对空间网格的适应性和不依赖其它时刻计算结果的特性使得拉普拉斯变换差分法在试井分析中有非常好的应用前景.