一类Marangoni对流边界层方程的近似解析解

利用Adomain解析拆分和Padé逼近方法对由Marangoni对流诱发的层流边界层问题进行了研究, 提供了一种求解边界层方程的解析分析方法. 得到了问题的近似解析解并对相应的流动及传热特性进行了探讨. 本文所提出的思想方法可以用于解决其他科学和工程技术问题. 关键词： Marangoni对流 非线性 Adomain拆分法 近似解析解     

一类带限定变换的二阶耦合线性微分方程组的解析解

用函数和方程变换将二阶耦合线性微分方程组转化为一阶非线性类椭圆方程，并给出了一次和二次限定变换下方程组的Jacobi椭圆函数解析解，所得结果修正了文献中超导特例的近似解，进一步肯定了超导边界层电场的存在性. 关键词： 微分方程 Jacobi椭圆函数 解析解 超导     

一类非线性微分方程的近似解析解

从理论上研究了一类广义扩散方程的求解问题. 利用相似变换和解析拆分技巧给出了求解该类非线性微分方程近似解的一种有效方法, 方程的解可以表示为一个收敛的幂级数. 近似解结果和数值结果非常符合，证明了所提出的方法的准确性和可靠性, 该方法可以用于解决其他科学和工程技术问题. 关键词： 广义扩散方程 非线性边界值问题 解析拆分 近似解析解     

强阻尼广义sine-Gordon方程特征问题的变分迭代法

研究了在数学、力学中广泛出现的一类非线性强阻尼广义sine-Gordon扰动微分方程问题. 首先, 引入行波变换, 求出退化方程的精确解. 再构造一个泛函, 创建了一个变分迭代算法, 最后, 求出原非线性强阻尼广义sine-Gordon扰动微分方程问题的近似行波解析解. 用变分迭代法可得到的各次近似解, 具有便于求解、精度高等特点. 求得的近似解析解弥补了单纯用数值方法的模拟解的不足.     

稳态问题混合边界积分方程的高精度求积法与分裂外推

提出了求积法解稳态问题的混合边界积分方程,它拥有高精度,低复杂度.通过并行地解粗网格上的离散方程,根据误差的多参数渐近展开,应用分裂外推算法得到高精度的近似解,同时获得后验误差估计.     

一个全球气候非线性振荡模型的近似解

研究了一个全球气候的非线性模型. 利用摄动理论和方法, 构造了相关问题解的渐近展开式, 该问题解的渐近展开式具有较高的近似度. 摄动渐近方法是一个解析方法, 得到的解还能够继续进行解析运算. 关键词： 非线性 摄动 全球气候     

Hulthén势任意l波束缚态的近似解析解

在任意l波的离心项1/r2用δ2e-δr/(1-e-δr)2近似表达的条件下,对Hulthen势的径向Schrodinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthen势任意l波束缚态的解析解.给出了解析的能谱方程和用超几何多项式表示的归一化的径向波函数,讨论了近似解析解的意义.     

单胶子交换梯形近似下Bethe-Salpeter方程赝标解

将在动量空间具有积分形式的单胶子交换梯形近似下Bethe-Salpeter方程化为微分方程,求出该方程在四动量为零时的赝标解全部分量,其中第一分量为已知的Goldstein解.     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .应用Jacobi椭圆函数展开法求得了零级近似方程的准确解 ,并由此得到一级近似方程和二级近似方程分别满足齐次Lam 方程和非齐次Lam 方程 ,应用Lam 函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解 .这样 ,就求得了非线性演化方程的多级准确解 .     

经典物理中的扰动时滞模型解

利用边界层函数法研究了一类经典物理中的扰动时滞模型. 构造了模型解的渐近表达式, 并讨论了它的渐近性态. 关键词： 经典物理 扰动 近似解     

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.     

基于Level Set方法的双层流体热毛细对流的数值研究

基于Level Set方法建立了双层流体热毛细对流的数学模型,通过变密度二阶投影法求解控制方程,C-N隐式技术用于扩散项更新,三阶龙格库塔技术用于对流项的更新,采用连续表面张力模型(CSF)模拟Marangoni效应。三维数值模拟了微重力环境下双层流体系统中交界面变形的热毛细对流,结果显示,在Marangoni效应的作用下,交界面在热端凸起,在冷端凹陷;随着Marangoni数增大,双层流体交界面的变形率随之增大,对流强度也随之增大;交界面与壁面的接触条件会影响热毛细对流的流场和温度场。     

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.     

微重力条件下熔-固相变对流与浮区对流的耦合

本文以空间材料生长为背景,用有限元法研究微重力条件下的浮区单晶生长过程,考虑了表面张力对流与浮区对流的耦合作用,计算了凝固界面形状,结果表明,晶体的生长速度是个重要的影响因素,生长时,单晶-熔体界面比多晶-熔体界面更倾斜;当生长速度超过临界值时,多晶-熔体界面附近的Marangoni涡会分裂出二次涡。 关键词：     

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.     

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.     

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     

绕汽柱热毛细对流的数值模拟

本文建立了一个在常重力及微重力情况下绕汽柱热毛细对流的数学模型,并采用有限差分法来积分非稳态动量方程和能量方程,得到了不同参数下热毛细对流的数值解．通过数值模拟,得到了不同参数下热毛细对流的速度矢量场,了解了有关无量纲参数对热毛细对流的影响规律．得出结论：热毛细对流不仅在微重力条件下存在,即使在重力场中,在特定情况下也是不能忽略的。     

Influence of substrate conductivity on circulation reversal in evaporating drops

Nonuniform evaporation from sessile droplets induces radial convection within the drop, which produces the well-known "coffee-ring" effect. The evaporation also induces a gradient in temperature and consequently a gradient in surface tension, generating a Marangoni flow. Here we investigate theoretically and experimentally the thermal Marangoni flow and establish criteria to gauge its influence. An asymptotic analysis indicates that the direction of the flow depends on the relative thermal conductivities of the substrate and liquid, k_{R} identical withk_{S}/k_{L}, reversing direction at a critical contact angle over the range 1.45相似文献   

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.