Experimental Study on Liquid Free Surface in Buoyant-Thermocapillary Convection

We investigate the surface deformations of buoyant-thermocapillary convection in a rectangular cavity due to gravity and temperature gradient between the two sidewalls. The cavity is 52mm×42 mm in horizontal cross section, the thickness of liquid layer h is changed from 2.5 mm to 6.5 mm. Surface deformations of h = 3.5 mm and 6.0mm are discussed and compared. Temperature difference is increased gradually, and the flow in the liquid layer will change from stable convection to unstable convection. Two kinds of optical diagnostic system with image processor are developed for study of the kinetics of buoyant-thermocapillary convection, they give out the information of liquid free surface. The quantitative results are calculated by Fourier transform and correlation analysis, respectively. With the increasing temperature gradient, surface deformations calculated are more declining. It is interesting phenomenon that the inclining directions of the convections in thin and thick liquid layers are different. For a thin layer, the convection is mainly controlled by thermocapillary effect. However, for a thick layer, the convection is mainly controlled by buoyancy effect. The surface deformation theoretically analysed is consistent with our experimental results. The present experiment proves that surface deformation is related to temperature gradient and thickness of the liquid layer. In other words, surface deformation lies on capillary convection and buoyancy convection.     

Benard-Marangoni convection in two-layered liquids

We describe experiments on Benard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wave number of the pattern near onset agrees with the linear stability prediction for the full two-layer problem. The square planform is in qualitative agreement with recent two-layer weakly nonlinear theories, which fail however to predict the transition to rolls.     

A parallel computer implementation of the Asymptotic Numerical Method to study thermal convection instabilities

We have developed a numerical model to efficiently compute steady-state combined buoyancy and thermocapillary convection solutions. It features a parallel computer implementation of an Asymptotic Numerical Method to perform steady-state path-following and locate bifurcation points in problems involving large size algebraic systems, up to few million degrees of freedom. The model has been first validated on a problem for which a reference solution exists and then is used to analyse the influence of the container size and shape on Rayleigh–Bénard–Marangoni convection and its related cellular pattern.     

The onset of convection in a finite container due to surface tension and buoyancy

A method for predicting instabilities which combines recent techniques from bifurcation theory with the finite-element method is described. It is applied to the prediction of the onset of convection driven by both surface tension and buoyancy in rectangular containers. For zero buoyancy, the critical values of the Marangoni number for the first two bifurcations from the trivial solution are found for a two-dimensional cavity of aspect ratio 2. The variation of these critical values with aspect ratio is obtained by continuation methods and this reveals an interlacing of modes as the container size increases. It is established that the bifurcation to an even number of cells is transcritical rather than pitchfork and the turning point on the subcritical branch is located as a function of aspect ratio. The hysteresis associated with the transcritical bifurcation is small. As the surface tension forces decrease to zero, so that the convection is driven by buoyancy alone, the amount of hysteresis associated with the transcritical bifurcation becomes vanishingly small. The reason for this is not fully understood.     

Oscillatory convection in binary mixtures: Thermodiffusion,solutal buoyancy,and advection

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numerically obtained solutions of the field equations in the form of spatially extended relaxed traveling waves, of standing waves, and of the transient growth of standing waves and their transition to traveling waves are discussed as well as spatially localized convective states of traveling waves that are surrounded by the quiescent fluid.     

Surface tension effects in the zero gravity inflow of a drop into a fluid

As a drop of fluid is deposited on the surface of a miscible fluid (that we call the solvent), it undergoes a strong pulling due to its surface rupture and it acquires a kinetic energy independently of gravity. For the drop and the solvent being of the same fluid we observe a drop injection at an initial velocity which scales as the square root of the surface tension of the drop against air. Once injected, the drop develops a transverse instability giving rise to an expanding ring. Viscosity terminates the process and stops the ring. We show that the final ring height follows a scaling law whereas two asymptotical scaling regimes can be identified for the ring radius. Received 31 August 1999     

磁场对二元合金凝固过程中糊状层稳定性的影响

利用线性稳定性方法研究了外加磁场对二元合金凝固过程中糊状层稳定性的影响,且模型同时考虑了温度场、浓度场和流动的耦合作用.利用计算得出的色散关系式分析了磁场对糊状层稳定性的影响,其中包括直接模式和振荡模式.给出了不同情况下外加磁场对糊状层稳定性的影响,发现磁洛伦兹力可以减小由浮力引起的失稳效应.振荡模式下外加磁场对糊状层产生稳定作用,但直接模式下外加磁场对糊状层的稳定作用具有不确定性.本文所给出结果为工业中利用外加磁场改善产品的质量提供了重要的理论参考.     

Experimental Investigation of Influence of Interfacial Tension on Convection of Two-Layer Immiscible Liquid

Bdnard-Marangoni convections of two-layer fluids heated from the bottom are investigated experimentally with a particle imagine velocimetry. The flows are visualized from the side, and various velocity fields near the onset of convection, such as three-layer vortex convective patterns, are observed when the depth ratio varies in a wide range. A new classification of the convective patterns is proposed with more detail than in previous studies. The analysis of the results indicates that the interface tension greatly influences the motion intensities of the bottom and top layers. The dimensionless wave number increases with the Bond number when the motion in the top layer is not more intense than that in the bottom layer, which agrees with the theoretical prediction.     

Dynamics and stability of volume-scavenging drop arrays: Coarsening by capillarity

N drops, pinned by circular contact lines, are arranged in an array and coupled by a network of conduits. Inertialess exchange of volume among drops is driven by capillarity through the minimization of total surface energy. Drops scavenge volume from one another based on pressure differences, proportional to the surface tension, and arising from curvature differences. The system coarsens in the sense that, with time, volume is increasingly localized and ends up in a single ‘winner’ drop. Numerical simulations show that the identity of the winner can depend discontinuously on the initial condition and connectivity network. This motivates a study of the corresponding N-dimensional nonlinear dynamical system. All fixed points and their linear stabilities, obtained analytically, are found to be independent of connectivity. To determine which of the stable fixed points will be the winner, manifolds separating the attracting regions are found using a method which combines local information (eigenvectors at fixed points) with global information (invariant manifolds due to symmetry). This method is demonstrated for three N=3 systems with various connectivity networks, and is used to explain the numerical observations.     

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.     

Influence of the surface deformability and variable viscosity on buoyant - thermocapillary instability in a liquid layer

The primary stationary and oscillatory Bénard-Marangoni instability is investigated in a fluid layer of infinite horizontal extent, bounded below by a rigid plane and above by a deformable upper surface, subjected to a vertical temperature gradient. Since the viscosity is temperature-dependent the consequences of relaxing Oberbeck-Boussinesq approximation and free surface deformability are theoretically examined by means of small disturbance analysis. The problem has been solved numerically by the Taylor series expansion method. The results obtained confirm that when the free surface is undeformable, stationary convection develops in the form of polygonal cells, and oscillatory motion cannot be detected. When the surface deformability is considered, stationary convection sets in, either as a short-wavelength hexagonal instability or as a long-wavelengh mode or as both, and oscillatory convection is also possible. The stability threshold for the short-wavelength mode depends mainly on the viscosity variation while the long-wavelength mode is determined by the surface deformation. Numerically, it is found that the neutral oscillatory Marangoni numbers are only negative. When a variable-viscosity model is used the theoretical and experimental results are in better agreement. Received 15 May 1997     

Instabilities of thermocapillary-buoyancy convection in open rectangular liquid layers

This article presents the experimental investigation on instabilities of thermocapillary-buoyancy convection in the transition process in an open rectangular liquid layer subject to a horizontal temperature gradient. In the experimental run,an infrared thermal imaging system was constructed to observe and record the surface wave of the rectangular liquid layer. It was found that there are distinct convection longitudinal rolls in the flow field in the thermocapillary-buoyancy convection transition process. There are different wave characterizations for liquid layers with different thicknesses. For sufficiently thin layers, oblique hydrothermal waves are observed, which was predicted by the linear-stability analysis of Smith Davis in 1983. For thicker layers, the surface flow is distinct and intensified, which is because the buoyancy convection plays a dominant role and bulk fluid flow from hot wall to cold wall in the free surface of liquid layers. In addition, the spatiotemporal evolution analysis has been carried out to conclude the rule of the temperature field destabilization in the transition process.     

Role of Convection Flow on the Pattern Formation in the Drying Process of Colloidal Suspension

We study the macroscopic drying patterns of aqueous suspensions of colloidal silica spheres. It was found that convection strength can influence pattern formation. Uniformed films are obtained at weaker convection strength. In addition, we make clear that it is not reasonable to discuss individually the effect of temperature and humidity on the colloid self-assembly. The physical mechanism is that these factors have relationship with the evaporation rate, which can affect the convection strength.     

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.     

Surface tension driven flow on a thin reaction front

Surface tension driven convection affects the propagation of chemical reaction fronts in liquids. The changes in surface tension across the front generate this type of convection. The resulting fluid motion increases the speed and changes the shape of fronts as observed in the iodate-arsenous acid reaction. We calculate these effects using a thin front approximation, where the reaction front is modeled by an abrupt discontinuity between reacted and unreacted substances. We analyze the propagation of reaction fronts of small curvature. In this case the front propagation equation becomes the deterministic Kardar-Parisi-Zhang (KPZ) equation with the addition of fluid flow. These results are compared to calculations based on a set of reaction-diffusion-convection equations.     

旋转环形浅液池内双组分溶液耦合热-溶质毛细对流渐近解

为了了解水平温度梯度作用下旋转环形浅液池内耦合热-溶质毛细对流基本特征, 采用匹配渐近展开法对旋转环形浅液池内耦合热-溶质毛细对流过程进行了求解, 获得了中心区域的速度、温度和浓度分布,分析了旋转、Soret效应、浮力、溶质扩散 系数和液池的几何尺寸对流动结构的影响.将所得到的渐近解和文献中的已有结果进行对比,证明了所求结果的正确性;在浅液池内,耦合热-溶质毛细力对流体流动起主导作用, 旋转和浮力对流动的影响较小,溶质扩散系数和几何尺寸有较明显影响;当各种耦合的 驱动力作用方向相同时,流动增强;否则, 流动减弱. 关键词： 旋转 环形浅液池 耦合热-溶质毛细对流 渐近解     

Rheological flow from a die and painting on a moving solid wall

1IntroductionThemanufacturesoffluidfilmandpolymerrequireanunderstandingofthehydrodynamicprocess[1,2].Theenlargedcross-sectionofthefluidjetwasobservedinthepolymerprocessing,wherethedieswellisanimportantphenomenon.TheSwellorDieSwelleffectisexplainedusuallybyrheologicalpropertiesoftheliquidmedium.TannersuggestedatheoryofDie-Swell,andassumedthatthevelocityvectorhasonlyonecomponentalongthejet[3].Becauseofthenon-uniformityofthecross-section,theflowfieldintheDie-Swelltheoryshouldbeatleasttwo-dime…     

大尺度环形液池内双层热毛细对流不稳定性

假设双层流体的交界面不发生变形,热毛细力作用于此交界面,三维数值研究了大尺度环形液池中双层流体系统在内外壁面温差加热下的热毛细对流不稳定性,其中外壁面维持高温,内壁面维持低温。计算结果显示,上下层流体的流动特性受Marangoni效应和浮力效应的影响;热毛细对流的振荡产生于内壁面附近,并沿着温度梯度的方向传播;随着温差的增大,热毛细对流的振荡逐渐增强,温度振荡波数增大。     

磁场对水平温度梯度下双层流体热对流的影响

在水平温度梯度下,双层流体交界面的表面张力会出现梯度,驱动热毛细对流运动,造成热剪切层内的扰动.本文数值模拟了不同重力条件下,双层流体内的对流现象,得出了在微重力时,对流运动将引起热剪切层内强烈的扰动.为了减弱这种扰动,我们利用磁场对流体的运动进行控制.为此,又对微重力条件下,不同方向应用磁场下的热剪切层内扰动行为进行了数值研究,结果显示,磁场对热剪切层稳定性有促进作用,加入法向的应用磁场最为有效.