Temperature pulsations and thermocapillary effects on the surface of a wavy heated liquid film

The temperature pulsations and wave characteristics in water film flow along a vertical plate with a heater are investigated. Using an infrared scanner, the temperature field on the film surface is measured for various heat flux densities on the heater. Experimental data on the variation of the temperature with time on a local segment of the liquid film surface during wave transmission are obtained. In the absence of a heat flux the data obtained are in good agreement with the results of other researchers for an isothermal liquid film. When the down-flowing liquid is heated, the thermocapillary forces lead to the formation of rivulets and a thin film between them. It is shown that in the inter-rivulet zone the relative wave amplitude increases due to the action of the thermocapillary forces.     

Effect of Thermocapillary Forces on the Initial Section of a Melt Film

The previous analysis of fields near the upper triple point of the floating–zone melting process is supplemented by the analysis of thermocapillary forces on the melt surface. It is shown that the effect of these forces is large in the general case, and a melt film with a macroscopic radius of curvature may be formed only if the temperature gradient over the melt surface and thermocapillary forces are small; in this case, the angular coordinates of the melt–film cross section are also small.     

Study of the thermocapillary effect on a wavy falling film using a fiber optical thickness probe

The wave flow of a water film down a vertical plate with a 150×150 mm heater has been experimentally studied. The effect of the heat flux on the film flow leads to the formation of periodically flowing rivulets and thin film between them due to the action of thermocapillary forces in spanwise direction. The local film thickness between rivulets is measured by means of a noncontact fiber optical probe. As the heat flux grows, the average film thickness continuously decreases but upon reaching about 50% of the initial thickness, the film spontaneously breaks down. It is found that the decrease of the wave amplitude between rivulets is caused by the reduction of the local Reynolds number and is in a qualitative agreement with the laws of the hydrodynamics for the isothermal case. That is, no appreciable effect of streamwise thermocapillary forces on the wave amplitudes is detected. The experimental results are in good agreement with recently published data obtained by the capacitance method.     

Computational analysis of convective instabilities in a liquid layer subjected to an inclined gradient of temperature

A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.     

Motion of a drop with allowance for thermocapillary forces

A study is made of the motion of a drop in a viscous medium of nonuniform temperature when the dependence of the surface tension on the temperature at the interface of the two media gives rise to additional tangential stresses leading to thermocapillary convection in fluids. The motions of a spherical drop and a deformed drop (when the surface of the drop is determined in the process of finding the solution) are considered. The shape of the drop surface is calculated for different values of the parameters of the problem. Dependences are obtained for the Reynolds number of the thermocapillary drift of drops in the absence of body forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 80–86, July–August, 1982.     

Hydrodynamics in weak force fields onset of steady thermocapillary convection in a spherical fluid layer under zero-g conditions

In the study of cellular convection in an infinite plane fluid layer with a free surface, both the Archimedes and thermocapillary forces [1–3] have been cited as reasons for the onset of convection. This has also been confirmed experimentally [4], When mass forces are absent or negligibly small it is natural to pose the question of the onset of pure thermocapillary convection or convection caused only by the surface tension gradients (see [2–3]). In the present paper, this problem is examined for a spherical fluid layer under zero-g conditions.     

Unsteady thermocapillary convection in a nonuniformly heated fluid layer

In many technological processes, thin extended layers of nonuniformly heated fluid are used [1–3]. If they are sufficiently thin, thermocapillary forces have a decisive influence on the occurrence and development of motion of the fluid [4–6]. Investigation of convective motion in such a layer is of great interest for estimating the intensity of heat and mass transfer in technological processes. This paper is a study of unsteady thermocapillary motion in a layer of viscous incompressible fluid with free surface in which a thermal inhomogeneity is created at the initial time. Approximate expressions are obtained for the fields of the velocity, temperature, and pressure in the fluid, and also for the shape of the free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1991.     

Experimental study of Marangoni bubble migration in normal gravity

Marangoni convection, whether thermal or solutal, is known to have a profound impact on many technological processes involving gas inclusions in a liquid phase. Evidently, similar phenomena may arise both in thermocapillary and solutocapillary situations, due to similarity of the motion driving mechanisms. However, the fact that the characteristic times of heat and surfactant diffusion generally differ by several orders of magnitude lends singularity to the behavior of Marangoni convection in inhomogeneous mixtures. Moreover, in the solutocapillary case one can meet the action of some additional effects associated with dissolution of the surfactant in a liquid, its adsorption at the interface and evaporation into a gas phase. This paper presents a comparative analysis of the results of ground experiments studying the behavior of air bubbles in a liquid under the action of thermocapillary and solutocapillary forces. The use of original experimental techniques makes it possible to eliminate the influence of gravity effects. A new Marangoni phenomenon—solutocapillary bubble migration—was detected and investigated. The results of studying thermal and concentration convective flows and bubble motion, in relation to bubble size, time, liquid layer thickness and fluids properties, are presented and discussed.     

半浮区热毛细对流的不稳定性与转捩

近二十年来,微重力流体开展了半浮区液桥热毛细对流的不稳定性与转捩的研究．文中给出了热毛细振荡对流发生的临界参数,分析了液桥几何位形（尺度比,体积比）、物理参数及传热参数对临界Ｍａｘａｎｇｏｎｉ的影响．报导了有关的地面模拟实验,微重力实验以及本问题的线性稳定性分析、能量分析和数值模拟结果,并介绍了定常轴对称热毛细对流通过非定常振荡热毛细对流到湍流的转捩过程和三种热毛细振荡对流的产生机理．     

半浮区液桥热毛细振荡流

采用非定常、三维直接数值模拟方法研究大Pr数半浮区液桥热毛细对流从定常流向振荡流的过渡过程．文中详细描述了热毛细振荡流的起振和振荡特征,给出了液桥横截面上振荡流的流场和温度分布．在地面引力场条件下计算的结果与地面实验的结果进行比较,得出液桥水平截面上的流场和温度分布图样以一定的速度旋转,自由表面固定点处流体的环向流速正、负交替变化的一致结论．     

热毛细对流温度场ESPI检测研究

在地面上用二维液体盒研究了热壁下气泡周围液体中的热毛细对流现象,并应用电子散斑干涉技术（ESP）对热毛细对流温度场进行了实时检测研究,给出了部分典型的实验结果。     

A proposed mechanism for hydrodynamically-controlled onset of significant void in microtubes

Data and analysis have shown that bubble nucleation and ebullition phenomena in microchannels are different than in large channels. The macroscale models and correlations often fail to predict data representing bubble ebullition processes in microchannels. It is hypothesized here that hydrodynamically-controlled onset of significant void in microchannels is due to bubble departure from wall cavities, and the latter process may be controlled by thermocapillary and aerodynamic forces that act on the bubble. Accordingly, the limited available relevant experimental data are semi-analytically modeled, and the soundness of the proposed hypothesis is shown.     

Objective function choice for control of a thermocapillary flow using an adjoint-based control strategy

The problem of suppressing flow oscillations in a thermocapillary flow is addressed using a gradient-based control strategy. The physical problem addressed is the “open boat” process of crystal growth, the flow in which is driven by thermocapillary and buoyancy effects. The problem is modeled by the two-dimensional unsteady incompressible Navier–Stokes and energy equations under the Boussinesq approximation. The goal of the control is to suppress flow oscillations which arise when the driving forces are such that the flow becomes unsteady. The control is a spatially and temporally varying temperature gradient boundary condition at the free surface. The control which minimizes the flow oscillations is found using a conjugate gradient method, where the gradient of the objective function with respect to the control variables is obtained from solving a set of adjoint equations. The issue of choosing an objective function that can be both optimized in a computationally efficient manner and optimization of which provides control that damps the flow oscillations is investigated. Almost complete suppression of the flow oscillations is obtained for certain choices of the objective function.     

热毛细对流温度场全息干涉检测研究

本文采用Ｈｅｌｅ－Ｓｈａｗ盒体,在地面上模拟二维热毛细对流,应用全息干涉技术对热毛细对流温度场进行了测试研究,为了获得感兴趣的热毛细对流温度增量分布,文中提出了将背景温度分布条纹与热毛细对流温度增量分布条纹相分离的方法。     

Marangoni convection in molten salts Physical modelling toward lower Prandtl numbers

Marangoni convection is involved in many technological processes. The substances of industrial interest are often governed by diffusive heat transport and their physical modelling is limited with respect to the Prandtl number Pr. The present paper addresses this deficiency. Studies were made on molten salts having Pr values in an intermediate range well below that of the typically employed organics. Since some of the selected species have a relatively high melting point, a high-temperature facility which allows studying thermocapillary convection at temperatures in excess of 1,000°C was built. The results presented here were obtained in a cylindrical geometry, although the equipment that was built is not restricted to this configuration because of its modular construction. Modelled after some applications, the fluid was heated centrically on top. The bulk was embedded in a large thermostatically controlled reservoir so as to establish the lower ambient reference temperature. A characteristic size of the experimental cell was chosen such that, on the one hand, the dynamic Bond number Bo did not become too high; on the other hand, the liquid had to have a certain depth to allow particle image velocimetry. The complicated balance between body forces and thermocapillary forces in the case of intermediate Bo was found to result in a distinct local separation into a bulk motion governed by natural convection with a recirculating Marangoni flow on top. In contrast to low viscosity organics, the vapour pressure of which increases considerably with decreasing Pr, high values of the Marangoni number can be reached. Comparisons of the topology of Marangoni vortices between molten salts with 2.3 ⩽ Pr ⩽ 6.4 and a silicone oil with Pr typically one order of magnitude higher suggest that the regime of non-negligible heat diffusion is entered.     

The three-dimensional stationary instability in dynamic thermocapillary shallow cavities

In various configurations with thermal convection, three-dimensional stationary patterns occur that consist of pairs of counter-rotating longitudinal rolls. These rolls are investigated in this paper under a variety of experimental conditions. The liquids used are ethanol and the silicone oil hexamethyldisiloxane. The upper surface of the liquid volume is free and very flat because measures against menisci at the side and end walls have been taken. The temperature gradient is applied horizontally via thermally conducting but transparent sapphire end walls, leading to thermocapillary forces at the free surface in addition to the buoyant forces at normal earth's gravity. The geometry of the liquid volume is either rectangular or axisymmetrical (annular). The rectangular set-up is transparent and especially suited for optical observations of tracers in the bulk of the liquid. The annular set-up has the advantages of a large azimuthal (transversal) extent and the absence of side walls. In it a wavelength of λ≈1.3d was observed (where d is the depth of the liquid volume). Temperatures and velocities are measured and used to characterize the instability. Also the region of existence of the instability is studied in layers shallower than in earlier experiments in order to give a larger ratio between thermocapillary and buoyant forces. To find the onset of the instability when increasing the temperature gradient, the amplitude of the instability was derived from measurements and extrapolated. This yields a significantly lower threshold (Ma^c=2300 ± 1000 for d=5 mm) than previous experimental studies. One implementation of the annular gap experiment was performed under microgravity (experiment MAGIA), the other experiments under normal gravity. The results of the experiment under microgravity indicate the absence of the three-dimensional stationary pattern under the absence of gravity. Received: 14 August 2000/Accepted: 17 April 2001     

液滴热毛细迁移问题的研究进展

液滴或气泡的迁移现象无论是在流体力学的基础研究中,还是在材料加工,化学工程等实际应用中都是一个很重要的课题。在微重力环境中,如果在液滴或气泡所在的母液中外加一个温度场,则液滴或气泡就会由于表面张力分布的不均匀而发生迁移运动。这种运动被称为Marangoni迁移或热毛细迁移运动。本文综述了液滴或气泡的热毛细迁移问题历史研究中理论分析,数值模拟以及实验方面的主要结果,阐述了该问题的研究发展过程。目前液滴迁移问题的研究状况,理论分析解还只限于线性及弱非线性的定常问题,数值模拟工作已经得到了在热对流作用比较小的时候液滴的非定常迁移过程,但是对于热对流影响很大的情况(Marangoni数大于100)则尚未得到过与实验中观测到的相一致的理论结果。本文在总结前人研究的基础上,同时给出了在对于热对流作用较大时液滴热毛细迁移非定常问题的最新的数值模拟的结果,并对该问题在此情况下产生的新的变化也给予了分析。最后,文中分析了当前研究中所存在的问题并进一步展望了液滴热毛细迁移问题在未来的发展方向。      

Thermocapillary instability of the equilibrium of a flat layer containing internal heat sources

In the absence of body forces, a factor which has a strong influence on the equilibrium stability of a nonuniformly heated liquid is the dependence of the coefficient of surface tension on the temperature and the thermocapillary effect generated by it. If the equilibrium temperature gradient is sufficiently great, then the presence of the thermocapillary forces on the free surface can lead to the occurrence of convective motion. The monotonie instability of the equilibrium of a flat layer was investigated in [1–3]. Analysis of nonmonotonic disturbances [4] showed that in the case of an undeformable free surface there is no oscillatory instability. In [5] it was found that oscillatory instability is possible if there is a nonlinear dependence of the coefficient of surface tension on the temperature. The present paper is devoted to numerical investigation of the equilibrium stability of a flat layer with respect to arbitrary disturbances. It is shown that for a deformable free boundary there appears an additional neutral curve, which corresponds to monotonie capillary instability. In addition, when the capillary convection mechanism is taken into account, there appears an oscillatory instability, which becomes the most dangerous in the region of small Prandtl and wave numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–31, March–April, 1991.I thank V. K. Andreev for a helpful discussion of the work.     

Three-dimensional numerical simulation of thermocapillary flow in a shallow cylindrical pool

In order to understand the characteristics of thermocapillary flow, we conducted a series of unsteady three-dimensional (3D) numerical simulations of thermocapillary flow for fluids with Prandtl number Pr = 0.011 and 1.0 in a shallow cylindrical pool with an azimuthal temperature non-uniform, an adiabatic solid bottom and free surface. The simulation results indicate that thermocapillary flow is steady 3D flow at the small temperature non-uniform. When temperature non-uniform exceeds some critical value, the flow will undergo a transition to 3D oscillatory flow, which is characterized by traveling oscillatory wave reversely along the flow direction on the free surface and diffusing to two sides at the same time. Further, the critical conditions for the flow transition are determined.     

基于POD-Galerkin降维方法的热毛细对流分岔分析

作为流动与传热相互耦合的非线性过程, 热毛细对流有着复杂的转捩过程, 探究流场和温度场随参数变化而发生的分岔现象, 是热毛细对流研究的一个重要课题. 基于本征正交分解的POD-Galerkin降维方法可以通过提取特征模态, 构建低维模型, 实现流场的快速计算. 数值分岔方法可以通过求解含参数动力系统的分岔方程, 直接计算稳定解和分岔点. 探究了将直接数值模拟方法、POD-Galerkin降维方法、数值分岔方法的优势结合, 以提高热毛细对流转捩过程分析效率的可行性. 利用直接数值模拟得到的流场和温度场数据, 构建了不同体积比下, 二维有限长液层热毛细对流的POD-Galerkin低维模型, 在低维模型上采用数值积分及数值分岔方法计算了分岔点, 得到了低维方程的分岔图. 在一定参数范围内, 在低维模型上模拟热毛细对流, 对雷诺数和体积比进行参数外推, 通过与直接数值模拟的结果对比, 验证了低维模型的准确性与鲁棒性. 说明了低维方程可以定性反映原高维系统的流动特性, 而定量方面, 由低维模型和直接数值模拟计算得到的周期解频率的相对误差大约为5%. 验证了利用POD-Galerkin降维方法研究热毛细对流的可行性.