Attempt to study Marangoni flow of low-Pr-number fluids using a liquid bridge of silver

In order to experimentally investigate the Marangoni flow of low-Prandtl-number fluids in a liquid bridge geometry under the condition of small Marangoni numbers close to the critical Marangoni numbers Ma_c1 and Ma_c2, the formation of a liquid bridge of silver was attempted. The available temperature difference between the upper and lower rods to obtain a small Marangoni number, such as Ma = 50, was calculated for a 5 mm high liquid bridge for several molten metals. For molten silver, the possible temperature difference was estimated to be 16 K, whereas, for molten silicon, this was 0.38 K, which is unrealistic for the purposes of experiments. For silver, a free surface can be obtained in the wide range of oxygen partial pressures, whereas, for molten silicon, the available oxygen partial pressure range is very small; equilibrium oxygen partial pressure for SiO₂ formation is as low as 1.1 × 10⁻¹⁴ Pa. A liquid bridge of molten silver was successfully prepared and temperature oscillation was observed; the estimated Marangoni number was 160 and oscillation frequency was 0.26 Hz.     

Thermocapillary-driven convection in supported and floating-zone crystallization

Marangoni flow was induced in a thin disk of molten tin with an atomically clean surface by heating it from below in an ultra high vacuum apparatus. The radial distribution of temperature was measured and no temperature oscillations were observed. Strong mechanical disturbances introduced at a Marangoni number of about 4300 died out quickly with time indicating that the system was stable. Mathematical models indicate that strong flows in a two cell structure exist under the conditions studied, and that the velocity profile in the cell near the surface is of the bouindary layer type which varies rapidly with depth.     

Correlation of oscillations of flow and temperature in floating zone under microgravity

The correlation between oscillations of flow and temperature of the Marangoni convection in a cylindric floating zone are studied. Photographs of the oscillating flow patterns are taken by triggering with a thermocouple signal of the temperature oscillation to reveal the frequency and phase correlations. Whilst both frequencies coincide, phase shift between temperature and flow oscillations exists.     

Onset of Marangoni convection in an infinite layer of an electrically conducting liquid under magnetic field

The onset of Marangoni convection in an electrically conducting liquid is studied theoretically for the case that the liquid is subjected to a vertical temperature gradient and a magnetic field with arbitrary orientation.The effects of the intensity of magnetic field, the angle of inclination of magnetic field and the Biot number at the free surface on both the critical Marangoni number and the flow pattern are made clear.     

微重力环境下蒸发液层热毛细对流的数值模拟

提出了一种新模型来研究由单一物质构成的液层在其纯蒸气中的蒸发.液层置于微重力环境中并且受到水平方向温度梯度的作用,液层的热毛细对流和蒸发耦合在一起,使得气液界面的传热传质规律更加复杂.用理论分析的方法求解了不考虑热毛细效应的纯蒸发模型,得出温度场分布和界面质量流量的解析表达式.对于热毛细对流和蒸发耦合情况,采用有限差分的投影算法同时求解Navier-Stokes方程和能量方程,得到了不同蒸发Biot数和Marangoni数下流场和温度场的稳态数值解.论述了蒸发Biot数和Marangoni数对界面传热传质的影响,提出并解释了蒸发和热毛细对流耦合的三种模式.      

Thermocapillary migration of bubbles and droplets

The migration of a droplet in a large liquid body possessing a uniform temperature gradient is analyzed in the creeping flow limit for small values of the Marangoni number (ε). The method of matched asymptotic expansions is used for the solution of the field equations. The migration velocity is calculated to 0(ε²) and the result reduces to that of Young, Goldstein and Block [10] in the limit of zero Marangoni number.     

热毛细对流模式转换及温度振荡特征

研究了矩形液池中由于两端温差引起的热毛细对流的温度振荡临界条件.在实验室中,设计了一个高分辨率的温度测量系统,用于实时观测并记录流体的温度.该系统主要由热电偶温度传感器、纳伏表和数据采集电脑3部分组成.得到了各种实验条件下温度振荡的临界条件,并且讨论了它与Prandtl数和Bond数之间的关系.利用flow3d软件数值模拟了微重力条件下的热毛细对流,发现了一种由于自由面变形和液层流场相互作用导致的晃荡的现象.     

环形浅液池内低Prandtl数流体超临界热毛细对流演化

为研究低Prandtl数（Pr）流体热毛细对流演化过程，对环形浅液池内Pr=0.011的流体热毛细对流进行三维数值模拟.研究发现:当Marangoni数较小时，流动为轴对称稳态流动；当Marangoni数超过某一临界值后，流动失稳并转变为热流体波，其波数随Marangoni数增加而减小，而波动主频增大；随着Marangoni数增加，流动加强，沿周向运动的热流体波演变为沿径向运动的径向波，其波数大大减小；当Marangoni数继续增加时，波动频谱曲线噪声增加，呈广谱特性.因此，在计算范围内热毛细对流的演化过程为:轴对称稳态流动-热流体波-单周期径向波-多周期三维振荡流动.      

A sounding rocket experiment on the marangoni convection

During a 6-minutes free flight of a sounding rocket an experiment on the thermal Marangoni convection in a right circular cylindric floating zone was carried out to verify the thermal Marangoni convection by flow visualisation for the first time at 10^?4 g. From the motion picture analysis the velocity distributions are obtained. The interdependence between the two velocity maxima and the S-shaped temperature distribution on the free surface is discussed. The influence of the heat transfer caused by the flow of the surrounding air induced by the thermal Marangoni convection itself is considered briefly.     

Upwards migration phenomenon on molten lunar regolith: New challenges and prospects for ISRU

As part of our research on the feasibility of producing commodities from lunar regolith by thermal-driven processes with minimal terrestrial precursors we need to characterize, reproduce, and understand thermophysical properties of the molten regolith still unforeseen under the lunar vacuum conditions at a scalable sample size. Two unanticipated phenomena, apparently caused by lunar melt’s surface tension under vacuum, have been revealed in our research work, vacuum void formation and upwards migration. In this paper we present our findings and thinkable explanation on the upwards migration phenomenon experimentally observed and consistently replicated as JSC-1A lunar regolith simulant melted at high vacuum. Upwards migration of molten lunar regolith will make future lunar ISRU’s melting processes both challenging as molten bulk material would migrate upwards along the container’s walls, and also promising on new opportunities for alternative ISRU’s sustainable processes as regolith’s upwards migration takes place in uniformed thin-film pattern. Among the potential ISRU’s processes that might use controlled thermal thin-film-based migration without the necessity of terrestrial precursors are production of feedstock for 3D printing, fractional separation of regolith’s component’s (O₂, metals, and alloys) via pyrolysis, film coating, purification of valuables solid crystals including silicon, and fabrication of key elements for microfluidic, and MEMS devices. Thermal upwards migration phenomenon on JSC-1A’s melt is formulated and explained by the authors as due to thermal Marangoni effect (also known as thermo-capillarity) in which temperature gradients within the melt’s bulk and along the crucible’s wall yield the surface tension large enough to supersede the gravitational force and yield the experimentally observed upwards thin-film migration. As far as the authors know, upwards thermal migration of molten JSC-1A (or other lunar simulant regolith) under vacuum has not been reported in the literature. A thermal mathematical model accounting for thermal Marangoni effect on molten JSC-1A agrees with what experimentally was observed, the formation of the meniscus on the melt-wall surface interface along with an incipient upwards migration in thin-film pattern along the crucible wall that, according to the model, experiences large temperature gradient, an important factor to trigger the thermal Marangoni effect along with the fact that surface tension of the molten lunar regolith material is temperature dependent.     

Marangoni convection in a liquid layer under the simultaneous action of a transverse magnetic field and rotation

Asymptotic stability characteristics with respect to the onset of Marangoni convection in a liquid layer under the simultaneous action of a large transverse magnetic field and a large rate of rotation are investigated. In certain parameter ranges there is a decrease in critical Marangoni number for increasing magnetic field and rotation depending on the coupling between interfacial perturbations and rotation.     

Improvement of flight hardware and isothermal Marangoni convection under micro-gravity conditions

During parabolic flights three different kinds of experiments were performed under reduced gravity conditions. The experiments were: I. A general learning process to work with hardware and fluid under micro-gravity conditions. II. The investigation of critical parts of hardware or critical moments in experiments. This can be a part in the preparation of future sounding rocket or Spacelab flights. III. The possibility to perform scientific experiments under micro-gravity conditions within 22 seconds. In the joined parabolic flights of march 1986 the main interest was to perform experiments with Marangoni convection due to concentration gradients along the gas-liquid interface under isothermal conditions. One experiment was performed with a horizontal surface tension gradient and the other observed Marangoni convection was due to the evaporation of a component from a solution under steady state conditions.     

Recent development of Marangoni flows theory and experimental results

Microgravity fluid dynamics deals with the thermodynamics and dynamics of fluid systems in low-gravity environments and, thus, covers a rather large variety of subjects /1/. Among them, free convection in systems with fluid-fluid interfaces has received renewed attention because these systems are found in many materials sciences processes and exhibit a number of new, interesting phenomena. This paper surveys some recent studies by the author and his coworkers on the free convection occurring in a system of two interfacing, immiscible fluids subject to an imposed temperature gradient in a gravity environment. In such a system, three classes of free convection may be distinguished: natural, Marangoni, and combined free convection, according to whether it is caused by thermally induced buoyant forces, Marangoni stresses, or both. For each class one may further distinguish different regimes according to the relative importance of convective and diffusive transport of momentum and internal energy.First, the use of order of magnitude analysis is illustrated to identify and determine the types of flow regimes that can be established for each class of free convection. Subsequently, the attention is focused on the study of the main features of the two classes of flow regimes that can be established when the leading driving action is the Marangoni stress: Marangoni boundary layers and Marangoni-Stokes flow. Finally, a brief review of the experimental experience of the author's team is reported, looking in particular at the space experiments performed on board the missions SL1 and D1 of the Spacelab.     

Direct observation of processes in a solidifying dispersion

The evolution of a dispersion under the action of temperature gradients and solidification was followed optically in a transparent molten salt (CsCl) with inclusions of Pb-droplets and gas bubbles. This system is believed to model a solidifying metallic alloy. Rejection of Pb-particles by the solidification front was observed, while large gas bubbles were incorporated. Thermocapillary convection at the gas bubbles considerably distorted the temperature field and even caused local remelting. Marangoni migration of bubbles was not observed, contrary to expectations.     

Study of the Marangoni convection around a surface tension minimum under microgravity conditions

At equilibrium, aqueous fatty alcohol solutions presents a surface tension minimum versus temperature. The influence of such an extremum on the Marangoni convection is studied. Two experiments have been performed under microgravity conditions (Texus 8 (1983) and Texus 9 (1984) flights). The velocity fields are determined by following the paths of tracer particles and furthermore, in the Texus 9 experiment, differential interferograms have been recorded.     

上随体Maxwell(UCM)流体热毛细液层弹性失稳的理论分析

通过对上随体Maxwell（UCM）流体热毛细液层线性稳定性的研究分析,发现流场会发生弹性失稳.扰动的增长速率随波数的增加而增加.与牛顿流体不同,UCM流体不存在临界Marangoni数,当波数达到某一临界值时会出现不稳定的弹性扰动波.该临界波数随弹性数和Marangoni数的增加而减小,当弹性数趋近于0时,流体即变为牛顿流体,而相应的临界波数趋于无穷.不同波数及传播方向上,弹性波的波速相同,而其增长速率在特定方向上达到最大.能量分析表明弹性波的扰动能量来自扰动应力做功.      

过冷核态池沸腾中的Marangoni效应

分析了过冷核态池沸腾过程中气泡横向运动现象,指出其成因在于相邻气泡界面温度差引起的Mara-ngoni对流对周围液体的吸引.通过对该流动的尺度分析,得到了气泡横向运动特征速度及其可观测度的估算公式,其预测结果与实验观测相一致.特别是对极细小的初始核化气泡,该公式预测了强烈的横向Marangoni对流会导致气泡顶端微射流的形成.该效应在加热面水平向下或微重力沸腾等气泡脱落频率较低的情形中尤为重要.      

纵向非均匀多孔介质Marangoni对流不稳定性

理论研究了纵向非均匀多孔介质中流体表面张力驱动的对流不稳定性.充满液体的多孔介质层从下方加热,上方自由表面冷却,形成可引起多孔介质液层Marangoni-Benaxd对流流动的纵向温度梯度.采用线性化的Brinkman-Forchheimier方程作为控制方程组,对孔隙率分别为线性函数、正弦三角函数分布的非均匀多孔介质液层的Marangoni-Benaxd问题进行了线性稳定性分析.通过采用Chebyshev-Tau谱方法求解广义特征值问题,得到了系统临界Maxangoni数随无量纲波数变化的中性稳定性曲线,分析和比较了孔隙率的变化对液层对流稳定性和流场结构的影响,获得了纵向非均匀多孔介质液层不稳定性现象的新特征.      

The effect of temperature gradient on the motion of a bubble in reduced gravity

The bubble motion is described as a function of thermal variation of surface tension of a bubble, temperature gradient, gravity, bubble diameter, viscosity and density. The relations among those values are shown in graphs, from which the requirements for the measurements to ascertain the velocity due to thermal variation of surface tension are made clear. According to these requirements, the experiments on the velocity of the bubble in a temperature gradient were conducted and the Marangoni effect on a bubble motion was ascertained.     

Oscillatory thermocapillary convection in floating zones under normal- and micro-gravity

The thermocapillary convection in a floating zone becomes oscillatory, exceeding a Marangoni number of approximately 10⁴. The oscillatory state of thermocapillary convection has been verified under 1 g and 10^?4 g and the features seem to be fairly independent of the gravity level. The transition point from the laminar to the oscillatory state (critical Marangoni number), however, depends on the magnitude and direction of the buoyant force.