Half-zone Liquid Bridge Research Articles

Thermocapillary-driven coherent structures by low-Stokes-number particles and their morphology in high-aspect-ratio liquid bridges

Thermocapillary-driven coherent structures by low-Stokes-number particles are experimentally investigated. Time-dependent convection is induced in a tall or high-aspect-ratio half-zone liquid bridge. We successfully realize coherent structures, which seem rigidly rotating by following the traveling-wave-type convection of mHTW=1 in azimuthal wave number due to so-called hydrothermal-wave instability. The Poincaré sections at different heights of a single particle forming the coherent structure are obtained in the rotating frame of reference by preparing a thin light sheet. Projected distribution of the multiple particles forming the coherent structure are also depicted to examine the correlation with the Poincaré points. The stability of the coherent structures is discussed by tracking the particles exhibiting turnover motion in the liquid bridge.

Numerical Simulation of Thermocapillary Convection in a Half-Zone Liquid Bridge Model with Large Aspect Ratio under Microgravity

The coupled momenta induced by thermal effects near interfaces cause complex three-dimensional flow structures, called thermocapillary flow or Marangoni convection. Thermocapillary convection is crucial for crystal growth quality, and the mainstream method used to study thermocapillary convection is the half-zone liquid bridge model. This paper designs a gas–liquid two-phase system and reports the numerical results on the instability and associated roll structures of thermocapillary convection in half-zone liquid bridge under microgravity environment. The gas and liquid transferred momentum and energy through the free surface. The geometry of interest is high aspect ratio (AR) silicone oil suspended between coaxial disks heated differentially. It was found that with the increase in AR, the vortex of thermocapillary convection gradually moves to the upper disk at the steady state. In the range of 2 < AR < 2.5, the vortex cell splits from 1 to 2, and the distance between the vortex center increases with the increase in AR. The flow field after the onset of instability exhibits a traveling wave with wave number m = 1 when AR ≤ 3 and exhibits a standing wave with wave number m = 1 when AR ≥ 3.5.

Coherent structures of m=1 by low-Stokes-number particles suspended in a half-zone liquid bridge of high aspect ratio: Microgravity and terrestrial experiments

Coherent strucutres of m = 1 are investigated via microgravity and terrestrial experiments in thermocapillary-driven convection in half-zone liquid bridge of high Prandtl number. Individual behaviors of low Stokes number particles are monitored in the laboratory frame and the rotating frame of reference to illustrate the correlation between the coherent structure and the thermal flow field induced by the hydrothermal wave instability.

Effect of aspect ratio on coupled solute-thermocapillary convection instability in half-zone liquid bridge

Floating zone method is an important technology for growth of high integrity and high uniformity single crystal materials due to its free of crucible contamination. However, capillary convection in the melt is a great challenge to floating zone crystal growth. In this paper, numerical simulations are performed to investigate the coupled solute-thermocapillary convection in SixGe1-x system of the half-zone liquid bridge. The impact of aspect ratio, As, is also investigated on stability of capillary convection. For As = 0.5, the results show that pure solute capillary convection is very weak, which presents 2-D axisymmetric structure. The temperature field is mainly determined by thermal diffusion, while the concentration field is dominated by convection and solute diffusion together. Coupled solute-thermocapillary convection exhibits 3-D periodic and rotating oscillatory flow with the azimuthal wavenumber m = 4, while the pure thermocapillary convection presents a 3-D steady non-axisymmetric flow while solute capillary convection is absent. This means that instability of convection will increase when two kinds of capillary convection are coupled. When the height of the liquid bridge is changed from 5 mm to 10 mm with a constant radius of 10 mm, azimuthal wavenumber, m, of coupled capillary convection shows a strong dependence on aspect ratio. The relationship between the azimuthal wavenumber and aspect ratio can be written as m ? As = 2 or m ? As = 2.2. Further results indicated that when velocity of the monitoring point is large, corresponding concentration is also high at that moment, but the phases of concentration and velocity are not completely synchronized.

A Numerical Study on the Exact Onset of Flow Instabilities in Thermo-Solutal Marangoni Convection Driven by Opposing Forces in a Half-Zone Liquid Bridge under Zero Gravity

The theoretical onset of the Marangoni convection instability occurring in a half-zone liquid bridge of the floating zone (FZ) growth of SixGe1–x has been investigated by numerical simulations. A half-zone model of the liquid bridge between a cold (bottom plane) and a hot (top plane) disk is considered. The highest Si concentration is on the top of the liquid bridge. Therefore, the driving forces for thermal and solutal Marangoni flows are in opposite directions in this configuration. The nonlinear equilibria and periodic orbits are obtained using the Newton–Krylov method, and their stability is analyzed with global linear stability analysis. A flow bifurcation analysis is conducted. The results show that when the solutal Marangoni number, MaC, ≤360, the primary flow bifurcation is from 2D axisymmetric to 3D steady flow. When MaC>360, the 2D axisymmetric flow becomes weakly periodic 2D axisymmetric, and eventually becomes chaotic. The critical thermal Marangoni number is monotonically increasing as MaC increases, and the flow is 2D axisymmetric when the solutal Marangoni forceis dominant. The stability evaluation for various thermal Marangoni number values at MaC=893 reveals that the onset of transition is from steady to periodic. However, the reverse transition does not occur at the same Marangoni number value. The simulation results show that the hysteresis behavior of the flow field exhibits an approximately 1% difference between two critical thermal Marangoni numbers. The present study suggests that the control parameters of FZ crystal growth should be smaller than the calculated critical values to avoid any flow-induced disturbances.

Thermal-flow patterns of [formula omitted] in thermocapillary liquid bridges of high aspect ratio with free-surface heat transfer

We investigate the thermal-flow patterns induced by the thermocapillary effect and their transition conditions in half-zone liquid bridges of high Prandtl number fluid; the effect of heat transfer between the liquid and the ambient gas through the liquid-bridge free surface is considered. We especially focus on the standing-wave-type oscillations after the transition onset, which were observed more frequently in the microgravity experiments (Matsugase et al., Int. J. Heat Mass Trans. (2015)) than the ground experiments, in a tall or high-aspect-ratio liquid bridge. We conduct a series of three-dimensional numerical simulations with the straight liquid bridge against a range of Biot number, and reproduce a pair of thermal waves of azimuthal wave number m=1 propagating in opposite azimuthal directions under large Biot-number conditions by increasing the thermocapillary effect. Through a series of ground experiments with the liquid bridge exposed to the forced flow of the ambient gas, we illustrate the thermal-flow patterns of m=1 and their transition conditions in terms of the Reynolds number for the forced flow of the ambient gas. We succeed in reproducing by both of experimental and numerical approaches the standing-wave-type oscillatory flows with ‘x’-shaped low temperature bands on the free surface, which had been observed only in long-term microgravity experiments. We illustrate that the ‘x’-shaped structure is realized by the higher azimuthal modal structures of the oscillatory convection.

Global Linear Stability Analysis of Thermo-solutal Marangoni Convection in a Liquid Bridge Under Zero Gravity

Marangoni convection is induced by the variation of surface tension along a free surface, which depends not only on temperature but also concentration. However, the onset of thermo-solutal Marangoni convection in a liquid bridge system is still unknown. Here, we perform a global linear stability analysis to determine the theoretical onset of the Marangoni convection occurring in the half-zone liquid bridge of the floating zone method of SixGe1−x crystal growth. The cylindrical liquid bridge is heated from the bottom and the highest Silicon concentration is on the top. The thermal and solutal Marangoni forces are in the same direction in this configuration. The stability diagram of the axisymmetric base flow is obtained by solving the large-scale eigenvalue problem using a Jacobian-free Arnoldi method. Oscillatory disturbance patterns appear with different azimuthal wavenumbers for unstable eigenmodes. The present linear stability analysis results explain our previous numerical simulation results.

Effect of Heat Loss on Hydrothermal wave Instability in Half-Zone Liquid Bridges of High Prandtl NumberFluid

Effect of Heat Loss on Hydrothermal wave Instability in Half-Zone Liquid Bridges of High Prandtl NumberFluid

Long-term Behaviors of a Single Particle Forming a Coherent Structure in Thermocapillary-driven Convection in Half-zone Liquid Bridge of High Prandtl-number Fluid

Long-term Behaviors of a Single Particle Forming a Coherent Structure in Thermocapillary-driven Convection in Half-zone Liquid Bridge of High Prandtl-number Fluid

Secondary instability induced by thermocapillary effect in half-zone liquid bridge of high Prandtl number fluid

Secondary instability induced by thermocapillary effect in half-zone liquid bridge of high Prandtl number fluid

Floquet analysis of spatially periodic thermocapillary convection in a low-Prandtl-number liquid bridge

Secondary instability of thermocapillary convection was investigated for a half-zone liquid bridge with low Prandtl number fluids. The liquid bridge was suspended between two cylindrical flat disks, which were maintained at different temperatures. The thermocapillary-driven flow formed an axisymmetric steady toroidal vortex. If the temperature difference between the two disks exceeded a certain threshold, the axisymmetric flow transitioned to an azimuthal periodic steady flow. The objective in the analysis of secondary instability is to examine the stability limit of this steady flow. Employing Floquet analysis, we obtained the neutral stability curves as a function of the aspect ratio (radius/height) of the liquid bridge and identified the critical modes. The critical modes of the Floquet analysis are referred to as critical Floquet modes and are classified by Floquet parameter β, which characterizes a set of azimuthal wave numbers of the Floquet mode. The Newton–Krylov method and Arnoldi method are implemented to solve the large-scale nonlinear equations and generalized eigenvalue problems, respectively. Two critical Floquet modes were observed having different Floquet parameters, β = 0 and β = 1, which appear preferential in the liquid bridge for high and low aspect ratios, respectively. The mode with β = 1 was steady for low aspect ratios and was able to change to an oscillatory mode with a frequency of oscillation that rapidly increased with increasing aspect ratio. We visualized the temperature and azimuthal velocity distributions of the critical Floquet modes and its Fourier components. We concluded that the mode with β = 1 leads to a pulsating oscillation, denoted as “P-type,” whereas that with β = 0 leads to a twisting oscillation, denoted as “T-type.” Both types of oscillations were reported in previous studies. The present neutral stability curves are for the most part in good agreement with critical Reynolds numbers previously obtained in numerical simulations.

Existence Conditions and Formation Process of Second Type of Spiral Loop Particle Accumulation Structure (SL-2 PAS) in Half-zone Liquid Bridge

We focus on unique phenomena known as particle accumulation structure (PAS), especially on the conditions of the existence for second-type spiral loop PAS (SL-2 PAS) and on their formation processes under normal gravity. We investigate the existence conditions as functions the aspect ratio of the liquid bridge and the Marangoni number, the intensity of the thermocapillary effect. We discuss the differences among SL-1 PAS, SL-2 PAS and the flow field without PAS through observation of the solid-like structures of the PAS in a rotating frame of reference with the hydrothermal wave, and through monitoring of the surface temperature by infrared camera. We evaluate the formation time of PAS by employing a modified accumulation measure by considering the effect of the particles’ size.

Ground experiment on the instability of buoyant-thermocapillary convection in large-scale liquid bridge with large Prandtl number

In order to cooperate with the Chinese TG-2 space experiment project, this paper studies the flow structure and critical conditions at the onset of transition and nonlinear regimes of bouyant-thermocapillary convection in large-scale liquid bridge with large Prandtl number under normal gravity. The surface temperature distribution is obtained by means of thermal infrared camera, to study the temperature oscillation, temporal-spatial analysis and modal structures of the temperature field. In addition, the fluid velocity field is measured by Particle Image Velocimetry, to study the internal flow field structure and flow characteristics in the transition process of the liquid bridge. It is found that the critical value of the buoyant-thermocapillary convection in the half-zone liquid bridge can be affected by geometric parameters. Under large Prandtl number conditions, the critical temperature difference will change nonlinearly with the volume ratio, and the convection will transit from steady flow to a sequence of instabilities. In addition, various wave patterns will appear with increasing Marangoni number, and with further increased temperature difference a chaos state will emerge.

Instability of thermocapillary convection in long liquid bridges of high Prandtl number fluids in microgravity

This paper reports experimental results on the instability of thermocapillary convection in long half-zone liquid bridges of high Prandtl number fluids (Pr=67, 112 and 207 for 5, 10 and 20 cSt silicone oils, respectively). The experiments were carried out in microgravity on the International Space Station, which allowed sufficiently long waiting period for the development of instability. Critical temperature differences were measured for liquid bridges of 30 and 50mm diameters and up to 62.5mm length. The resultant critical Marangoni numbers (Mac) were obtained for a wide range of aspect ratio (=height/diameter), AR, up to AR=2.0. Linear stability analyses for Pr=67 were also carried out to obtain numerical data for comparison. The present experimental results for Pr=67 indicate 5.0×103<Mac<2.0×104 for large AR (AR>1.25) and they are in good agreement with the present linear stability analysis result. In contrast, the present results are considerably smaller than the previous data (Pr=74) taken in the Space Shuttle experiments. It is shown that this difference is due to the effect of heating rate of the liquid bridge. The data for oscillation frequency and azimuthal mode number are also presented. The non-dimensional oscillation frequencies as well as Mac for Pr=67 have shown a sudden decrease at around AR=1.25, suggesting the bifurcation of neutral stability curves.

Evaluation of existence region and formation time of particle accumulation structure (PAS) in half-zone liquid bridge

We focused on the particle accumulation structure (PAS) produced by the thermocapillary effect in a half-zone liquid bridge. Although models of the formation of the PAS have been previously proposed, they have not been experimentally verified. An assessment of the region in which the PAS exists is very subjective and often dependent on the observer, and this has necessitated the development of an objective and quantitative evaluation method. We therefore conducted a series of experiments to verify the physical model of the particle path lines in a rotating frame of reference using the fundamental frequency of the hydrothermal wave. We evaluated the intensity of the particle accumulation based on a modification of the “accumulation measure” proposed by Kuhlmann and Muldoon (Phys. Rev. E, 2012) to objectively and quantitatively determine the existence region of the SL-1 PAS. The results of the quantitative experiment revealed that the best aspect ratio (ratio of the height to radius) of the liquid bridge for the SL-1 PAS was about 0.64, and that the PAS formation time was nearly the same as the thermal diffusion time under the considered conditions (184 words, within 200 words).

096 HZ液柱内対流構造に及ぼす温度差と濃度差に起因するマランゴニ対流の共存効果

096 HZ液柱内対流構造に及ぼす温度差と濃度差に起因するマランゴニ対流の共存効果

10913 液柱マランゴニ対流における振動流遷移に及ぼす熱損失の影響

Marangoni Convection transits from laminar to oscillatory flow under the certain temperature difference. Recently, it is shown that a transition condition is significantly affected by the heat transfer at the free surface. It should be occurred that a driving force is changed as a result of the surface temperature variation due to the surface heat transfer. Marangoni convection induced in a half-zone liquid bridge is observed to make clear the relation between the surface temperature distribution and onset condition of oscillatory flow with changing relative liquid bridge temperature against the ambient temperature. Critical Marangoni number is clearly changed in heat transfer, hi this regime, the surface temperature distribution and surface velocity are also changed.

Transition of thermocapillary convection in a full-zone liquid bridge

Themocapillarity is of fundamental importance in material processing. The floating-zone method is a material processing for producing and purifying single crystals of metals and oxides. It is widely known that, using this method, a transition to three-dimensional oscillatory thermocapillary convection takes place in the melt. The oscillatory convection causes detrimental striations in the crystal structure. In this study, flow transition points (critical Marangoni numbers) and flow structures were investigated in a thermocapillary convection in a model of floating-zone method (full-zone liquid bridge) of the high Prandtl number fluid (Pr =28.1) under the normal gravity condition. In the liquid bridge, the convection changes from two-dimensional steady flow to three-dimensional oscillatory one at a flow transition point. The convection was visualized by tracer particles in order to find the flow transition point and the shape of the modal structures in the oscillatory flow. The dominant modal structures near the flow transition point were estimated using the shape of the particle free zone on a horizontal plane of the liquid bridge and superposition of several waves with azimuthal wave numbers by the method of the least squares. In the present study, the critical Marangoni number of the full-zone liquid bridge was almost one-half of that of the half-zone liquid bridge in aspect ratio 0.45 to 1.3 (aspect ratio: half-height of liquid bridge over radius of rods). The dominant modal structures were combination of azimuthal wave numbers with 1, 2, and 3 in a range of the aspect ratio concerned. It was found that the azimuthal wave numbers of the dominant modal structures did not depend on the aspect ratio. The dominant modal structures were a standing or a travelling wave, and changed from one to another irregularly. Trade-off of a power and a phase locking between each modal structure were observed.

Hydrothermal Wave Instability in a High-Aspect-Ratio Liquid Bridge of Pr &gt; 200

The long-duration fluid physics experiments on a thermocapillary-driven flow have been carried out on the Japanese Experiment Module ‘Kibo’ aboard the International Space Station (ISS) since 2008. In these experiments, various aspects of thermocapillary convection in a half-zone (HZ) liquid bridge of high Prandtl number fluid have been examined under the advantages of the long-duration high-quality microgravity environment. In 2010, the authors succeeded to realize nonlinear convective fields in the HZ liquid bridge of rather high aspect ratio. Special attention was paid on to the complex convective fields, especially on the behaviors of the hydrothermal wave (HTW) over the free surface visualized by an infrared camera. In order to evaluate the characteristics of the nonlinear convective behaviors and their transition processes, the authors indicate the images taken by the infrared camera describing the time evolution of HTW, the spatio-temporal diagram, the Fourier analysis, and the pseudo-phase space, reconstructed from the time series of the scalar information of the liquid bridge, that is, surface temperature variation. In this paper, the authors introduce the signature of complex HTW behaviors observed at the long-duration on-orbit experiments, and make comparisons with some previous terrestrial and microgravity experiments.

Formation of Particle Accumulation Structure (PAS) in Half-Zone Liquid Bridge under an Effect of Thermo-Fluid Flow of Ambient Gas

Formation of Particle Accumulation Structure (PAS) in Half-Zone Liquid Bridge under an Effect of Thermo-Fluid Flow of Ambient Gas