The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity

Mendis, Radeesha Laknath Agampodi; Sekimoto, Atsushi; Okano, Yasunori; Minakuchi, Hiroyoshi; Dost, S.

doi:10.3390/cryst11020116

Cited by 13 publications

(3 citation statements)

References 22 publications

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“…When considering the combined e ect of thermal and solutal Marangoni ows for the uids with low Prandtl number and high Schmidt number, the primary bifurcation is from a 2D axisymmetric ow to an oscillatory three-dimensional ow. A recent study on the relative contribution of solutal Marangoni convection has shown that the ow bifurcations of high-Prandtl-number uids and high-Schmidt-number uids are identical (see, for instance, Agampodi Mendis et al, 2021). In the system considered in the aforementioned studies, the thermal and solutal Marangoni ows developing in the bridge were in the same direction.…”

Section: Introductionmentioning

confidence: 97%

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

Laknath

Mendis

Sekimoto

et al. 2021

J. Chem. Eng. Japan

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The theoretical onset of the Marangoni convection instability occurring in a half-zone liquid bridge of the oating zone (FZ) growth of Si x Ge 1-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 ows are in opposite directions in this con guration. The nonlinear equilibria and periodic orbits are obtained using the Newton-Krylov method, and their stability is analyzed with global linear stability analysis. A ow bifurcation analysis is conducted. The results show that when the solutal Marangoni number, Ma C , ≤360, the primary ow bifurcation is from 2D axisymmetric to 3D steady ow. When Ma C >360, the 2D axisymmetric ow becomes weakly periodic 2D axisymmetric, and eventually becomes chaotic. The critical thermal Marangoni number is monotonically increasing as Ma C increases, and the ow is 2D axisymmetric when the solutal Marangoni forceis dominant. The stability evaluation for various thermal Marangoni number values atMa C 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 ow eld exhibits an approximately 1% di erence 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 ow-induced disturbances.

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Section: Introductionmentioning

confidence: 97%

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

Laknath

Mendis

Sekimoto

et al. 2021

J. Chem. Eng. Japan

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“…Their simulation results were in good agreement with the experimental data. Mendis et al [ 12 ] proposed a 3D numerical simulation model to investigate the effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge. Different aspect ratios were investigated for a disk with cold top and hot bottom surfaces under zero gravity.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel

Sari,

Wu,

Ahmadein

et al. 2024

Materials

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Due to the high computational costs of the Eulerian multiphase model, which solves the conservation equations for each considered phase, a two-phase mixture model is proposed to reduce these costs in the current study. Only one single equation for each the momentum and enthalpy equations has to be solved for the mixture phase. The Navier–Stokes and energy equations were solved using the 3D finite volume method. The model was used to simulate the liquid–solid phase transformation of a Fe-0.82wt%C steel alloy under the effect of both thermocapillary and buoyancy convections. The alloy was cooled in a rectangular ingot (100 × 100 × 10 mm3) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m2/K, which allows for heat exchange with the outer medium. The purpose of this work is to study the effect of the surface tension on the flow and segregation patterns. The results before solidification show that Marangoni flow was formed at the free surface of the molten alloy, extending into the liquid depth and creating polygonized hexagonal patterns. The size and the number of these hexagons were found to be dependent on the Marangoni number, where the number of convective cells increases with the increase in the Marangoni number. During solidification, the solid front grew in a concave morphology, as the centers of the cells were hotter; a macro-segregation pattern with hexagonal cells was formed, which was analogous to the hexagonal flow cells generated by the Marangoni effect. After full solidification, the segregation was found to be in perfect hexagonal shapes with a strong compositional variation at the free surface. This study illuminates the crucial role of surface-tension-driven Marangoni flow in producing hexagonal patterns before and during the solidification process and provides valuable insights into the complex interplay between the Marangoni flow, buoyancy convection, and solidification phenomena.

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“…Marangoni convection is very common in many industrial applications, such as crystal growth [1][2][3], welding [4][5][6][7], and evaporation [8,9]. During crystal growth, the buoyancy convection is weakened under microgravity, and Marangoni convection becomes the dominant convection.…”

Section: Introductionmentioning

confidence: 99%

Effects of Temperature Difference and Heat Loss on Oscillation Characteristics of Thermo-Solutocapillary Convection in Toluene/N-Hexane Mixed Solution

2023

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During the crystal growth process using the floating zone method, the uneven distribution of impurities on the surface of the melt can trigger a coupling mechanism between solutocapillary convection driven by the concentration gradient and thermocapillary convection driven by the temperature gradient, resulting in the Marangoni convection at the free surface. When the temperature and concentration gradients reach certain values, the crystal surface and interior exhibit time-dependent, periodic oscillations, leading to the formation of micrometer-scale impurity stripes within the crystal. This study focuses on the effects of temperature difference and heat loss in a liquid bridge under microgravity on the structure and interface oscillation characteristics of thermo-solutocapillary convection, aiming to explore the coupling phenomenon of this oscillation and provide valuable information for crystal growth processes. An improved level set method is employed to accurately track every displacement of the interface, while the surface tension is addressed using the CSF model. In addition, the area compensation method is used to maintain simulation quality balance. A comprehensive analysis is performed on the oscillation characteristics of thermo-solutocapillary convection at the free surface, ranging from the temperature, concentration, deformation, and velocity distributions at the upper and middle heights of the liquid bridge. The results indicate that under small temperature differences (ΔT = 1 − 3), the transverse velocity at the upper end exhibits a single-periodic oscillation, while the longitudinal velocity presents a double-periodic oscillation. At the intermediate height, both the transverse and longitudinal velocities display a single-periodic oscillation. Under a large temperature difference (ΔT = 6), the oscillation of velocities at the upper end and the middle position become multi-periodic. In addition, heat loss has certain regular effects on the oscillatory flow of thermo-solutocapillary convection within a certain range. The velocity, amplitude, and frequency of the upper end and the middle position at the free surface decrease gradually, and the oscillation intensity also weakens with the increase in heat loss (Bi = 0.2 − 0.6). These new discoveries can provide a valuable reference for optimizing the crystal growth process, thereby enhancing the quality and performance of crystal materials.

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The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity

Cited by 13 publications

References 22 publications

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

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 Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel

Effects of Temperature Difference and Heat Loss on Oscillation Characteristics of Thermo-Solutocapillary Convection in Toluene/N-Hexane Mixed Solution

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