ABSTRACT
In this study, the volume of fluid (VOF) method was used to capture the free surface deformation of the liquid bridge. The temperature difference (ΔT) between the two ends of the liquid bridge and its height-diameter ratio (Hr) were varied, and the simulation results were combined with spectral analysis so as to investigate their effects on the shape of the interface of the liquid bridge. The results show that the interface shape of the liquid bridge is similar to a ‘waist', which is wider at the top and bottom and slightly narrower in the middle. Additionally, two vortices with opposite and symmetric flow directions are formed in the liquid bridge. Notably, the dominant frequencies of the velocity and temperature oscillations in the liquid bridge are the same. With the increase of temperature difference and height-diameter ratio, the degree of deformation of the interface increases, but the rate of its increase gradually decreases. The velocity within the liquid bridge oscillates around a stable mean value (S), which increases with temperature difference and height-diameter ratio. Conversely, the dominant frequency of these velocity oscillations diminishes with elevated temperature difference and height-diameter ratio. Furthermore, at height-diameter ratio is 1.5, the main vortex within the liquid bridge splits from one vortex cell into two separate vortex cells.
KEYWORDS
PAPER SUBMITTED: 2025-09-12
PAPER REVISED: 2025-10-09
PAPER ACCEPTED: 2025-10-16
PUBLISHED ONLINE: 2025-11-08
- Lan, C.W., Chian, J.H., Three-Dimensional Simulation of Marangoni Flow and Interfaces in Floating-Zone Silicon Crystal Growth, Journal of Crystal Growth, 230 (2001), 1-2, pp. 172-180
- Surovovs, M., et al., Numerical Modelling of Melting Front Structures during Floating Zone Silicon Crystal Growth, Journal of Crystal Growth, 643 (2024), pp. 127788
- Kranert, C., et al., Facet Growth Kinetics and Diameter Fluctuations in Molten Zone Si Crystal Growth, Journal of Crystal Growth, 652 (2025), pp. 128024
- Jayakrishnan, R., Tiwari, S., On Three-Dimensional Flow Structures and Oscillatory Instability due to Free Surface Heat Loss in Half-Floating Zones under Microgravity, Advances in Space Research, 67 (2021), 10, pp. 3354-3377
- Agampodi Mendis, R.L., et al., The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity, Crystals, 11 (2021), 2, pp. 116
- Zhang, Y., et al., Effect of Marangoni Number on Thermocapillary Convection and Free-Surface Deformation in Liquid Bridges, Journal of Thermal Science, 25 (2016), 2, pp. 178-187
- Fan, J.G., Liang, R.Q., Numerical Simulation of Thermocapillary Convection in a Half-Zone Liquid Bridge Model with Large Aspect Ratio under Microgravity, Symmetry, 14 (2022), 3, pp. 452
- Sim, B.C., et al., Dynamic Free-Surface Deformations in Axisymmetric Liquid Bridges, Advances in Space Research, 34 (2004), 7, pp. 1627-1634
- Kang, Q., et al., Space Experimental Study on Wave Modes under Instability of Thermocapillary Convection in Liquid Bridges on Tiangong-2, Physics of Fluids, 32 (2020), 3, pp. 34107
- Chen, S., et al., Dynamic Mode Decomposition of Thermocapillary Convection in GaAs Melt Liquid Bridge between Unequal Ends, International Journal of Heat and Mass Transfer, 216 (2023), pp. 124612
- Raming, G., et al., Numerical Investigation of the Influence of EM-Fields on Fluid Motion and Resistivity Distribution during Floating-Zone Growth of Large Silicon Single Crystals, Journal of Crystal Growth, 230 (2001), 1, pp. 108-117
- Minakuchi, H., et al., A Three-Dimensional Numerical Simulation Study of the Marangoni Convection Occurring in the Crystal Growth of SixGe1−x by the Float-Zone Technique in Zero Gravity, Journal of Crystal Growth, 266 (2004), 1-3, pp. 140-144
- Yan, Y.Z., et al., A Simplified Finite Element Model for Numerical Simulation of Temperature Field and Optimization of Parameters in Single Crystal Growth by Optical Floating Zone Technique, Journal of Crystal Growth, 468 (2017), pp. 923-932
- Sabanskis, A., et al., 3D Modeling of Doping from the Atmosphere in Floating Zone Silicon Crystal Growth, Journal of Crystal Growth, 457 (2017), pp. 65-71
- Zou, Y., et al., Effect of Rotating Magnetic Field on Thermal Convection and Dopant Transport in Floating-Zone Crystal Growth, Microgravity Science and Technology, 32 (2020), 3, pp. 349-361
- Jin, C.H., et al., Numerical Simulation of Thermo-Solutal Marangoni Convection in a Full Floating Zone with Radiative Heat Transfer under Zero Gravity, Journal of Crystal Growth, 570 (2021), pp. 126204
- Dossa, S.S., Derby, J.J., Modeling Optical Floating Zone Crystal Growth in a High-Pressure, Single-Lamp Furnace, Journal of Crystal Growth, 591 (2022), pp. 126723
- Shevtsova, V., et al., Subcritical and Oscillatory Dynamic Surface Deformations in Non-Cylindrical Liquid Bridges, Fluid Dynamics & Materials Processing, 4 (2008), 1, pp. 43-54
- Huang, H.L., et al., Thermocapillary Flow and Free-Surface Deformation of Liquid Bridge under Different Magnetic Fields, Applied Thermal Engineering, 135 (2018), pp. 83-94
- Jayakrishnan, R., Tiwari, S., Influence of Co-Axial Airflow and Volume Ratio on Thermo-Capillary Convection in Half Floating Zones, Computers & Fluids, 179 (2019), pp. 248-264
- Yano, T., Nishino, K., Numerical Study on the Effects of Convective and Radiative Heat Transfer on Thermocapillary Convection in a High-Prandtl-Number Liquid Bridge in Weightlessness, Advances in Space Research, 66 (2020), 8, pp. 2047-2061
- Mendis, R.L.A., et al., Global Linear Stability Analysis of Thermo-Solutal Marangoni Convection in a Liquid Bridge under Zero Gravity, Microgravity Science and Technology, 32 (2020), 4, pp. 729-735
- Carrión, L.M., et al., Influence of the Dynamical Free Surface Deformation on the Stability of Thermal Convection in High-Prandtl-Number Liquid Bridges, International Journal of Heat and Mass Transfer, 146 (2020), pp. 118831
- Le, C.C., et al., Oscillatory Thermocapillary Convection in Deformed Half Zone Liquid Bridges of Low Prandtl Number Fluids, International Communications in Heat and Mass Transfer, 127 (2021), pp. 105499
- Jin, C., et al., Numerical Simulation of Thermo-Solutal Marangoni Convection in a Floating Half-Zone with Radiation Effects under Zero Gravity, International Journal of Heat and Mass Transfer, 194 (2022), pp. 123010
- Zou, Y., et al., Effect of Aspect Ratio on Coupled Solute-Thermocapillary Convection Instability in Half-Zone Liquid Bridge, Thermal Science, 26 (2022), 6, pp. 4489-4502
- Wang, Y., et al., Effect of Prandtl Number on the Flow Instabilities in Thermocapillary Liquid Bridges between two Coaxial Disks with Different Radii, International Journal of Heat and Mass Transfer, 205 (2023), pp. 123895
- Yan, S.L., et al., Adaptive Mesh Refinement for VOF Modeling Gas-Liquid Two-Phase Flow: A Summary of Some Algorithms and Applications, Chemical Engineering Science, 306 (2025), pp. 121291
- Selver, R., Experiments on the Transition from the Steady to the Oscillatory Marangoni Convection of a Floating-Zone under Various Cold Wall Temperatures and Various Ambient Air Temperature Effects, Microgravity Science and Technology, 17 (2005), 4, pp. 25-35
- Cheng, M., Kou, S., Detecting Temperature Oscillation in a Silicon Liquid Bridge, Journal of Crystal Growth, 218 (2000), 1, pp. 132-135
- Minakuchi, H., et al., Three-Dimensional Numerical Simulation of Thermal and Solutal Marangoni Convection in a Liquid Bridge under Zero-Gravity Field, Aerospace Technology Japan, 10 (2012), 28, pp. 15-20
- Zhang, Y., et al., The Effect of Aspect Ratio and Axial Magnetic Field on Thermocapillary Convection in Liquid Bridges with a Deformable Free-Surface, Engineering Applications of Computational Fluid Mechanics, 10 (2015), 1, pp. 16-28
- Yano, T., et al., 3-D PTV Measurement of Marangoni Convection in Liquid Bridge in Space Experiment, Experiments in Fluids, 53 (2011), 1, pp. 9-20
