International Scientific Journal

Thermal Science - Online First

online first only

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. And 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 wave number (m) of coupled capillary convection shows a strong dependence on aspect ratio. The relationship between the azimuthal wave number 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.
PAPER REVISED: 2022-02-16
PAPER ACCEPTED: 2022-06-13
  1. Granata, V., et al., Crystal growth of the Ca2RuO4-Ru metal system by the floating-zone technique, Journal of Alloys and Compounds, 832. (2020), p. 154890
  2. Agamaliyev, Z.A., et al., A Model for Crystal Growth of Solid Solutions in the InAs-GaAs System by a Modified Floating-Zone Technique, Inorganic Materials, 55. (2019), 3, pp. 205-209
  3. Muiznieks, A., et al., 7 - Floating Zone Growth of Silicon A2, in: Handbook of Crystal Growth (Second Edition), (Ed., P. Rudolph), Elsevier: Boston. 2015, pp. 241-279
  4. Han, X.-F., et al., Numerical analysis of dopant concentration in 200 mm (8 inch) floating zone silicon, Journal of Crystal Growth, 545. (2020), p. 125752
  5. Tsukada, T., 22 - The Role of Marangoni Convection in Crystal Growth A2 in: Handbook of Crystal Growth (Second Edition), (Ed., P. Rudolph), Elsevier: Boston. 2015, pp. 871-907
  6. Yang, S., et al., The Effect of Uniform Magnetic Field on Spatial-Temporal Evolution Of Thermocapillary Convection with The Silicon Oil Based Ferrofluid, Thermal Science, 24. (2020), 6, pp. 4159-4171
  7. Melnikov, D.E., et al., Modeling of the experiments on the Marangoni convection in liquid bridges in weightlessness for a wide range of aspect ratios, International Journal of Heat and Mass Transfer, 87. (2015), pp. 119-127
  8. Schwabe, D., et al., Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity, Journal of Fluid Mechanics, 491. (2003), pp. 239-258
  9. Takagi, K., et al., Experimental study on transition to oscillatory thermocapillary flow in a low Prandtl number liquid bridge, Journal of Crystal Growth, 233. (2001), 1, pp. 399-407
  10. Yang, S., et al., A New Cognition on Oscillatory Thermocapillary Convection for High Prandtl Number Fluids, Thermal Science, 25. (2021), 6, pp. 4761-4772
  11. Jayakrishnan, R.,S. Tiwari, Influence of co-axial airflow and volume ratio on thermo-capillary convection in half floating zones, Computers & Fluids, 179. (2019), pp. 248-264
  12. Smith, M.K.,S.H. Davis, Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities, Journal of Fluid Mechanics, 132. (1983), pp. 119-144
  13. Smith, M.K.,S.H. Davis, Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities, Journal of Fluid Mechanics, 132. (1983), pp. 145-162
  14. Lyubimova, T.P., et al., Thermo- and soluto-capillary convection in the floating zone process in zero gravity conditions, Journal of Crystal Growth, 303. (2007), 1, pp. 274-278
  15. Lyubimova, T.P.,R.V. Scuridyn, Numerical modelling of three-dimensional thermo- and solutocapillary-induced flows in a floating zone during crystal growth, The European Physical Journal Special Topics, 192. (2011), 1, pp. 41-46
  16. 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, pp. 140-144
  17. Minakuchi, H., et al., The relative contributions of thermo-solutal Marangoni convections on flow patterns in a liquid bridge, Journal of Crystal Growth, 385. (2014), pp. 61-65
  18. Minakuchi, H., et al., Effect of thermo-solutal Marangoni convection on the azimuthal wave number in a liquid bridge, Journal of Crystal Growth, 468. (2017), pp. 502-505
  19. Surovovs, K., et al., Hydrodynamical aspects of the floating zone silicon crystal growth process, Journal of Crystal Growth, 401. (2014), pp. 120-123
  20. Zhou, X.M.,X.L. Huai, Free Surface Deformation of Thermo-Solutocapillary Convection in Axisymmetric Liquid Bridge, Microgravity Science And Technology, 27. (2015), 1, pp. 39-47
  21. Chen, J.-C., et al., Three-Dimensional Numerical Simulation of Pure Solutocapillary Flow in a Shallow Annular Pool for Mixture Fluid with High Schmidt Number, Microgravity Science and Technology, 28. (2016), 1, pp. 49-57
  22. Huang, H., et al., Effect of Marangoni number on thermocapillary convection in a liquid bridge under microgravity, International Journal of Thermal Sciences, 118. (2017), pp. 226-235
  23. Mendis, R.L.A., 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, p. 116
  24. 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
  25. Liang, R., et al., Effect of Horizontal Vibrations on Thermo-Solutocapillary Convection and Free Surface of Liquid Bridge, Microgravity Science and Technology, 32. (2020), 5, pp. 847-855
  26. Campbell, T.A., et al., Float zone growth and characterization of Ge1−xSix (x⩽10at%) single crystals, Journal of Crystal Growth, 226. (2001), 2, pp. 231-239
  27. Abbasoglu, S.,I. Sezai, Three-dimensional modelling of melt flow and segregation during Czochralski growth of GexSi1−x single crystals, International Journal of Thermal Sciences, 46. (2007), 6, pp. 561-572
  28. Fadaly, E.M.T., et al., Direct-bandgap emission from hexagonal Ge and SiGe alloys, Nature, 580. (2020), 7802, pp. 205-209
  29. Zou, Y., et al., Instability of coupled thermo-solute capillary convection in liquid bridge and control by rotating magnetic field, Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics, 49. (2017), 6, pp. 1280-1289
  30. Levenstam, M.,G. Amberg, Hydrodynamical instabilities of thermocapillary flow in a half-zone, Journal of Fluid Mechanics, 297. (1995), pp. 357-372
  31. 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
  32. Preisser, F., et al., Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface, Journal of Fluid Mechanics, 126. (1983), pp. 545-567
  33. Wanschura, M., et al., Convective instability mechanisms in thermocapillary liquid bridges, Physics of Fluids, 7. (1995), 5, pp. 912-925