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

Abstract

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.

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Acknowledgements

This research partly used computational resources of Research Institute for Information Technology, Kyushu University. This work was partially supported by JSPS KAKENHI Grant Number JP19K22015

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Correspondence to Atsushi Sekimoto.

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Mendis, R.L.A., Sekimoto, A., Okano, Y. et al. Global Linear Stability Analysis of Thermo-solutal Marangoni Convection in a Liquid Bridge Under Zero Gravity. Microgravity Sci. Technol. 32, 729–735 (2020). https://doi.org/10.1007/s12217-020-09798-9

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  • DOI: https://doi.org/10.1007/s12217-020-09798-9

Keywords

  • Numerical simulation
  • Global linear stability analysis
  • Floating zone method
  • Liquid bridge