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

Mendis, Radeesha Laknath Agampodi; Sekimoto, Atsushi; Okano, Yasunori; Minakuchi, Hisashi; Dost, Sadik

doi:10.1007/s12217-020-09798-9

Original Article
Published: 02 June 2020

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

Radeesha Laknath Agampodi Mendis¹,
Atsushi Sekimoto ORCID: orcid.org/0000-0001-9660-3997¹,
Yasunori Okano¹,
Hisashi Minakuchi² &
Sadik Dost³

Microgravity Science and Technology volume 32, pages 729–735 (2020)Cite this article

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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 Si_xGe_1−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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Authors and Affiliations

Department of Materials Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan
Radeesha Laknath Agampodi Mendis, Atsushi Sekimoto & Yasunori Okano
Department of Mechanical Engineering, University of the Ryukyus, Nishihara, Okinawa, 903-0213, Japan
Hisashi Minakuchi
Crystal Growth Laboratory, University of Victoria, Victoria, BC, Canada
Sadik Dost

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Radeesha Laknath Agampodi Mendis
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Atsushi Sekimoto
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Yasunori Okano
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Hisashi Minakuchi
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Sadik Dost
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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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Received: 21 November 2019
Accepted: 30 April 2020
Published: 02 June 2020
Issue Date: August 2020
DOI: https://doi.org/10.1007/s12217-020-09798-9

Keywords

Numerical simulation
Global linear stability analysis
Floating zone method
Liquid bridge