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The effects of geometry and heating rate on thermocapillary convection in the liquid bridge

Published online by Cambridge University Press:  25 October 2019

Qi Kang Open the ORCID record for Qi Kang [Opens in a new window] ,
Di Wu Open the ORCID record for Di Wu [Opens in a new window] ,
Li Duan Open the ORCID record for Li Duan [Opens in a new window] ,
Liang Hu Open the ORCID record for Liang Hu [Opens in a new window] ,
Jia Wang Open the ORCID record for Jia Wang [Opens in a new window] ,
Pu Zhang Open the ORCID record for Pu Zhang [Opens in a new window]  and
Wenrui Hu
Qi Kang*
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Di Wu
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Li Duan*
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Liang Hu
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Jia Wang
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Pu Zhang
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Wenrui Hu
Affiliation:
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email addresses for correspondence: kq@imech.ac.cn, duanli@imech.ac.cn
†Email addresses for correspondence: kq@imech.ac.cn, duanli@imech.ac.cn
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Abstract

The experimental study on thermocapillary convection in liquid bridges of large Prandtl number has been carried out on Tiangong-2 in space. The purpose of these experiments is to study the oscillation instability of thermocapillary convection, and to discover and recognize the mechanism of destabilization of thermocapillary convection in the microgravity environment in space. In this paper, the geometry of a half-floating-zone liquid bridge is featured by the aspect ratio Ar and volume ratio Vr, and its influence on critical conditions of oscillatory thermocapillary convection is studied. More than 700 sets of space experiments have been finished. The critical conditions and oscillation characteristics of thermocapillary convection instability in the Ar–Vr parameter space have been fully obtained under microgravity conditions for the first time. It is found that the Ar–Vr parameter space can be divided into two regions of different critical conditions and oscillation characteristics: the region of low frequency oscillation, and the region of high frequency oscillation. More importantly, we obtain the complete configuration of these two stability neutral curves, and find that the low frequency mode is a ‘’ type curve. Based on this, we discuss the influence of heating rate on the oscillation mode. It is found that the heating rate affects the selection of critical mode, which results in a jump change of critical temperature difference. The findings of this study are helpful to better understand the critical modes and transition processes of thermocapillary convection in liquid bridges with different configurations.

JFM classification

Convection: Marangoni convection Drops and Bubbles: Thermocapillarity Interfacial Flows (free surface): Liquid bridges
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 951 - 982
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Copyright
© 2019 Cambridge University Press 

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References

Albanese, C., Carotenuto, L., Castagnolo, D., Ceglia, E. & Monti, R. 1995 An investigation on the ‘Onset’ of oscillatory Marangoni flow. Adv. Space Res. 16 (7), 87–94.Google Scholar
Chen, Q. S. & Hu, W. R. 1998 Influence of liquid bridge volume on instability of floating half zone convection. Intl J. Heat Mass Transfer 41 (6–7), 825–837.Google Scholar
Chun, C. H. & Wuest, W. 1979 Experiments on the transition from the steady to the oscillatory Marangoni-convection of a floating zone under reduced gravity effect. Acta Astronaut. 6 (9), 1073–1082.Google Scholar
Cröll, A., Müller-Sebert, W., Benz, K. W. & Nitsche, R. 1991 Natural and thermocapillary convection in partially confined silicon melt zones. Microgravity Sci. Technol. 3 (4), 204–215.Google Scholar
Cröll, A., Tegetmeier, A., Nagel, G. & Benz, K. W. 1994 Floating-zone growth of GaAs under microgravity during the D2-mission. Cryst. Res. Technol. 29 (3), 335–342.Google Scholar
Dejam, M. & Hassanzadeh, H. 2011 Formation of liquid bridges between porous matrix blocks. AIChE J. 57 (2), 286–298.Google Scholar
Dejam, M., Hassanzadeh, H. & Chen, Z. 2014a Reinfiltration through liquid bridges formed between two matrix blocks in fractured rocks. J. Hydrol. 519, 3520–3530.Google Scholar
Dejam, M., Hassanzadeh, H. & Chen, Z. 2014b Shape of liquid bridges in a horizontal fracture. J. Fluid Flow Heat Mass Transfer 1, 1–8.Google Scholar
Dejam, M., Hassanzadeh, H. & Chen, Z. 2015 Capillary forces between two parallel plates connected by a liquid bridge. J. Porous Media 18 (3), 179–188.Google Scholar
Eyer, A., Leiste, H. & Nitsche, R. 1985 Floating zone growth of silicon under microgravity in a sounding rocket. J. Cryst. Growth 71 (1), 173–182.Google Scholar
Hu, W. R., Shu, J. Z., Zhou, R. & Tang, Z. M. 1994 Influence of liquid bridge volume on the onset of oscillation in floating zone convection. I. Experiments. J. Cryst. Growth 142 (3–4), 379–384.Google Scholar
Hu, W. R. & Tang, Z. M. 2013 Onset of oscillatory thermocapillary convection. In Mechanics Down Under, pp. 85–99. Springer.Google Scholar
Hu, W. R., Tang, Z. M. & Li, K. 2008 Thermocapillary convection in floating zones. Appl. Mech. Rev. 61 (1), 010803.Google Scholar
Kang, Q., Jiang, H., Duan, L., Zhang, C. & Hu, W. R. 2019a The critical condition and oscillation-transition characteristics of thermocapillary convection in the space experiment on SJ-10 satellite. Intl J. Heat Mass Transfer 135, 479–490.Google Scholar
Kang, Q., Wang, J., Duan, L., Su, Y., He, J., Wu, D. & Hu, W. R. 2019b The volume ratio effect on flow patterns and transition processes of thermocapillary convection. J. Fluid Mech. 868, 560–583.Google Scholar
Kang, Q., Wu, D., Duan, L., He, J., Hu, L., Duan, L. & Hu, W. 2019c Surface configurations and wave patterns of thermocapillary convection onboard the SJ10 satellite. Phys. Fluids 31 (4), 044105.Google Scholar
Kawamura, H., Nishino, K., Matsumoto, S. & Ueno, I. 2012 Report on microgravity experiments of Marangoni convection aboard international space station. J. Heat Transfer 134 (3), 031005.Google Scholar
Mashayekhizadeh, V., Kharrat, R., Ghazanfari, M. H. & Dejam, M. 2012 An experimental investigation of fracture tilt angle effects on frequency and stability of liquid bridges in fractured porous media. Petrol. Sci. Technol. 30 (8), 807–816.Google Scholar
Masud, J., Kamotani, Y. & Ostrach, S. 1997 Oscillatory thermocapillary flow in cylindrical columns of high Prandtl number fluids. J. Thermophys. Heat Transfer 11 (1), 105–111.Google Scholar
Nishino, K., Yano, T., Kawamura, H., Matsumoto, S., Ueno, I. & Ermakov, M. K. 2015 Instability of thermocapillary convection in long liquid bridges of high Prandtl number fluids in microgravity. J. Cryst. Growth 420, 57–63.Google Scholar
Preisser, F., Schwabe, D. & Scharmann, A. 1983 Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface. J. Fluid Mech. 126, 545–567.Google Scholar
Ryzhkov, I. I. 2011 Thermocapillary instabilities in liquid bridges revisited. Phys. Fluids 23 (8), 082103.Google Scholar
Sakurai, M., Ohishi, N. & Hirata, A. 2004 Effect of liquid bridge form on oscillatory thermocapillary convection under 1 g and μg conditions. Acta Astronaut. 55 (12), 977–983.Google Scholar
Sakurai, M., Ohishi, N. & Hirata, A. 2007a Oscillatory thermocapillary convection in a liquid bridge. Part 1 – 1g experiments. J. Cryst. Growth 308 (2), 352–359.Google Scholar
Sakurai, M., Ohishi, N. & Hirata, A. 2007b Oscillatory thermocapillary convection in a liquid bridge. Part 2. Drop shaft experiments. J. Cryst. Growth 308 (2), 360–365.Google Scholar
Schatz, M. F. & Neitzel, G. P. 2001 Experiments on thermocapillary instabilities. Annu. Rev. Fluid Mech. 33 (1), 93–127.Google Scholar
Schwabe, D. 2005 Hydrothermal waves in a liquid bridge with aspect ratio near the Rayleigh limit under microgravity. Phys. Fluids 17 (11), 112104.Google Scholar
Schwabe, D., Scharmann, A., Preisser, F. & Oeder, R. 1978 Experiments on surface tension driven flow in floating zone melting. J. Cryst. Growth 43 (3), 305–312.Google Scholar
Shevtsova, V., Mialdun, A., Kawamura, H., Ueno, I., Nishino, K. & Lappa, M. 2011 Onset of hydrothermal instability in liquid bridge. Experimental benchmark. Fluid Dyn. Mater. Process. 7 (1), 1–27.Google Scholar
Sim, B. C. & Zebib, A. 2002 Thermocapillary convection in liquid bridges with undeformable curved surfaces. J. Thermophys. Heat Transfer 16 (4), 553–561.Google Scholar
Smith, M. K. & Davis, S. H. 1983 Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. J. Fluid Mech. 132, 119–144.Google Scholar
Sumner, L. B. S., Neitzel, G. P., Fontaine, J. P. & Dell’Aversana, P. 2001 Oscillatory thermocapillary convection in liquid bridges with highly deformed free surfaces: experiments and energy-stability analysis. Phys. Fluids 13 (1), 107–120.Google Scholar
Velten, R., Schwabe, D. & Scharmann, A. 1991 The periodic instability of thermocapillary convection in cylindrical liquid bridges. Phys. Fluids A 3 (2), 267–279.Google Scholar
Wang, J., Wu, D., Duan, L. & Kang, Q. 2017 Ground experiment on the instability of buoyant-thermocapillary convection in large-scale liquid bridge with large Prandtl number. Intl J. Heat Mass Transfer 108, 2107–2119.Google Scholar
Xu, J. J. & Davis, S. H. 1984 Convective thermocapillary instabilities in liquid bridges. Phys. Fluids 27 (5), 1102–1107.Google Scholar
Xun, B., Li, K. & Hu, W. R. 2010 Effect of volume ratio on thermocapillary flow in liquid bridges of high-Prandtl-number fluids. Phys. Rev. E 81 (3), 036324.Google Scholar
Yano, T. & Nishino, K. 2015 Effect of liquid bridge shape on the oscillatory thermal Marangoni convection. Eur. Phys. J. Special Topics 224 (2), 289–298.Google Scholar
Yano, T., Nishino, K., Matsumoto, S., Ueno, I., Komiya, A., Kamotani, Y. & Imaishi, N. 2018 Report on microgravity experiments of dynamic surface deformation effects on Marangoni instability in high-Prandtl-number liquid bridges. Microgravity Sci. Technol. 30 (5), 599–610.Google Scholar