Microgravity Science and Technology

, Volume 30, Issue 6, pp 865–876 | Cite as

Oscillation Transition Routes of Buoyant-Thermocapillary Convection in Annular Liquid Layers

  • Longsheng Duan
  • Li DuanEmail author
  • Huan Jiang
  • Qi KangEmail author
Original Article
Part of the following topical collections:
  1. Approaching the Chinese Space Station - Microgravity Research in China


There are various oscillation transition routes of buoyant-thermocapillary convection in an annular liquid layer. Three types of transition routes including quasi-periodic bifurcation, period-doubling bifurcation and tangent bifurcation have been observed. In our ground experiments, the depth of liquid layer is in a range of 1.6–2.4 mm. The silicone oil with Prandtl number of 28.6 is selected as the liquid medium. The temperature oscillation is detected by a single-point temperature measuring system and the surface oscillation is measured by a laser displacement-sensor with high resolution. The step-heating mode is adopted in the experiments. Transition routes of temperature oscillation and surface oscillation are studied systematically, and the relationship between them is discussed, too.


Transition route Buoyant-thermocapillary convection Bifurcation Temperature oscillation Surface oscillation Step-heating mode 



This work is funded by Joint fund of National Natural Science Foundation of China: Study on the oscillations, transition routes and volume effects of thermocapillary convection (U1738116), Chinese Academy of Sciences: SJ-10 Satellite Program under grant No. XDA04020405 and XDA04020202-05, and China Manned Space Engineering program (TG-2).


  1. Benz, S., Hintz, P., Riley, R.J., Neitzel, G.P.: Instability of thermocapillary–buoyancy convection in shallow layers. Part 2. Suppression of hydrothermal waves. J. Fluid Mech. 5(359), 165–180 (2000)zbMATHGoogle Scholar
  2. Broze, G., Hussain, F.: Transitions to chaos in a forced jet: Intermittency, tangent bifurcations and hysteresis. J. Fluid Mech. 311(311), 37–71 (1996)MathSciNetCrossRefGoogle Scholar
  3. Bucchignani, E., Stella, F.: Rayleigh-Benard convection in limited domains: part 2—transition to chaos. Num. Heat Transf. Part A—Appl. 36(1), 17–34 (1999)CrossRefGoogle Scholar
  4. Chen, Z.-W., Li, Y.-S., Zhan, J.-M.: Double-diffusive Marangoni convection in a rectangular cavity: onset of convection. Phys. Fluids 22, 034106 (2010)zbMATHCrossRefGoogle Scholar
  5. Delbourgo, R., Kenny, B.G.: Universal features of tangent bifurcation. Aust. J. Phys. 38(1), 1–22 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  6. Gollub, J.P., Benson, S.V.: Many routes to turbulent convection. J. Fluid Mech. 100, 449–470 (1980)CrossRefGoogle Scholar
  7. Grebogi, C., Ott, E., Yorke, J.A.: Crises, sudden changes in chaotic attractors, and transient chaos. Phys. D Nonlinear Phenom. 7(1–3), 181–200 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  8. Hale, J.K.: Dynamics and bifurcations. Texts Appl. Math. 3(2–3), 719–731 (1991)MathSciNetGoogle Scholar
  9. Hu, W.R., Tang, Z.M.: Floating Zone Convection in Crystal Growth Modeling. Science Press, Beijing (2003)Google Scholar
  10. Jakeman, E., Hurle, D.T.J.: Thermal oscillations and their effect on solidification processes. Rev. Phys. Technol. 3(1), 3 (1972)CrossRefGoogle Scholar
  11. Jiang, H., Duan, L., Kang, Q.: A peculiar bifurcation transition route of thermocapillary convection in rectangular liquid layers. Exp. Thermal Fluid Sci. 88, 8–15 (2017a)CrossRefGoogle Scholar
  12. Jiang, H., Duan, L., Kang, Q.: Instabilities of thermocapillary-buoyancy convection in open rectangular liquid layers. Chin. Phys. B 26(11), 316–323 (2017b)Google Scholar
  13. Li, Y.-S., Chen, Z.-W., Zhan, J.-M.: Double-diffusive Marangoni convection in a rectangular cavity: transition to chaos. Int. J. Heat Mass Transf. 53(23/24), 5223–5231 (2010)zbMATHCrossRefGoogle Scholar
  14. Mukutmoni, D., Yang, K.T.: Rayleigh-Benard convection in a small aspect ratio enclosure 2. Bifurcation to chaos. J. Heat Transf.—Trans. ASME 115(2), 367–376 (1993)CrossRefGoogle Scholar
  15. Mukutmoni, D., Yang, K.T.: Thermal-convection in small enclosures—an atypical bifurcation sequence. Int. J. Heat Mass Transf. 38(1), 113–126 (1995)zbMATHCrossRefGoogle Scholar
  16. Napolitano, L.G., Monti, R., Russo, G.: Some results of the Marangoni free convection experiment. In: European Symposium on Material Sciences under Microgravity, pp 15–22 (1984)Google Scholar
  17. Ostrach, S.: Low-gravity fluid flows. Ann. Rev. Fluid Mech. 14(1), 313–345 (1982)zbMATHCrossRefGoogle Scholar
  18. Peng, Z., Bin, Z., Li, D., Qi, K.: Characteristics of surface oscillation in thermocapillary convection. Exp. Thermal Fluid Sci. 35, 1444–1450 (2011)CrossRefGoogle Scholar
  19. Peng, Z., Li, D., Qi, K.: Transition to chaos in thermocapillary convection. Int. J. Heat Mass Transf. 57, 457–464 (2013)CrossRefGoogle Scholar
  20. Schwabe, D., Möller, U., Schneider, J., Scharmann, A.: Instabilities of shallow dynamic thermocapillary liquid layers. Phys. Fluids A Fluid Dyn. 4(1992), 2368–2381 (1992)CrossRefGoogle Scholar
  21. Schwabe, D., Zebib, A., Sim, B.C.: Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity. J. Fluid Mech. 491(491), 239–258 (2003)zbMATHCrossRefGoogle Scholar
  22. Shi, W., Imaishi, N.: Hydrothermal waves in differentially heated shallow annular pools of silicone oil. J. Cryst. Growth 290(1), 280–291 (2006)CrossRefGoogle Scholar
  23. Shi, W., Ermakov, M.K., Li, Y.R., et al.: Influence of buoyancy force on thermocapillary convection instability in the differentially heated annular pools of silicon melt. Micrograv. Sci. Technol. 21(1), 289–297 (2009)CrossRefGoogle Scholar
  24. Sim, B.C., Zebib, A., Schwabe, D.: Oscillatory thermocapillary convection in open cylindrical annuli. Part 2. Simulations. J. Fluid Mech. 491(491), 259–274 (2003)zbMATHCrossRefGoogle Scholar
  25. Smith, M.K., Davis, S.H.: The instability of sheared liquid layers. J. Fluid Mech. 121(121), 187–206 (1982)MathSciNetzbMATHGoogle Scholar
  26. Stella, F., Bucchignani, E.: Rayleigh-Benard convection in limited domains: Part 1—Oscillatory flow. Num. Heat Transf. Part A-Appl. 36(1), 1–16 (1999)Google Scholar
  27. Yan, A., Li, K., Tang, Z.M., Cao, Z.H., Hu, W.R.: Period-doubling bifurcations of the thermocapillary convection in a floating half zone. Sci. China Phys. Mech. Astron. 53(9), 1681–1686 (2010)CrossRefGoogle Scholar
  28. Yasnou, V., Gaponenko, Y., Mialdun, A., et al.: Influence of a coaxial gas flow on the evolution of oscillatory states in a liquid bridge. Int. J. Heat Mass Transf. 123, 747–759 (2018)Google Scholar
  29. Yu, J.J., Wu, C.M., Li, Y.R., Chen, J.C.: Thermal-solutal capillary-buoyancy flow of a low prandtl number binary mixture with a − 1 capillary ratio in an annular pool. Phys. Fluids 28(8), 55 (2016)CrossRefGoogle Scholar
  30. Zhang, L., Luo, J.Q., Wu, C.M., Yu, J.J., Li, Y.R.: Thermocapillary convection in a binary mixture with moderate prandtl number in a shallow annular pool. Micrograv. Sci. Technol. 30(1–2), 33–42 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018
corrected publication 2018

Authors and Affiliations

  1. 1.Key Laboratory of Microgravity, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations