Skip to main content

On the Impact of Body Forces in Low Prandtl Number Liquid Bridges

  • Chapter
  • First Online:
Advanced Technologies, Systems, and Applications V (IAT 2020)

Abstract

The influence of different body forces on the frequencies of the oscillatory regime in liquid bridges of molten silicone is studied. To do so, three different gravity levels are applied: the first related with Earth gravitational acceleration, the second with International Space Station reboosting maneuvers and the third with zero gravitational acceleration. In addition, different Marangoni numbers are considered in order to compare the influence of bulk body forces on them. Finally, a short study of the possible impact of the relationship between length and diameter of a liquid bridge on the number of instability modes is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Riemann, H., Luedge, A.: Floating zone crystal growth. In: Crystal Growth of Si for Solar Cells. Springer, Berlin (2009)

    Google Scholar 

  2. Muiznieks, A., Virbulis, J., Lüdge, A., Riemann, H., Werner, N.: Floating zone growth of silicon. In: Handbook of Crystal Growth. Bulk Crystal Growth: Basic Techniques, vol. II, Part A. Elsevier, Amsterdam (2015)

    Google Scholar 

  3. Rost, H.J., Luedge, A., Riemann, H., Kirscht, F., Schulze, T.W.: Float zone (FZ) silicon: a potential material for advanced commercial solar cells? Cryst. Res. Technol. 47, 273–278 (2012)

    Article  Google Scholar 

  4. Leypoldt, J., Kuhlmann, H.C., Rath, H.J.: Three-dimensional numerical simulation of thermocapillary flows in cylindrical liquid bridges. J. Fluid Mech. 414, 285–307 (2000)

    Article  Google Scholar 

  5. Yasushiro, S., Sato, T., Imaishi, N., Yoda, S.: Three dimensional Marangoni flow in liquid bridge of low Pr fluid. Space Forum 6, 39–47 (2000)

    Google Scholar 

  6. Lappa, M., Savino, R., Monti, R.: Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity. Int. J. Heat Mass Transf. 44, 1983–2003 (2001a)

    Article  Google Scholar 

  7. Huang, H., Zhu, G., Zhang, Y.: Effect of Marangoni number on thermocapillary convection in a liquid bridge under microgravity. Int. J. Therm. Sci. 118, 226–235 (2017)

    Article  Google Scholar 

  8. Jurado, R., Pallarès, J., Gavaldà, J., Ruiz, X.: On the impact of the ISS reboosting maneuvers during thermodiffusion experiments of ternary liquid systems: Pure diffusion. Int. J. Thermal Sci. 132: 186–198 (2017)

    Google Scholar 

  9. Jurado, R., Pallarès, J., Gavaldà, J., Ruiz, X.: Effect of reboosting manoeuvres on the determination of the Soret coefficients of DCMIX ternary systems. Int. J. Thermal Sci. 142, 205–219 (2019)

    Google Scholar 

  10. Lappa, M., Imaischi, N.: 3D numerical simulation of on ground Marangoni flow instabilities in liquid bridges of low Prandtl number fluid. Int. J. Numer. Methods Heat Fluid Flows 13, 309–339 (2003)

    Article  Google Scholar 

  11. Shevtsova, V.: Thermal convection in liquid bridges with curved free surfaces: Benchmark of numerical solutions. J. Cryst. Growth 280, 632–651 (2005)

    Article  Google Scholar 

  12. Melnikov, D.E., Shevtsova, V., Yano, T., Nishino, K.: Modeling of the experiments on the Marangoni convection in liquid bridges in weightlessness for a wide range of aspect ratios. Int. J. Heat Mass Transf. 87, 119–127 (2015)

    Article  Google Scholar 

  13. OpenFOAM user guide

    Google Scholar 

  14. Hb_vib_vehicle_Progress_71P_Reboost_2019-05-23.pdf. https://gipoc.grc.nasa.gov/wp/pims/handbook/

  15. NASA PIMS website: https://gipoc.grc.nasa.gov/wp/pims/acceleration-archives/

  16. Jurado, R., Gavaldà, J., Simón, M.J., Pallarés, J., Laverón-Simavilla, A., Ruiz, X., Shevtsova, V.: Some considerations on the vibrational environment of the DSC-DCMIX1 experiment onboard ISS. ActaAstronautica 129, 345–356 (2016)

    Google Scholar 

  17. Yang, Y.K., Kou, S.: Temperature oscillation in a tin liquid bridge and critical Marangoni number dependency on Prandtl number. J. Cryst. Growth 222, 135–143 (2001)

    Article  Google Scholar 

  18. Lappa, M., Savino, R., Monti, R.: Three-dimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ration. Int. J. Numer. Meth. Fluids 36, 53–90 (2001b)

    Article  Google Scholar 

  19. Nakamura, S., Hibiya, T., Imaishi, N., Hirao, K., Nishizawa, S., Hirata, A., Mukai, K., Yoda, S., Morita, T.S.: Temperature fluctuations of the Marangoni flow in a liquid bridge of molten silicon under microgravity on board the TR-14 rocket. J. Crystal Growth 207, 55–61 (1989)

    Google Scholar 

  20. Croll, A., Muller, S.W., Nitsche, R.: The critical Marangoni number for the onset of time-dependent convection in silicon. Mater. Res. Bull. 24, 995 (1989)

    Article  Google Scholar 

  21. Hibiya, T., Nakamura, S.: Fluid flow in silicon melt with free surface. Adv. Space Res. 24(10), 1225–1230 (1999)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Universitat Rovira i Virgili (URV) grant number DLRF4741.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. Šeta .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Šeta, B. et al. (2021). On the Impact of Body Forces in Low Prandtl Number Liquid Bridges. In: Avdaković, S., Volić, I., Mujčić, A., Uzunović, T., Mujezinović, A. (eds) Advanced Technologies, Systems, and Applications V. IAT 2020. Lecture Notes in Networks and Systems, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-030-54765-3_14

Download citation

Publish with us

Policies and ethics