Skip to main content
Log in

Numerical Investigation of Thermocapillary Convection in a Liquid Layer with Free Surface

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

Effects of Marangoni number, aspect ratio and gravity level on thermocapillary convection in a liquid layer is investigated numerically, in which the level set method is employed to capture free surface deformation. The computational results show that, with the increase of Marangoni number the free surface deformation is increased and it can lead to free surface rupture if the Marangoni number is large enough. The end walls has a damping effect on the free surface deformation, and as the aspect ratio (A =L/(0.5H)) decreases the deformability of free surface is reduced. The gravity can damp the free surface deformation, particularly as gravity level varies from 0.0001g 0 to g 0 the free surface deformability decreases steeply.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Babu, V., Korpela, S.A.: Three-dimensional thermocapillary convection in a cavity. Comput. Fluids. 18, 229–238 (1990)

    Article  Google Scholar 

  • Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  • Carpenter, M., Homsy, G.M.: High Marangoni number convection in a square cavity. Part II. Phys. Fluids A 2, 137–149 (1990)

    Article  MATH  Google Scholar 

  • Gupta, N.R., Hossein, H.H., Borhan, A.: Thermocapillary flow in double-layer fluid structures: an effective single-layer model. J. Colloid Interface Sci. 293, 158–171 (2006)

    Article  Google Scholar 

  • Hamed, M., Floryan, J.M.: Marangoni convection. Part 1. A cavity with differentially heated sidewalls. J. Fluid Mech 405, 79–110 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Koster, J.N.: Early mission report on the four ESA facilities: biorack; bubble, drop and particle unit; critical point facility and advanced protein crystallization facility flown on the IML-2 spacelab mission. Microgr. News ESA 7, 2–7 (1994)

    Google Scholar 

  • Lappa, M.: On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces. Fluid Dyn. Mater. Proc. 1, 1–19 (2005)

    Google Scholar 

  • Mundrane, M., Xu, J., Zebib, A.: Thermocapillary convection in a rectangular cavity with a deformable interface. Adv. Space Res. 16, 41–53 (1995)

    Article  Google Scholar 

  • Ni, M.J., Komori, S., Abdou, M.: A variable-density projection method for interfacial flows. Numer. Heat Tran. B 44, 553–574 (2003)

    Article  Google Scholar 

  • Peltier, L. J., Biringen, S.: Time-dependent thermocapillary convection in a rectangular cavity: numerical results for a moderate Prandtl number fluid. J. Fluid Mech. 257, 339–357 (1993)

    Article  MATH  Google Scholar 

  • SaB, V., Kuhlmann, H.C., Rath, H.J.: Investigation of three-dimensional thermocapillary convection in a cubic container by a multi-grid method. Int. J. Heat Mass Transfer. 39, 603– 613 (1996)

    Article  Google Scholar 

  • Saghir, M.Z., Abbaschian, R., Raman, R.: Numerical analysis of thermocapillary convection in axisymmetric liquid encapsulated InBi. J. Crys. Grow 169, 110–117 (1996)

    Article  Google Scholar 

  • Smith, M. K., Davis, S. H.: Instabilities of dynamic thermocapillary liquid layers. Part 1: Convective instabilities. J. Fluid Mech. 132, 119–144 (1983)

    Article  MATH  Google Scholar 

  • Strani, M., Piva, R., Graziani, G.: Thermocapillary convection in a rectangular cavity: asymptotic and numerical simulation. J. Fluid Mech. 130, 347–376 (1983)

    Article  MATH  Google Scholar 

  • Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146–159 (1994)

    Article  MATH  Google Scholar 

  • Tang, Z.M., Li, K., Hu, W.R.: Influence of free surface curvature of a liquid layer on the critical Marangoni convection. Int. J. Heat Mass Transfer. 51(21–22), 5102–5107 (2008)

    Article  MATH  Google Scholar 

  • Xu, J., Zebib, A.: Oscillatory two- and three-dimensional thermocapillary convection. J. Fluid Mech. 364, 187–209 (1998)

    Article  MATH  Google Scholar 

  • Xun, B., Li, K., Hu, W.R.: Instability of thermocapillary flow in liquid layers under microgravity. Sci. China Phys. Mech. Astron. 55(4), 684–692 (2012)

    Article  Google Scholar 

  • Zhou, X.M., Huang, H.L.: Numerical simulation of steady thermocapillary convection in a two-layer system using level set method. Microgravity Sci. Technol. 22, 223–232 (2010)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No.501206165).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaoming Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, X., Huai, X. Numerical Investigation of Thermocapillary Convection in a Liquid Layer with Free Surface. Microgravity Sci. Technol. 25, 335–341 (2014). https://doi.org/10.1007/s12217-014-9361-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12217-014-9361-5

Keywords

Navigation