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Instability of thermocapillary flow in liquid layers under microgravity

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Abstract

The instability of the thermocapillary flow in liquid layers is studied in the present paper using the linear stability analysis. Based on the two-dimensional steady flow state, the three-dimensional disturbance with a wave number in the spanwise direction is considered. The effects of the aspect ratio and free surface shape of the liquid layer on the flow instability are studied, and the results are compared with the case with the two-dimensional disturbance.

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References

  1. Davis S H. Thermocapillary instabilities. Anu Rev Fluid Mech, 1987, 19: 403–435

    Article  ADS  MATH  Google Scholar 

  2. Schatz M F, Neitzel G P. Experiments on thermocapillary instability. Anu Rev Fluid Mech, 2001, 33: 93–129

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  4. Smith M K. Instability mechanisms in dynamic thermocapillary liquid layers. Phys Fluids, 1986, 29: 3182–3186

    Article  ADS  Google Scholar 

  5. Smith M K. The nonlinear stability of dynamic thermocapillary liquid layers. J Fluid Mech, 1988, 194: 391–415

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  7. Carpenter M, Homsy G M. High marangoni number convection in a square cavity: Part II. Phys Fluids, 1990, A2: 137–149

    ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  9. Saβ 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, 1996, 39: 603–613

    Article  Google Scholar 

  10. 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, 2005, 1: 1–19

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  13. Schimmel F, Albensoeder S, Kuhlmann H. Stability of thermocapillarydriven flow in rectangular cavities. Proc Appl Math Mech, 2005, 5: 583–584

    Article  Google Scholar 

  14. Golub G H, Van Loan C F. Matrix Computation. Baltimore: Johns Hopkins University Press, 1996

    Google Scholar 

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Correspondence to WenRui Hu.

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Recommended by Hu WenRui (CAS Academician)

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Xun, B., Li, K. & Hu, W. Instability of thermocapillary flow in liquid layers under microgravity. Sci. China Phys. Mech. Astron. 55, 684–692 (2012). https://doi.org/10.1007/s11433-012-4663-3

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  • DOI: https://doi.org/10.1007/s11433-012-4663-3

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