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Suppression of dripping from a ceiling.

J M Burgess1, A Juel, W D McCormick

  • 1Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.

Physical Review Letters
|February 15, 2001
PubMed
Summary

Gravitationally unstable liquid layers can be stabilized by thermocapillarity. A critical temperature difference prevents instability, with the most unstable wavelength becoming infinitely long at this point.

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Area of Science:

  • Fluid dynamics
  • Surface physics

Background:

  • Isothermal liquid layers suspended from a surface are inherently unstable due to gravity (Rayleigh-Taylor instability).
  • Temperature gradients can influence fluid behavior through surface tension effects (thermocapillarity).

Purpose of the Study:

  • To investigate the stabilizing effect of thermocapillarity on gravitationally unstable liquid layers.
  • To determine the critical temperature difference required for stabilization.
  • To analyze the relationship between temperature difference and instability wavelengths.

Main Methods:

  • Experimental measurements of the most unstable wave number.
  • Linear stability analysis of the liquid-gas layer system.
  • Imposing a vertical temperature difference across the layer, heated from below.

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Main Results:

  • A vertical temperature difference above a critical value, (DeltaT)(c), stabilizes the liquid layer.
  • The stabilizing force is provided by temperature-dependent surface tension (thermocapillarity).
  • Experimental measurements for DeltaT < (DeltaT)(c) align with linear stability predictions.
  • The instability manifests at long wavelengths, with the most unstable wavelength approaching infinity at (DeltaT)(c).

Conclusions:

  • Thermocapillarity can effectively counteract gravitational instability in suspended liquid layers.
  • The critical temperature difference is a key parameter for controlling layer stability.
  • Instability onset is characterized by a transition to infinite wavelengths.