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Related Experiment Videos

Draining Collars and Lenses in Liquid-Lined Vertical Tubes.

Jensen1

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, United Kingdom

Journal of Colloid and Interface Science
|January 7, 2000
PubMed
Summary

Liquid collars draining in tubes can grow or shrink depending on the modified Bond number (B). Below B=0.5960, collars grow and may snap off to form lenses, while higher B values lead to shrinking or snapping off under certain conditions.

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Area of Science:

  • Fluid dynamics
  • Rheology
  • Surface science

Background:

  • Understanding liquid behavior in confined geometries is crucial for various industrial processes.
  • Annular liquid collars in viscous films present complex drainage dynamics.
  • Gravity and surface tension forces govern the stability and evolution of these liquid structures.

Purpose of the Study:

  • To investigate the nonlinear stability criteria for draining annular liquid collars in a viscous film within a vertical tube.
  • To determine the conditions under which collars grow or shrink and ultimately 'snap off' or form stable lenses.
  • To analyze the influence of the modified Bond number (B) on collar dynamics.

Main Methods:

  • Utilized asymptotic methods to analyze the drainage dynamics of annular liquid collars.

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  • Derived nonlinear stability criteria based on the balance between gravitational forces and viscous shear stresses.
  • Investigated the role of the modified Bond number (B = rho g a^2 / (sigma epsilon)) in predicting collar behavior.

    • Main Results:

    • Established critical values for the modified Bond number (B) that dictate collar stability and evolution.
    • Found that for 0 < B < 0.5960, collars grow and snap off; for 0.5960 < B < 1.769, behavior depends on initial size and tube length; for 1.769 < B < 11.235, collars typically shrink.
    • Demonstrated that surfactant immobilization reduces critical B values but does not alter snapping-off distance.

    Conclusions:

    • Collar drainage dynamics are highly sensitive to the modified Bond number, influencing whether they grow, shrink, or snap off.
    • Gravitationally driven snap-off is favored in long tubes with radii smaller than the capillary length.
    • The study provides a framework for predicting the fate of liquid collars in confined viscous films.