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Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
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Updated: Mar 12, 2026

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films
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Stability of thin liquid curtains.

E S Benilov1, R Barros1, S B G O'Brien1

  • 1Department of Mathematics, University of Limerick, Limerick V94 T9PX, Ireland.

Physical Review. E
|November 15, 2016
PubMed
Summary

Thin liquid curtains are stable to small perturbations, contrary to prior theories. Large upstream-propagating perturbations can cause instability, leading to a new stability criterion for liquid curtain dynamics.

Area of Science:

  • Fluid dynamics
  • Surface tension phenomena
  • Hydrodynamics

Background:

  • Thin liquid curtains are crucial in various industrial applications.
  • Previous theoretical models suggested potential instabilities in liquid curtains.
  • Experimental observations often contradicted theoretical predictions regarding curtain stability.

Purpose of the Study:

  • To investigate the stability of thin liquid curtains against two-dimensional perturbations.
  • To reconcile theoretical predictions with experimental findings on liquid curtain behavior.
  • To establish a precise stability criterion for liquid curtains.

Main Methods:

  • Utilizing the lubrication approximation for analyzing perturbation dynamics.
  • Examining perturbations with wavelengths comparable to or exceeding curtain thickness.

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  • Deriving an existence condition for upstream propagating perturbations.
  • Main Results:

    • Demonstrated that thin liquid curtains are stable to small perturbations, aligning with experimental data.
    • Identified that large perturbations can induce instability if they propagate upstream.
    • Confirmed that upstream propagation can disrupt the curtain at its outlet.

    Conclusions:

    • All thin liquid curtains exhibit stability against small perturbations.
    • An effective stability criterion can be derived from the conditions for upstream propagating perturbations.
    • The study provides a refined understanding of liquid curtain stability, resolving theoretical discrepancies.