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Bond Number Revisited: Axisymmetric Macroscopic Pendant Drop.

Gersh O Berim1, Eli Ruckenstein1

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Summary

New Rb numbers characterize axisymmetric pendant drops using only input parameters, unlike traditional methods. These numbers predict drop breakup and surface tension, showing good agreement with experimental data.

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Area of Science:

  • Physical Chemistry
  • Fluid Dynamics
  • Surface Science

Background:

  • Cylindrical pendant drops characterized by Rb numbers.
  • Axisymmetric pendant drops are more common in experiments.

Purpose of the Study:

  • Modify existing Rb numbers for axisymmetric pendant drops.
  • Develop new dimensionless numbers based on the Young-Laplace equation.
  • Provide a method using only input parameters for drop characterization.

Main Methods:

  • Rigorous solution of the Young-Laplace equation for drop profile.
  • Definition of new Rb numbers (Rbθ and Rb) based on input parameters.
  • Comparison of theoretical predictions with literature experimental data.

Main Results:

  • New Rb numbers are defined using drop volume, gravity, densities, surface tension, and contact angle.
  • Unlike traditional numbers, new Rb numbers do not require unknown drop dimensions.
  • The new numbers effectively predict drop breakup, determine surface tension, and estimate shape deviation.

Conclusions:

  • The modified Rb numbers offer a more practical approach to characterizing axisymmetric pendant drops.
  • These numbers provide a valuable tool for fluid dynamics and surface science research.
  • Demonstrated good agreement between theoretical predictions and experimental results.