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Bond Number Revisited: Two-Dimensional Macroscopic Pendant Drop.

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Summary

Two new dimensionless numbers, Rb1 and Rb2, are introduced to describe pendant drop shape and stability using only input parameters. These numbers aid in predicting drop breakup and estimating shape more accurately.

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Area of Science:

  • Fluid dynamics
  • Surface science
  • Physical chemistry

Background:

  • The Bond number is crucial for describing macroscopic pendant drop shape and stability.
  • Traditional Bond number calculations require experimentally derived drop characteristics, limiting their predictive power.

Purpose of the Study:

  • To revisit the definition of the Bond number.
  • To introduce two new dimensionless numbers, Rb1 and Rb2, for pendant drop analysis.
  • To provide numbers that rely solely on input parameters.

Main Methods:

  • Definition of two new dimensionless numbers, Rb1 and Rb2, for 2D pendant drops.
  • Formulation of these numbers using input parameters: drop volume, gravity, fluid densities, surface tension, and contact angle.
  • Comparison with the traditional Bond number, highlighting the exclusion of unknown experimental characteristics.

Main Results:

  • Rb1 and Rb2 are defined for pendant drops with constant contact angle and constant drop-solid contact width, respectively.
  • These new numbers incorporate only measurable input parameters.
  • The new numbers are shown to be applicable for predicting drop breakup conditions and estimating drop shape.

Conclusions:

  • The newly introduced numbers Rb1 and Rb2 offer a more direct and predictive approach to analyzing pendant drop behavior.
  • These numbers overcome limitations of the traditional Bond number by relying exclusively on initial input parameters.
  • The findings facilitate improved prediction of drop stability and shape in various scientific and industrial applications.