Bond Number Revisited: Two-Dimensional Macroscopic Pendant Drop

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.