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Why a falling drop does not in general behave like a rising bubble.

Manoj Kumar Tripathi1, Kirti Chandra Sahu1, Rama Govindarajan2

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A settling drop is not generally equivalent to a rising bubble. However, equivalence occurs for density ratios near unity, especially with low inertia and high surface tension, revealing distinct fluid dynamics and break-up behaviors.

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Area of Science:

  • Fluid dynamics
  • Multiphase flow
  • Interface phenomena

Background:

  • The dynamics of rising bubbles and settling drops are fundamental in fluid mechanics.
  • Understanding their equivalence is crucial for modeling various natural and industrial processes.
  • Previous studies have explored similarities and differences under specific conditions.

Purpose of the Study:

  • To investigate the conditions under which a settling drop can be considered dynamically equivalent to a rising bubble.
  • To analyze the influence of density ratio, inertia, and surface tension on bubble-drop equivalence.
  • To compare the accuracy of Hadamard's solution versus the Boussinesq approximation for these phenomena.

Main Methods:

  • Theoretical analysis using Hadamard's exact solution and Boussinesq approximation.
  • Development of scaling relationships.
  • Numerical simulations of bubble and drop dynamics.
  • Analysis of vorticity concentration and shape evolution.

Main Results:

  • Bubble-drop equivalence is established for density ratios close to unity, moderate inertia, and high surface tension.
  • Hadamard's solution is more accurate than the Boussinesq approximation.
  • Vorticity concentration in lighter fluids significantly differentiates drop and bubble behavior when density ratios deviate from unity.
  • Distinct shape oscillations and break-up mechanisms are observed for drops and bubbles as Galilei and Bond numbers increase.

Conclusions:

  • Bubble-drop equivalence is a nuanced phenomenon, highly dependent on the density ratio.
  • The distribution of vorticity plays a critical role in dictating dynamic differences.
  • Understanding these differences is key to predicting shape evolution and break-up in multiphase flows.