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Shape of a recoiling liquid filament.

Francesco Paolo Contò1, Juan F Marín2, Arnaud Antkowiak3,4

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This study reveals capillary waves and neck formation during liquid filament retraction. The research analytically proves capillary wave characteristics and neck size, offering a comprehensive view of the recoiling process.

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Area of Science:

  • Fluid Dynamics
  • Rheology
  • Surface Science

Background:

  • Capillary retraction is a fundamental process in fluid dynamics.
  • Previous studies, like Taylor and Culick's, focused on retraction velocity.
  • A detailed understanding of the filament profile evolution and associated phenomena is lacking.

Purpose of the Study:

  • To analytically investigate the capillary retraction of a Newtonian semi-infinite liquid filament.
  • To identify distinct regions and phenomena during filament recoiling.
  • To characterize capillary waves and neck formation.

Main Methods:

  • Utilized analytical methods to derive a long-time asymptotic-state expansion.
  • Employed a one-dimensional free-surface slender cylindrical flow model.
  • Based the model on three-dimensional axisymmetric Navier-Stokes equations.

Main Results:

  • Identified three distinct regions: steady filament, growing spherical blob, and intermediate zone.
  • Demonstrated the natural development of travelling capillary waves and a neck.
  • Analytically proved capillary wave wavelength (approx. 3.63 times filament radius in inviscid limit).
  • Analyzed wave characteristics and neck size in relation to the Ohnesorge number.

Conclusions:

  • The study provides a comprehensive picture of liquid filament recoiling.
  • Findings extend beyond classic retraction velocity results.
  • Analytical results show good agreement with literature and numerical simulations.