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Universal Rim Thickness in Unsteady Sheet Fragmentation.

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Area of Science:

  • Fluid Dynamics
  • Rheology
  • Droplet Formation

Background:

  • Unsteady fluid fragmentation into droplets is vital for epidemiology (pathogen transport) and industrial applications (paints, combustion).
  • Existing research primarily focuses on steady fragmentation, leaving unsteady processes, like droplet breakup from impacts, less understood.
  • The destabilization of a rim in an expanding fluid sheet dictates final droplet size but lacks a clear theoretical explanation.

Purpose of the Study:

  • To investigate the poorly understood unsteady rim destabilization during droplet fragmentation.
  • To identify the governing physical principles behind the selection of final spray droplets in unsteady fragmentation.
  • To establish a robust and universal criterion for unsteady fluid sheet fragmentation.

Main Methods:

  • Combined theoretical analysis with advanced image analysis techniques.
  • Studied a canonical unsteady fragmentation process: drop impact on a finite surface.
  • Analyzed the dynamics of a free expanding fluid sheet with time-varying properties and a bounded rim.

Main Results:

  • Identified a universal criterion: the rim thickness is governed by a local instantaneous Bond number (Bo) of unity.
  • This criterion is defined using the instantaneous, local, unsteady rim acceleration.
  • The criterion demonstrated robustness and universality across various surface geometries and impact scenarios (drops on films).

Conclusions:

  • The local instantaneous Bond number equal to unity reliably predicts unsteady rim thickness in fluid sheet fragmentation.
  • This criterion is applicable to a range of unsteady inviscid fluid sheet fragmentation phenomena.
  • Further investigation is needed to determine the applicability of this criterion under viscous and viscoelastic conditions.