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Period adding cascades: experiment and modeling in air bubbling.

Felipe Augusto Cardoso Pereira1, Eduardo Colli, José Carlos Sartorelli

  • 1Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, 05315-970 São Paulo, Brazil.

Chaos (Woodbury, N.Y.)
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Summary

Period adding cascades in air bubbling dynamics were reproduced using a simple hydrodynamical model. This model accurately predicts bubble detachment and parameter influences, offering insights into complex fluid dynamics.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Period adding cascades are observed in diverse natural and engineered systems, including fluid dynamics.
  • Previous studies have documented these cascades in various phenomena, but a simple, predictive model for air bubbling was lacking.

Purpose of the Study:

  • To develop and validate a simple model that reproduces period adding cascades in air bubbling from a submerged nozzle.
  • To investigate the influence of key physical parameters on the bubbling dynamics.

Main Methods:

  • A hydrodynamical model based on force balance was formulated, tracking bubble position and air chamber pressure via differential equations.
  • The model was reduced to a one-dimensional iterative map representing air pressures at bubble detachment.
  • Model predictions were compared with experimental data.

Main Results:

  • The model successfully reproduced the period adding cascades observed in experimental air bubbling.
  • The model demonstrated good agreement with experimental data.
  • The model accurately predicted the effects of parameters such as hose length, needle radius, and needle length.

Conclusions:

  • A simplified hydrodynamical model effectively captures the complex dynamics of period adding cascades in air bubbling.
  • The model provides a valuable tool for understanding and predicting the behavior of bubbling systems.
  • This work contributes to the broader understanding of period adding phenomena across different scientific disciplines.