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Unpredictable air bubble dynamics in viscous fluids arise from sensitive dependence on initial conditions. Even minor perturbations can lead to vastly different bubble propagation and breakup outcomes.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Chaos theory typically describes systems highly sensitive to initial conditions.
  • Air bubble propagation in viscous fluids is a complex nonlinear system.

Purpose of the Study:

  • To investigate unpredictable dynamics in a nonlinear system of air bubble propagation.
  • To identify conditions leading to sensitive dependence on initial conditions in this system.

Main Methods:

  • Subjecting steadily-propagating bubbles to finite-amplitude perturbations (localised constrictions).
  • Combining high-precision experimental results with simulations of a depth-averaged lubrication model.

Main Results:

  • Identified localised regions of flow rate yielding unpredictable bubble evolutions.
  • Observed visibly-indistinguishable bubbles evolving into multiple stable states or altered topologies.
  • Determined behaviour driven by sensitive dependence near an unstable periodic orbit.

Conclusions:

  • Demonstrated chaos-like unpredictability in a bubble propagation system.
  • Highlighted the role of unstable periodic orbits in driving complex system behaviour.
  • Showcased the interplay between initial conditions, perturbations, and long-term outcomes.