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This study investigates the snapping instability of elastic shells in viscous flow, revealing a new valve design for passive flow control. The research combines experiments and simulations to understand fluid-induced elastic instabilities.

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Area of Science:

  • Fluid mechanics
  • Elasticity
  • Soft matter physics

Background:

  • The umbrella flipping problem describes the snapping instability of elastic shells under viscous flow at low Reynolds numbers.
  • Understanding this phenomenon is crucial for developing novel fluid-responsive systems.

Purpose of the Study:

  • To determine the instability threshold of a spherical elastic shell in viscous flow.
  • To develop a snapping-based valve for passive hydraulic resistance control.

Main Methods:

  • Precision desktop-scale experiments
  • Fluid-structure simulations
  • Shell theory and fluid mechanics analysis
  • Scaling analysis

Main Results:

  • The instability threshold was determined as a function of geometrical and material parameters.
  • A functional snapping-based valve was devised, demonstrating robust, passive flow control.
  • The study provides a prototypical example of fluid-induced elastic instability.

Conclusions:

  • The findings offer a fundamental understanding of fluid-induced elastic instabilities in viscous flows.
  • The developed valve presents a novel application in soft hydraulics and flow-responsive structures.
  • This work lays the groundwork for future research in bio-inspired and adaptive fluidic devices.