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Area of Science:

  • Fluid dynamics
  • Rheology
  • Pattern formation

Background:

  • Investigating interfacial instabilities in rotating Hele-Shaw cells.
  • Focusing on a two-fluid system where the interface forms an elastic layer due to a chemical reaction.
  • Examining the influence of centrifugal forces on fluid behavior.

Purpose of the Study:

  • To find equilibrium shapes in centrifugally driven interfacial elastic fingering.
  • To understand the development of interfacial instabilities under combined centrifugal and elastic forces.
  • To classify the resulting stationary shapes based on system parameters.

Main Methods:

  • Utilizing a vortex sheet formalism for analysis.
  • Solving a nonlinear differential equation for interface curvature (shape equation).
  • Employing a zero vorticity condition to determine equilibrium.

Main Results:

  • Observed a rich variety of stationary shapes arising from the interplay of forces.
  • Generated visually striking equilibrium morphologies.
  • Classified shape families using effective bending rigidity and radius of gyration parameters.

Conclusions:

  • The study successfully identified and classified equilibrium shapes in a complex fluid system.
  • Demonstrated the significant role of elastic forces in stabilizing interfacial patterns against centrifugal drive.
  • Provided a framework for understanding pattern formation in rotating elastic-fringe systems.