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Area of Science:

  • Fluid dynamics
  • Interface phenomena
  • Complex systems

Background:

  • Hele-Shaw cells are crucial for studying fluid dynamics.
  • Understanding interfacial patterns is key in multiphase flow.
  • Curved geometries introduce unique physical challenges.

Purpose of the Study:

  • To investigate generalized elastica-like equilibrium shapes at fluid interfaces.
  • To analyze the influence of geometric properties in curved rotating Hele-Shaw cells.
  • To understand the balance between capillary and centrifugal forces.

Main Methods:

  • Utilizing a vortex-sheet formalism to compute interface curvature.
  • Applying linear perturbation theory to analyze interfacial modes.
  • Examining stationary interface solutions in a curved rotating Hele-Shaw cell.

Main Results:

  • Identified a family of stationary interface solutions.
  • Demonstrated that geometric properties impact interfacial patterns.
  • Showed that two dominant interfacial modes reproduce complex patterns.

Conclusions:

  • The interplay of capillary and centrifugal forces governs equilibrium shapes.
  • Cell geometry and fluid dynamics are intrinsically linked to interfacial modes.
  • The study provides insights into morphological features of fluid interfaces.