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Elastic fingering in a rotating Hele-Shaw cell.

Benjamin Foster1, Edgar Knobloch1

  • 1Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.

Physical Review. E
|July 19, 2023
PubMed
Summary
This summary is machine-generated.

This study investigates fluid fingering instability in rotating systems with elastic membranes. It reveals how membrane properties and rotation influence instability patterns and finger shapes.

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Area of Science:

  • Fluid dynamics
  • Materials science
  • Nonlinear dynamics

Background:

  • Investigates fingering instability in a rotating Hele-Shaw cell with an elastic membrane separating two fluids.
  • Considers both inextensible and highly extensible membranes, analyzing the impact of membrane tension.

Purpose of the Study:

  • To analyze the steady-state fingering instability driven by centrifugal forces.
  • To explore the competition between Rayleigh-Taylor-like instability and restoring forces (curvature, tension).
  • To compute nonlinear finger states, including self-contact, mixed modes, and chiral states.

Main Methods:

  • Employs numerical continuation to compute primary and secondary finger states.
  • Analyzes the influence of rotation rate and external pressure on instability patterns.
  • Examines the role of system scale relative to natural length scale.

Main Results:

  • Identifies a centrifugally driven Rayleigh-Taylor-like instability when inner fluid density exceeds outer fluid density.
  • Demonstrates that instability is controlled by curvature and tension, determining finger scale.
  • Computes nonlinear states, including symmetry-broken chiral states, and presents results via bifurcation diagrams.

Conclusions:

  • The ratio of system scale to natural length scale dictates primary bifurcation ordering and secondary bifurcation onset.
  • Membrane properties (tension, extensibility) significantly influence the fingering instability dynamics.
  • The study provides a comprehensive analysis of nonlinear fingering phenomena in rotating elastic membrane systems.