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Gravity-driven instability in a spherical Hele-Shaw cell.

J A Miranda1, F Parisio, F Moraes

  • 1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901 Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 17, 2001
PubMed
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Interfacial instability in spherical Hele-Shaw cells is studied. Fingering structures form due to pressure and gravity, showing a tendency toward tip-sharpening.

Area of Science:

  • Fluid dynamics
  • Interface phenomena
  • Instability analysis

Background:

  • Hele-Shaw cells are used to study fluid flow in confined geometries.
  • Interfacial instabilities occur when immiscible fluids interact under flow conditions.
  • Spherical Hele-Shaw cells introduce unique geometric effects on fluid interfaces.

Purpose of the Study:

  • To derive the equation of motion for interface perturbation amplitudes in a spherical Hele-Shaw cell.
  • To analyze the linear stability of the interface under pressure and gravity.
  • To investigate the formation and characteristics of fingering structures.

Main Methods:

  • Derivation of the equation of motion for interface perturbation amplitudes.
  • Application of a mode coupling approach.

Related Experiment Videos

  • Linear stability analysis considering pressure and gravity.

    • Main Results:

    • Mode growth rates are dependent on interface perimeter and gravitational force.
    • Fingering structures are observed to form.
    • A tendency toward finger tip-sharpening is identified.

    Conclusions:

    • The study provides a theoretical framework for understanding interfacial instabilities in spherical Hele-Shaw cells.
    • Pressure and gravity are key drivers of fingering patterns.
    • The observed tip-sharpening phenomenon warrants further investigation.