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Saffman-Taylor problem on a sphere.

F Parisio1, F Moraes, J A Miranda

  • 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 20, 2001
PubMed
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This study extends the Saffman-Taylor problem to spherical Hele-Shaw cells, revealing that positive curvature inhibits finger tip-splitting in fluid interfaces. The research analyzes both linear and nonlinear flow regimes for enhanced stability understanding.

Area of Science:

  • Fluid dynamics
  • Interface morphology
  • Hele-Shaw flow

Background:

  • The Saffman-Taylor problem describes fluid interface instability in Hele-Shaw cells.
  • Classic studies focus on planar geometries, limiting understanding of curved systems.

Purpose of the Study:

  • To extend the Saffman-Taylor problem to spherical Hele-Shaw cells.
  • To investigate the impact of spatial curvature on interfacial pattern formation.
  • To analyze linear and nonlinear flow regimes in curved geometries.

Main Methods:

  • Derivation of the mode-coupling differential equation for interface perturbation amplitudes.
  • Analysis of both linear and nonlinear flow regimes.
  • Investigation of positive spatial curvature effects on interfacial patterns.

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Main Results:

  • Positive spatial curvature in spherical Hele-Shaw cells inhibits finger tip-splitting.
  • Fluid-fluid interface stability is sensitive to surface curvature.
  • Hele-Shaw flow on weakly negative curved surfaces is also considered.

Conclusions:

  • Spherical Hele-Shaw cells offer a new platform for studying interfacial instabilities.
  • Curvature is a critical parameter influencing Saffman-Taylor dynamics.
  • Findings contribute to understanding fluid behavior in confined, curved geometries.