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Microscopic selection of fluid fingering patterns.

D A Kessler1, H Levine

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan, Israel. kessler@dave.ph.biu.ac.il

Physical Review Letters
|June 1, 2001
PubMed
Summary
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In viscous fingering, small surface tension leads to chaotic patterns, not macroscopic selection. The small-scale cutoff entirely dictates pattern formation, aligning with microscopic solvability theory.

Area of Science:

  • Fluid dynamics
  • Pattern formation
  • Nonlinear dynamics

Background:

  • Viscous fingering is a classic instability in fluid dynamics.
  • Understanding pattern selection in these systems is crucial for various applications.
  • Previous theories suggested macroscopic selection mechanisms.

Purpose of the Study:

  • To investigate viscous fingering pattern selection in the limit of small surface tension.
  • To determine if macroscopic selection occurs independently of small-scale cutoffs.
  • To elucidate the role of microscopic solvability in pattern formation.

Main Methods:

  • Detailed numerical simulations of anisotropic viscous fingering.
  • Analysis of pattern evolution under varying surface tension conditions.

Related Experiment Videos

  • Comparison of simulation results with microscopic solvability theory.

    • Main Results:

    • No macroscopic selection of viscous fingering patterns was observed.
    • The small-scale cutoff was found to completely control pattern formation.
    • Ordered patterns are selected only for sufficiently large surface tensions.
    • Extremely small surface tensions result in chaotic behavior and no regular patterns.

    Conclusions:

    • Pattern selection in viscous fingering is governed by microscopic solvability, not macroscopic effects.
    • The small-scale cutoff plays a critical role in determining the emergent patterns.
    • Chaotic behavior dominates at very low surface tensions, preventing ordered pattern formation.