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Related Experiment Videos

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study.

R Folch1, J Casademunt, A Hernández-Machado

  • 1Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study introduces a phase-field simulation for two-fluid dynamics in Hele-Shaw cells, accurately capturing phenomena like Saffman-Taylor fingers and multifinger competition across various viscosity contrasts.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Materials science

Background:

  • Hele-Shaw cells are crucial for studying fluid interfaces.
  • Simulating multiphase flow with arbitrary viscosity contrast presents challenges.
  • Phase-field methods offer a promising approach for interface dynamics.

Purpose of the Study:

  • To implement and validate a phase-field simulation for two-fluid dynamics in a Hele-Shaw cell.
  • To investigate phenomena including linear instability, stationary Saffman-Taylor fingers, and multifinger competition.
  • To assess the method's accuracy against analytical and numerical benchmarks.

Main Methods:

  • Phase-field simulation technique.
  • Modeling of two immiscible fluids with arbitrary viscosity ratios.

Related Experiment Videos

  • Rectangular Hele-Shaw cell geometry.
  • Analysis of linear dispersion, finger dynamics, and multifinger competition.

    • Main Results:

    • The phase-field method successfully simulates various fluid dynamics regimes.
    • Quantitative agreement with analytical predictions and existing numerical results was achieved.
    • Convergence to the sharp interface limit was demonstrated for linear dispersion.
    • The simulation accurately captures Saffman-Taylor finger formation and competition.

    Conclusions:

    • The developed phase-field simulation is a robust tool for studying two-fluid dynamics.
    • It accurately reproduces key phenomena in Hele-Shaw flows.
    • This method offers a viable and potentially advantageous alternative to traditional simulation techniques.