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Cahn-hilliard theory for unstable granular fluids

van Noije TP1, Ernst

  • 1Instituut voor Theoretische Fysica, Universiteit Utrecht, Postbus 80006, 3508 TA Utrecht, The Netherlands.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

This study introduces a theory for hydrodynamic fluctuations in cooling granular fluids, explaining pattern formation through density clustering and vortex generation. Findings match simulations of inelastic hard disk fluids.

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Area of Science:

  • Physics
  • Materials Science
  • Fluid Dynamics

Background:

  • Freely cooling granular fluids exhibit complex emergent structures.
  • Understanding early-stage evolution of density and flow fields is crucial.

Purpose of the Study:

  • To propose a Cahn-Hilliard-type theory for hydrodynamic fluctuations in granular fluids.
  • To quantitatively describe spatial correlations and structure formation.
  • To identify mechanisms driving pattern selection.

Main Methods:

  • Developed a Cahn-Hilliard-type theoretical framework.
  • Analyzed unstable modes and selective noise reduction for pattern selection.
  • Derived analytic expressions for spatial correlation functions and structure factors.

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Main Results:

  • Identified two key mechanisms: density clustering (spinodal decomposition-like) and vortex pattern formation (selective noise reduction).
  • Observed a shift in the density field's structure factor maximum to smaller wave numbers over time.
  • Demonstrated good agreement between derived analytic expressions and molecular dynamics simulations.

Conclusions:

  • The proposed theory quantitatively describes early-stage structure formation in cooling granular fluids.
  • The identified mechanisms provide insight into pattern selection and evolution.
  • The findings are validated by simulations of inelastic hard disk fluids.