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Related Experiment Videos

Spatial and temporal coarse graining for dispersion in randomly packed spheres.

Ulrich M Scheven1, Pabitra N Sen

  • 1Schlumberger-Doll Research, Old Quarry Road, Ridgefield, Connecticut 06877, USA.

Physical Review Letters
|December 18, 2002
PubMed
Summary

Molecular displacement propagators were measured in bead packs. Results show non-Gaussian behavior at low diffusion lengths, deviating from advection-diffusion equations, but approach Gaussian shapes with increased displacement.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Understanding molecular displacement is crucial in porous media.
  • Stokes flow in bead packs is a model system for complex fluid dynamics.
  • Non-Gaussian diffusion deviates from standard advection-diffusion models.

Purpose of the Study:

  • To measure the propagator for molecular displacements in Stokes flow.
  • To investigate the influence of sphere size and diffusion on displacement patterns.
  • To determine the conditions under which advection-diffusion equations are valid.

Main Methods:

  • Experimental measurement of the propagator P(zeta, t) and its cumulants.
  • Systematic variation of normalized mean displacement (/d) and diffusion length (L(D)=sqrt[2D(m)t]/d).

Related Experiment Videos

  • Use of monodisperse bead packs with varying sphere sizes (d) and diffusion coefficients (D(m)).

    • Main Results:

    • Experimental results scale with normalized mean displacement and diffusion length.
    • Non-Gaussian propagator observed for L(D)/d < 0.2, even for large mean displacements (>10d).
    • A Gaussian shape is approached as L(D)/d > 0.3, indicating a transition in diffusion behavior.

    Conclusions:

    • The advection-diffusion equation is not obeyed under certain conditions of low diffusion length and high displacement.
    • Scaling with normalized mean displacement and diffusion length provides a unifying framework for the data.
    • The study elucidates the transition from non-Gaussian to Gaussian diffusion in porous media flow.