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Related Experiment Videos

Diffusion on random-site percolation clusters: theory and NMR microscopy experiments with model objects.

Andreas Klemm1, Ralf Metzler, Rainer Kimmich

  • 1Sektion Kernresonanzspektroskopie, Universität Ulm, 89069 Ulm, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
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This study experimentally verified anomalous diffusion on percolation clusters using nuclear magnetic resonance microscopy. Researchers compared dynamical and static exponents, confirming fractional diffusion equation predictions.

Area of Science:

  • Physics
  • Materials Science
  • Chemical Engineering

Background:

  • Anomalous diffusion deviates from standard Brownian motion, often observed in complex media.
  • Percolation theory describes systems with randomly distributed elements, impacting transport properties.

Purpose of the Study:

  • To experimentally investigate anomalous diffusion in quasi-two-dimensional random-site percolation models.
  • To compare dynamical and static fractal dimensions derived from diffusion and structural measurements.
  • To validate solutions of the fractional diffusion equation for anomalous transport.

Main Methods:

  • Fabrication of quasi-two-dimensional percolation model objects using computer-generated templates.
  • Nuclear magnetic resonance (NMR) microscopy to map proton spin density and track interdiffusion.

Related Experiment Videos

  • Analysis of proton/deuteron interdiffusion profiles to determine anomalous diffusion parameters.

    • Main Results:

    • Proton/deuteron interdiffusion profiles were recorded and analyzed for anomalous diffusion.
    • Experimental comparison of the fractal dimension of the random walk (dynamical exponent) and the fractal dimension of the percolation object (static exponent).
    • Anomalous diffusion constants were evaluated and compared to Brownian diffusion.

    Conclusions:

    • The study experimentally verified anomalous solutions of the fractional diffusion equation.
    • Deviations in concentration profiles confirmed anomalous diffusion on percolation clusters.
    • The findings provide experimental validation for theoretical models of diffusion in complex, disordered systems.