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Diffusing diffusivity: a model for anomalous, yet Brownian, diffusion.

Mykyta V Chubynsky1, Gary W Slater1

  • 1Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada.

Physical Review Letters
|September 13, 2014
PubMed
Summary
This summary is machine-generated.

Researchers developed a new model for "anomalous yet Brownian" diffusion. This model explains how diffusing colloidal particles can exhibit normal diffusion with non-Gaussian displacement distributions, using a concept called "diffusing diffusivity".

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Colloidal particle diffusion often exhibits normal diffusion, characterized by linear mean-square displacement (MSD).
  • However, non-Gaussian displacement distributions G(x,t) with exponential tails have been observed alongside linear MSD, termed 'anomalous yet Brownian' diffusion.
  • Existing models struggle to explain this phenomenon across diverse systems.

Purpose of the Study:

  • To present a generic model explaining anomalous yet Brownian diffusion.
  • To demonstrate that diffusivity memory, without direction memory, can lead to both linear MSD and non-Gaussian G(x,t).
  • To explore the implications of a 'diffusing diffusivity' concept.

Main Methods:

  • Developed a theoretical model incorporating a random walk for the diffusivity itself ('diffusing diffusivity').
  • Analyzed the model's predictions for mean-square displacement (MSD) and displacement distribution G(x,t).
  • Investigated the impact of different diffusivity distributions on G(x,t).

Main Results:

  • The model successfully reproduces linear MSD and non-Gaussian G(x,t) at short times.
  • The 'diffusing diffusivity' concept provides a unified explanation for the observed phenomena.
  • G(x,t) is predicted to be exponential at short times for exponential diffusivity distributions, with exponential fits remaining accurate for other distributions.
  • The model can be adapted to describe subdiffusion.

Conclusions:

  • The proposed generic model offers a robust explanation for anomalous yet Brownian diffusion.
  • The concept of diffusing diffusivity is key to understanding particle dynamics in complex systems.
  • This framework provides a foundation for further studies into anomalous diffusion phenomena and their modifications.