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Updated: Jul 11, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Crossover from superdiffusive to diffusive mixing in plastically deformed solids
P Bellon1, R S Averback, S Odunuga
1Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
Physical Review Letters
|October 13, 2007
Summary
We found that how particles mix in strained solids changes from superdiffusive to diffusive as separation distance increases. This provides insight into plastic deformation mechanisms and precipitate dissolution.
Area of Science:
- Materials Science
- Solid Mechanics
- Computational Materials Science
Background:
- Plastic deformation in solids involves complex shearing events.
- Understanding mixing dynamics is crucial for predicting material behavior.
- Richardson's pairs are a model system for studying mixing in turbulent and complex media.
Purpose of the Study:
- To derive expressions for the effective diffusion coefficient of Richardson's pairs in plastically strained solids.
- To investigate the crossover from superdiffusive to diffusive mixing.
- To provide new insights into deformation mechanisms in nanocrystalline and amorphous systems.
Main Methods:
- Derivation of analytical expressions for the effective diffusion coefficient.
- Utilizing molecular dynamics simulations.
- Analyzing systems including nanocrystalline and amorphous solids.
Main Results:
- Expressions for effective diffusion coefficient as a function of pair separation distance (R).
- Prediction of a crossover from superdiffusive to diffusive mixing at a specific R.
- Simulation results supporting the analytical predictions.
Conclusions:
- The crossover in mixing behavior is linked to the coherence length of shearing events.
- This analysis offers new insights into plastic deformation mechanisms.
- Superdiffusive mixing can be observed experimentally via precipitate dissolution rates.
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