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Nonlocal Effects in Inhomogeneous Flows of Soft Athermal Disks
Kuniyasu Saitoh1,2, Brian P Tighe3
1Research Alliance Center for Mathematical Sciences, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
Physical Review Letters
|May 31, 2019
Summary
Nonlocal effects significantly impact soft, athermal disk flows near jamming. Standard local models fail, but nonlocal relations accurately capture stress profiles without diverging length scales.
Area of Science:
- Soft matter physics
- Rheology of granular materials
Background:
- Jamming transition in soft matter systems
- Nonlocal effects in fluid dynamics
- Athermal granular flows
Purpose of the Study:
- Investigate nonlocal effects on inhomogeneous soft athermal disk flows
- Understand rheology near the jamming transition
- Develop accurate constitutive models for granular flows
Main Methods:
- Numerical simulations using molecular dynamics
- Modeling Kolmogorov flows with imposed sinusoidal profiles
- Analysis of wave-number dependence and particle migration
Main Results:
- Rheology is strongly wave-number-dependent
- Particle migration alone does not explain stress profiles
- Nonlocal constitutive relations (fourth-order gradients) capture stress profiles
- No diverging length scale observed, unlike in yield stress fluids
Conclusions:
- Nonlocal constitutive relations are essential for describing inhomogeneous soft matter flows
- Standard local models are insufficient for these systems
- The jamming transition in soft athermal disks exhibits unique nonlocal characteristics
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