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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Nonlocal constitutive relation for steady granular flow.

Ken Kamrin¹, Georg Koval

¹Department of Mechanical Engineering, MIT, Cambridge, Massachusetts 01239, USA.

Physical Review Letters

|June 12, 2012

Summary

This summary is machine-generated.

We developed a new model for flowing granular materials that accurately captures grain size effects and rate-independence in steady flow. This nonlocal fluidity relation extends existing models and shows good agreement with simulations.

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Area of Science:

Physics
Materials Science
Fluid Dynamics

Background:

Recent modeling efforts for emulsions provide a foundation.
Flowing granular materials exhibit complex behaviors, including finite-size effects.
Local Bagnold-type granular flow laws are insufficient for certain granular flows.

Purpose of the Study:

To propose a nonlocal fluidity relation for flowing granular materials.
To incorporate grain size effects and finite-size phenomena into granular flow models.
To extend and validate a new granular flow model against discrete element method simulations.

Main Methods:

Expressing the local Bagnold-type granular flow law in terms of a fluidity ratio.
Extending the local law with a nonlocal Laplacian term scaled by grain size.
Calibrating the model against discrete element method (DEM) data for 2D annular shear and inhomogeneous flow.

Main Results:

The proposed model successfully captures finite-size effects in steady granular flow.
It accurately describes the divergence from local rheology due to grain size.
The model demonstrates rate-independence in slowly flowing zones and agrees with DEM simulations in various geometries.

Conclusions:

The nonlocal fluidity relation provides a more comprehensive description of granular material flow.
The model effectively accounts for the influence of grain size on rheology.
This work offers a validated tool for simulating granular flows in different configurations.