[Paper Review] The non-local repercussions of partial jamming in dense granular flows

Prashidha Kharel, Pierre Rognon|arXiv (Cornell University)|May 2, 2016

Granular flow and fluidized beds1 references3 citations

TL;DR

This paper proposes a kinematic, cluster-based non-local model for dense granular flows, deriving a non-local continuum equation from the spatial redistribution of vorticity due to transient jammed particle clusters. The model links the non-local length scale directly to cluster size, showing that non-local behavior emerges universally in glassy materials when partial jamming occurs, with similar predictive power to the established Cooperative model despite differing length scale profiles.

ABSTRACT

This paper establishes a link between the non-local behaviour of granular materials and the presence of transient clusters of jammed particles within the flow. These clusters are first evidenced in simulated dense granular flows subjected to plane shear, and are found to originate from a mechanism of multiple orthogonal shear banding. A continuum non-local model, similar in form to the non-local Cooperative model, is then derived by considering the spatial redistribution of vorticity induced by these clusters. The non-locality length scale is thus expressed in terms of the cluster size. The purely kinematic nature of this derivation indicates that non-local behaviour should be expected in all glassy materials, regardless of their local constitutive law, as long as they partially jam during flow.

Motivation & Objective

• To identify the micro-kinematic origin of non-local behavior in dense granular flows.
• To determine whether transient clusters of jammed particles can explain non-local rheology in glassy materials.
• To derive a continuum non-local model based purely on kinematics, without relying on force networks or stress diffusion.
• To test whether cluster size can replace the cooperativity length scale in existing non-local models.
• To assess the predictive capability of the cluster-based model against DEM simulations in various flow geometries.

Proposed method

• Performing discrete element method (DEM) simulations of dense granular flows under plane shear and Poiseuille flow conditions.
• Identifying transient clusters of jammed particles via a local vorticity-based criterion, with cluster size defined as the spatial extent of correlated vorticity fluctuations.
• Defining a non-local length scale ℓ(y) as the minimum of d/√|I(y)| and the distance to the nearest wall or sign change in μ(y), ensuring physical consistency near boundaries.
• Deriving a continuum non-local model using a vorticity redistribution mechanism, leading to a PDE similar to the Cooperative model but with cluster size as the length scale.
• Solving the model numerically using an implicit finite difference scheme (bvp5c in MATLAB), with zero-gradient boundary conditions on shear rate.
• Comparing model predictions with simulated inertial number profiles and evaluating sensitivity to length scale profile and average values.

Experimental results

Research questions

• RQ1 Can transient clusters of jammed particles be identified in dense granular flows, and do they exhibit a characteristic size that scales with the inertial number?
• RQ2 How can the spatial redistribution of vorticity due to these clusters be used to derive a non-local continuum model?
• RQ3 Is the non-local length scale in such a model equivalent to the cluster size, and does this lead to similar macroscopic predictions as existing non-local models?
• RQ4 Does the cluster-based model perform comparably to the Cooperative model in capturing flow profiles across different geometries?
• RQ5 Is the predictive power of non-local models more sensitive to the average length scale than to its spatial profile?

Key findings

• Transient clusters of jammed particles were consistently observed in DEM simulations of dense granular flows, with average cluster size ℓ scaling as d/√I, consistent with a power-law dependence on the inertial number.
• The derived non-local model, with length scale ℓ(y) defined by Eq. (11), successfully captures the measured inertial number profiles in both plane shear and Poiseuille flows, with discrepancies comparable to those of the Cooperative model.
• Despite significant differences in the spatial profiles of the length scale (diverging at yield in the Cooperative model vs. bounded in the cluster model), both models yield similar predictions, indicating low sensitivity to profile details.
• The average cluster size ⟨ℓ⟩ and average cooperativity length ⟨ξ⟩ were found to be similar across various flow configurations, suggesting that non-local models may depend more on the spatial average of the length scale than its local variation.
• The cluster-based model provides a purely kinematic explanation for non-locality, independent of stress diffusion or force chain networks, offering a new, physically interpretable basis for non-local behavior in glassy materials.
• The results suggest that non-local behavior should be universal in glassy materials as long as partial jamming occurs, regardless of local constitutive law, due to the inherent kinematic redistribution of vorticity by clusters.