Exploring nonlocality in planar shear granular flows: Insights from perturbation analysis

A steady dense granular flow in a planar shear configuration, incorporating nonlocal effect into the conventional local μ(I) rheology, is analyzed via the perturbation analysis, using the classical local solution as the zero-order solution. The first-order perturbation is found to be a balance between bulk inertial and nonlocally distributed total stress, controlled by a newly discovered dimensionless nonlocality thinning factor ζ. The explicit analytical solution can reproduce the S-shaped velocity profile and the parabola-like shear rate distributions, with the degree of deviation from the local solution controlled solely by ζ: Bagnold's scaling is recovered at large ζ when inertia thins out the nonlocal effect. This ζ is coupled to the flow height H to deliver the cooperativity length scale, Lc=H/ζ, for the current nonlocal gradient expansion model, which is examined against the literature data as a function of IM. As a side note, experimental and numerical literature data are employed to fit the wall-to-center shear rate ratio to furnish a self-contained explicit solution.