Power-Law Scaling in Granular Rheology across Flow Geometries

Abstract

Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio μ by a power of dimensionless temperature Θ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model.

Efficacy of simple continuum models for diverse granular intrusions

“…The elastic and external forces are integrated via Newton's laws of motion to calculate particle velocities and positions in DEM. In the past few decades, DEM has played a major role in the advancement of the field of granular media 11,12 .…”

Microscopic Origin of Nonlocal Rheology in Dense Granular Materials

“…(5), with C f ≈ 1.6 in this case. Finally, additional successful comparisons with data from Kim and Kamrin [25], obtained for different geometries and different values of interparticle friction, are shown in the Supplemental Material (Fig. S2) [24].…”

“…S2) [24]. Comparisons with data from Kim and Kamrin [25] shows that the parameter C f appears to depend on interparticle friction. Additionally, variations of C f among the different datasets can also presumably be attributed to the different definitions and averaging procedures used to compute velocity fluctuations in the different studies.…”

DEM simulations of quasi-two-dimensional flow of spherical particles on a heap without sidewalls

“…Also, as shown recently in ref. [18] and [19], the granular temperature also plays a key role in determining the rheology of such systems and hence, along with µ and I, the granular temperature also needs to be considered,especially for the region where I > 0.03. Fig.…”