Additive rheology of complex granular flows

Abstract

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Time scales and rheology of visco-cohesive granular flows

“…This is what we observed from 3D simulations of packings of spherical particles with capillary forces, as shown in Fig. 2 with ↵ ' 0.09 [7]. The viscous forces may be either due to the action of a saturating liquid or lubrication forces acting at the gaps between particles in wet granular materials.…”

“…For example, for capillary forces, we may set 0 c = s d = f c /(⇡d 2 ), where s is the surface tension of the liquid. This di↵ers from the exact expression of c given by equation (7). For this reason, in equation (10) ⇠ should be replaced by ↵⇠.…”

“…The relative cohesion is defined by the cohesion index ⇠ = c / p . For the same reason, the e↵ective friction coe cient should now be defined with respect to this reference normal stress: For each set of simulations, the symbols and their colors correspond to the parameters that are varied with their ranges, all other parameters being kept constant [7].…”

“…On the other hand, in the case of viscocohesive granular materials, the cohesive stress is added to the confining stress and a single control parameter is defined from four di↵erent stress scales [6]. Besides understandable arguments such as delineating the shear-rate dependent internal stresses from shear-rate independent stresses, the rationale behind such an "additive rheology" needs to be clarified from a particle-scale standpoint [7].…”

Flows of cohesive granular media

“…The friction coefficient and the volume fraction then become functions of the inertial number and the cohesion number: µ = µ(I, C) and φ = φ(I, C). Some numerical studies [13,14] using a simple JKR-like [15], yet non-hysteretic adhesion force model and others [16,17] using capillary adhesion force model have verified these scaling and reported that µ(I, C) and φ(I, C) increases and decreases, respectively, with increasing I and C. A new set of scaling laws involving a generalized inertial number has also been proposed [18,19].…”