Abstract
In the presence of viscous and cohesive interactions between particles, a granular flow is governed by several characteristic time and stress scales that determine its rheological properties (shear stress, packing fraction, effective viscosities). In this paper, we revisit and extend the scaling arguments used previously for dry cohesionless granular flows and suspensions. We show that the rheology can be in principle described by a single dimensionless control parameter that includes all characteristic times. We also briefly present simulation results for 2D sheared suspensions and 3D wet granular flows where the effective friction coefficient and packing fraction are consistently described as functions of this unique control parameter.
Highlights
In the presence of viscous and cohesive interactions between particles, a granular flow is governed by several characteristic time and stress scales that determine its rheological properties
As perfect rigid particles and friction law involve no intrinsic stress scale, the shear stresses in quasi-static flows are contained in a Coulomb cone, which bears on the description of the shear strength in terms of stress ratios [1]
The ratio of shear stress to the normal stress is an e↵ective friction coe cient μ whose evolution with shear strain describes the quasi-static rheology together with that of dilatancy, which due to rate independence in the quasi-static limit, is a ratio of volumetric strain to shear strain. We refer to such states as quasi-static flow states (QSFS)
Summary
In the presence of viscous and cohesive interactions between particles, a granular flow is governed by several characteristic time and stress scales that determine its rheological properties (shear stress, packing fraction, e↵ective viscosities). Numerical simulations suggest that the rheology can still be described by a single dimensionless control parameter involving the ratio of a linear combination of viscous and kinetic stresses to the confining stress [4, 5]. Scales, and only their ratio is relevant for the evolution of μ and [2]: 1) shear time ti = ̇ 1 and 2) relaxation time tp = d(⇢s/ p)1/2 of a particle of mass density ⇢s and diameter d under the action of a confining stress p.
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