A general(ized) local rheology for wet granular materials

Abstract

We study the rheology of dry and wet granular materials in the steady quasistatic regime using the discrete element method in a split-bottom ring shear cell with focus on the macroscopic friction. The aim of our study is to understand the local rheology of bulk flow at various positions in the shear band, where the system is in critical state. We develop a general(ized) rheology, in which the macroscopic friction is factorized into a product of four functions, on top of the classical ( ) m I rheology, each of which depends on exactly one dimensionless control parameter, quantifying the relative importance of different micro-mechanical machanisms. These four control parameters relate the time scales of shear rateġ t , particle stiffness t k , gravity t g and cohesion t c , respectively, with the governing time scale of confining pressure t p . Whileġ t is large and thus of little importance for most of the slow flow data studied, it increases the friction in critical state, where the shear rate is high and decreases friction by relaxation (creep) where the shear rate is low. t g and t k are comparable to t p in the bulk, but become more or less dominant relative to t p at the extremes of low pressure at the free surface and high pressure deep inside the bulk, respectively. The effect of wet cohesion on the flow rheology is quantified by t c decreasing with increasing cohesion. Furthermore, the proposed rheological model predicts well the shear thinning behavior both in the bulk and near the free surface; shear thinning rate becomes less near the free surface with increasing cohesion.

Effect of cohesion on local compaction and granulation of sheared soft granular materials

“…We use a linear visco-elastic frictional contact model in combination with Willet's capillary bridge model [3,6,10]. In order to see the effect of varying cohesive strength on the macroscopic rheology of wet materials, we vary the intensity of the maximum capillary force f max cap = πdσ cos θ, by varying the surface tension of the liquid σ, while keeping the volume of liquid bridges constant, (V b = 75 nl), corresponding to a liquid saturation of 8% of the voidage.…”

“…1, where the subscriptsγ, p, k and c denote strain-rate, pressure, stiffness and cohesion respectively [10]. In addition, we define the global Bond number as Bo g = f max cap /(p mean d p 2 ), where p mean is the mean pressure in the system (at about half filling height H/2).…”

“…The macroscopic quantities are obtained by spatial coarse graining with temporal averaging of the system in steady state as detailed in [6,10]. We study the effect of the above mentioned dimensionless numbers on the local volume fraction φ in the critical state [10].…”

“…We study the effect of the above mentioned dimensionless numbers on the local volume fraction φ in the critical state [10]. The local volume fraction is expected to be dependent on various factors like the dilation, compression and the inter-particle friction.…”

“…The dependence of the macroscopic friction coefficient μ = τ/p on p * and I has been studied in [9,10]. In order to complete the rheology for soft, compressible particles, a relation for the solid volume fraction (packing fraction) as function of pressure and shear rate is missing for dry non-cohesive materials.…”