Rheophysics of granular materials with interstitial fluid : a numerical simulation study

Abstract : We numerically simulate the shear flow of dense assemblies of 3D frictional spherical grains under a fixed normal stress P in steady-state, either in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci and attractive forces, or in the fully saturated state, when the mechanical properties of suspensions in Stokes flow are controlled by hydrodynamic and contact forces. Dry grain assemblies are used as a reference system for which the rheological properties - in particular the approach to the critical state – are rather well known and can be measured with good accuracy. A non-saturating wetting fluid creates capillary attractive intergranular forces, the effects of which on the rheology are investigated in the pendular state, with shear rates ranging from quasistatic to inertial regimes. The system behavior is characterized by the dependence of internal friction coefficient, solid fraction, normal stress differences and internal state parameters on two dimensionless control parameters: the inertial number, I and the reduced pressure, P*, comparing confining forces to contact tensile strength. We focus on steady homogeneous flows, excluding localized flow patterns which we observe to occur for low P* (of order 0.1). The apparent internal friction coefficient increases to 0.9 in the quasistatic limit for P*=0.4, from its dry value 0.35, while solid fraction decreases from 0.59 to 0.52. We relate the significant effect of capillary forces on the macroscopic behavior of the system, up to P* values of several unities, to fabric anisotropy parameters of contact and distant interactions. As P* decreases, many cohesive contacts are observed to survive the tumbling motion associated to the shear flow, and their average age exceeds the reciprocal shear rate. Corresponding clusters of grains with enduring capillary bonds gather a large proportion of grains and percolate through the sample. The results are shown to be moderately sensitive to saturation within the pendular range, yet rather strongly affected by the hysteretic nature of liquid bridges. In the presence of viscous forces, assuming lubrication effects to dominate the hydrodynamic interactions, we adopt a simplified version of the (overdamped) Stokesian dynamics approach, in which hydrodynamic interactions only couple close neighbours. Rheological properties are strongly influenced by direct intergranular contacts and friction, which are permitted due to a very small distance lubrication cutoff modeling surface asperities. The same critical state as in the dry case is approached in the quasistatic limit. We discuss expressions of rheological laws involving the viscous number instead of the inertial number, and the divergence of effective viscosities in steady flow and in isotropic random suspensions as either the critical state or the random close packing solid fraction are approached
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Saeed Khamseh. Rheophysics of granular materials with interstitial fluid : a numerical simulation study. Material chemistry. Université Paris-Est, 2014. English. ⟨NNT : 2014PEST1025⟩. ⟨tel-01103346v2⟩

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