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Register a new userSignatures of granular microstructure in dense shear flows
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Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5]. Since shear bands mark areas of flow, material failure and energy dissipation, they play a crucial role for many industrial, civil engineering and geophysical processes[6]. They also appear in related contexts, such as in lubricating fluids confined to ultra-thin molecular layers[7]. Detailed information on motion within a shear band in a three-dimensional geometry, including the degree of particle rotation and inter-particle slip, is lacking. Similarly, only little is known about how properties of the individual grains - their microstructure - affect movement in densely packed material[5]. Combining magnetic resonance imaging, x-ray tomography, and high-speed video particle tracking, we obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.
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Dense suspensions are non-Newtonian fluids which exhibit strong shear thickening and normal stress differences. Using numerical simulation of extensional and shear flows, we investigate how rheological properties are determined by the microstructure which is built under flows and by the interactions between particles. By imposing extensional and shear flows, we can assess the degree of flow-type dependence in regimes below and above thickening. Even when the flow-type dependence is hindered, nondissipative responses, such as normal stress differences, are present and characterise the non-Newtonian behaviour of dense suspensions.
We report a new lift force model for intruders in dense, granular shear flows. Our derivation is based on the thermal buoyancy model of Trujillo & Hermann[L. Trujillo and H. J. Herrmann, Physica A 330, 519 (2003).], but takes into account both granular temperature and pressure differences in the derivation of the net buoyancy force acting on the intruder. In a second step the model is extended to take into account also density differences between the intruder and the bed particles. The model predicts very well the rising and sinking of intruders, the lift force acting on intruders as determined by discrete element model (DEM) simulations and the neutral-buoyancy limit of intruders in shear flows. Phenomenologically, we observe a cooling upon the introduction of an intruder into the system. This cooling effect increases with intruder size and explains the sinking of large intruders. On the other hand, the introduction of small to mid-sized intruders, i.e. up to 4 times the bed particle size, leads to a reduction in the granular pressure compared to the hydrostatic pressure, which in turn causes the rising of small to mid-sized intruders.
The question of how a disordered materials microstructure translates into macroscopic mechanical response is central to understanding and designing materials like pastes, foams and metallic glasses. Here, we examine a 2D soft jammed material under cyclic shear, imaging the structure of ~50,000 particles. Below a certain strain amplitude, the structure becomes conserved at long times, while above, it continually rearranges. We identify the boundary between these regimes as a yield strain, defined without rheological measurement. Its value is consistent with a simultaneous but independent measurement of yielding by stress-controlled bulk rheometry. While there are virtually no irreversible rearrangements in the steady state below yielding, we find a largely stable population of plastic rearrangements that are reversed with each cycle. These results point to a microscopic view of mechanical properties under cyclic deformation.
We experimentally investigate the rheology and stress fluctuations of granules densely suspended in silicone oil. We find that both thickening strength and stress fluctuations significantly weaken with oil viscosity $eta_0$. Comparison of our rheological results to the Wyart-Cates model for describing different dynamic jamming states suggests a transition from frictional contacts to lubrication interactions as $eta_0$ increases. To clarify the contribution from viscous interactions to the rheology, we systematically measure stress fluctuations in various flow states. Reduction of stress fluctuations with $eta_0$ indicates that a strong lubrication layer greatly inhibits force correlations among particles. Measuring stress fluctuations in the strong shear thickening regime, we observe a crossover from asymmetric Gamma to symmetric Gaussian distributions and associated with it a decrease of lateral (radial) correlation length $xi$ with increasing shear rate.
We consider dense rapid shear flow of inelastically colliding hard disks. Navier-Stokes granular hydrodynamics is applied accounting for the recent finding cite{Luding,Khain} that shear viscosity diverges at a lower density than the rest of constitutive relations. New interpolation formulas for constitutive relations between dilute and dense cases are proposed and justified in molecular dynamics (MD) simulations. A linear stability analysis of the uniform shear flow is performed and the full phase diagram is presented. It is shown that when the inelasticity of particle collision becomes large enough, the uniform sheared flow gives way to a two-phase flow, where a dense solid-like striped cluster is surrounded by two fluid layers. The results of the analysis are verified in event-driven MD simulations, and a good agreement is observed.
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