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Register a new userMeasurements of Particle Dynamics in Slow, Dense Granular Couette Flow
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Authors
Daniel M. Mueth
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Experimental measurements of particle dynamics on the lower surface of a 3D Couette cell containing monodisperse spheres are reported. The average radial density and velocity profiles are similar to those previously measured within the bulk and on the lower surface of the 3D cell filled with mustard seeds. Observations of the evolution of particle velocities over time reveal distinct motion events, intervals where previously stationary particles move for a short duration before jamming again. The cross-correlation between the velocities of two particles at a given distance $r$ from the moving wall reveals a characteristic lengthscale over which the particles are correlated. The autocorrelation of a single particles velocity reveals a characteristic timescale $tau$ which decreases with distance from the inner moving wall. This may be attributed to the increasing rarity at which the discrete motion events occur and the reduced duration of those events at large $r$. The relationship between the RMS azimuthal velocity fluctuations, $delta v_theta(r)$, and average shear rate, $dotgamma(r)$, was found to be $delta v_theta propto dotgamma^alpha$ with $alpha = 0.52 pm 0.04$. These observations are compared with other recent experiments and with the modified hydrodynamic model recently introduced by Bocquet et al.
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The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using emph{in situ} imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale Non-Smooth Contact Dynamics (NSCD) simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation.
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We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random packing undergo chain-like collective displacements in response to diffusing spots of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the coarse grained dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135,000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.
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