Stress and large-scale spatial structures in dense, driven granular flows

We study the appearance of large-scale dynamical heterogeneities in a simplified model of a driven, dissipative granular system. Simulations of steady-state gravity-driven flows of inelastically colliding hard disks show the formation of large-scale linear structures of particles with a high collision frequency. These chains can be shown to carry much of the collisional stress in the system due to a dynamical correlation that develops between the momentum transfer and time between collisions in these "frequently-colliding" particles. The lifetime of these dynamical stress heterogeneities is seen to grow as the flow velocity decreases towards jamming, leading to slowly decaying stress correlations reminiscent of the slow dynamics observed in supercooled liquids.Comment: 8 pages, 6 figure

Linear stability, transient energy growth and the role of viscosity stratification in compressible plane Couette flow

Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow with {\it stratified} viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers ($M$). For a given $M$, the critical Reynolds number ($Re$) is significantly smaller for the uniform shear flow than its non-uniform shear counterpart. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for ``mode I'' instability, whereas it occurs in the bulk of the flow domain for ``mode II''. For the non-modal analysis, it is shown that the maximum amplification of perturbation energy, $G_{\max}$, is significantly larger for the uniform shear case compared to its non-uniform counterpart. For $\alpha=0$, the linear stability operator can be partitioned into ${\cal L}\sim \bar{\cal L} + Re^2{\cal L}_p$, and the $Re$-dependent operator ${\cal L}_p$ is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: $G(t/{\it Re}) \sim {\it Re}^2$. A reduced inviscid model has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, it is shown that the {\it viscosity-stratification} of the underlying mean flow would lead to a delayed transition in compressible Couette flow

First normal stress difference and crystallization in a dense sheared granular fluid

The first normal stress difference (${\mathcal N}_1$) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in {\it dilute} granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behaviour in the {\it dense} limit. As in the elastic hard-sphere fluids, ${\mathcal N}_1$ remains {\it positive} (if the stress is defined in the {\it compressive} sense) for dilute and moderately dense flows, but becomes {\it negative} above a critical density, depending on the restitution coefficient. This sign-reversal of ${\mathcal N}_1$ occurs due to the {\it microstructural} reorganization of the particles, which can be correlated with a preferred value of the {\it average} collision angle $\theta_{av}=\pi/4 \pm \pi/2$ in the direction opposing the shear. We also report on the shear-induced {\it crystal}-formation, signalling the onset of fluid-solid coexistence in dense granular fluids. Different approaches to take into account the normal stress differences are discussed in the framework of the relaxation-type rheological models.Comment: 21 pages, 13 figure