5 research outputs found
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 (). For a given , the
critical Reynolds number () 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, , is significantly larger for the uniform shear case compared
to its non-uniform counterpart. For , the linear stability operator
can be partitioned into , and the
-dependent operator 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: . 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 () 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, 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 occurs due to the {\it
microstructural} reorganization of the particles, which can be correlated with
a preferred value of the {\it average} collision angle 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