38 research outputs found
Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas
Using particle simulations of the uniform shear flow of a rough dilute
granular gas, we show that the translational and rotational velocities are
strongly correlated in direction, but there is no orientational
correlation-induced singularity at perfectly smooth () and rough
() limits for elastic collisions (); both the translational and
rotational velocity distribution functions remain close to a Gaussian for these
two limiting cases. Away from these two limits, the orientational as well as
spatial velocity correlations are responsible for the emergence of non-Gaussian
high velocity tails. The tails of both distribution functions follow stretched
exponentials, with the exponents depending on normal () and tangential
() restitution coefficients.Comment: Physical Review Letters (accepted
Nonmodal energy growth and optimal perturbations in compressible plane Couette flow
Nonmodal transient growth studies and estimation of optimal perturbations
have been made for the compressible plane Couette flow with three-dimensional
disturbances. The maximum amplification of perturbation energy over time,
, is found to increase with increasing Reynolds number ,
but decreases with increasing Mach number . More specifically, the optimal
energy amplification (the supremum of over both the
streamwise and spanwise wavenumbers) is maximum in the incompressible limit and
decreases monotonically as increases. The corresponding optimal streamwise
wavenumber, , is non-zero at M=0, increases with increasing
, reaching a maximum for some value of and then decreases, eventually
becoming zero at high Mach numbers. While the pure streamwise vortices are the
optimal patterns at high Mach numbers, the modulated streamwise vortices are
the optimal patterns for low-to-moderate values of the Mach number. Unlike in
incompressible shear flows, the streamwise-independent modes in the present
flow do not follow the scaling law , the reasons
for which are shown to be tied to the dominance of some terms in the linear
stability operator. Based on a detailed nonmodal energy analysis, we show that
the transient energy growth occurs due to the transfer of energy from the mean
flow to perturbations via an inviscid {\it algebraic} instability. The decrease
of transient growth with increasing Mach number is also shown to be tied to the
decrease in the energy transferred from the mean flow () in
the same limit
Variable-cell method for stress-controlled jamming of athermal, frictionless grains
A new method is introduced to simulate jamming of polyhedral grains under
controlled stress that incorporates global degrees of freedom through the
metric tensor of a periodic cell containing grains. Jamming under
hydrostatic/isotropic stress and athermal conditions leads to a precise
definition of the ideal jamming point at zero shear stress. The structures of
tetrahedra jammed hydrostatically exhibit less translational order and lower
jamming-point density than previously described `maximally random jammed' hard
tetrahedra. Under the same conditions, cubes jam with negligible nematic order.
Grains with octahedral symmetry jam in the large-system limit with an abundance
of face-face contacts in the absence of nematic order. For sufficiently large
face-face contact number, percolating clusters form that span the entire
simulation box. The response of hydrostatically jammed tetrahedra and cubes to
shear-stress perturbation is also demonstrated with the variable-cell method.Comment: 10 pages, 8 figure
Universality of shear-banding instability and crystallization in sheared granular fluid
The linear stability analysis of an uniform shear flow of granular materials
is revisited using several cases of a Navier-Stokes'-level constitutive model
in which we incorporate the global equation of states for pressure and thermal
conductivity (which are accurate up-to the maximum packing density )
and the shear viscosity is allowed to diverge at a density (), with all other transport coefficients diverging at . It is
shown that the emergence of shear-banding instabilities (for perturbations
having no variation along the streamwise direction), that lead to shear-band
formation along the gradient direction, depends crucially on the choice of the
constitutive model. In the framework of a dense constitutive model that
incorporates only collisional transport mechanism, it is shown that an accurate
global equation of state for pressure or a viscosity divergence at a lower
density or a stronger viscosity divergence (with other transport coefficients
being given by respective Enskog values that diverge at ) can induce
shear-banding instabilities, even though the original dense Enskog model is
stable to such shear-banding instabilities. For any constitutive model, the
onset of this shear-banding instability is tied to a {\it universal} criterion
in terms of constitutive relations for viscosity and pressure, and the sheared
granular flow evolves toward a state of lower "dynamic" friction, leading to
the shear-induced band formation, as it cannot sustain increasing dynamic
friction with increasing density to stay in the homogeneous state. A similar
criterion of a lower viscosity or a lower viscous-dissipation is responsible
for the shear-banding state in many complex fluids.Comment: 26 page
Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids
The average number of constraints per particle in
mechanically stable systems of Platonic solids (except cubes) approaches the
isostatic limit at the jamming point (), though
average number of contacts are hypostatic. By introducing angular alignment
metrics to classify the degree of constraint imposed by each contact,
constraints are shown to arise as a direct result of local orientational order
reflected in edge-face and face-face alignment angle distributions. With
approximately one face-face contact per particle at jamming chain-like
face-face clusters with finite extent form in these systems.Comment: 4 pages, 3 figures, 4 tabl