66 research outputs found
Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas
The decay of a small homogeneous perturbation of the temperature of a dilute
granular gas in the steady uniform shear flow state is investigated. Using
kinetic theory based on the inelastic Boltzmann equation, a closed equation for
the decay of the perturbation is derived. The equation involves the generalized
shear viscosity of the gas in the time-dependent shear flow state, and
therefore it predicts relevant rheological effects beyond the quasi-elastic
limit. A good agreement is found when comparing the theory with molecular
dynamics simulation results. Moreover, the Onsager postulate on the regression
of fluctuations is fulfilled
Internal energy fluctuations of a granular gas under steady uniform shear flow
The stochastic properties of the total internal energy of a dilute granular
gas in the steady uniform shear flow state are investigated. A recent theory
formulated for fluctuations about the homogeneous cooling state is extended by
analogy with molecular systems. The theoretical predictions are compared with
molecular dynamics simulation results. Good agreement is found in the limit of
weak inelasticity, while systematic and relevant discrepancies are observed
when the inelasticity increases. The origin of this behavior is discussed
The Enskog equation for confined elastic hard spheres
A kinetic equation for a system of elastic hard spheres or disks confined by
a hard wall of arbitrary shape is derived. It is a generalization of the
modified Enskog equation in which the effects of the confinement are taken into
account and it is supposed to be valid up to moderate densities. From the
equation, balance equations for the hydrodynamic fields are derived,
identifying the collisional transfer contributions to the pressure tensor and
heat flux. A Lyapunov functional, , is identified. For any
solution of the kinetic equation, decays monotonically in time
until the system reaches the inhomogeneous equilibrium distribution, that is a
Maxwellian distribution with a the density field consistent with equilibrium
statistical mechanics
Homogeneous hydrodynamics of a collisional model of confined granular gases
The hydrodynamic equation governing the homogeneous time evolution of the
temperature in a model of confined granular gas is studied by means of the
Enskog equation. The existence of a normal solution of the kinetic equation is
assumed as a condition for hydrodynamics. Dimensional analysis implies a
scaling of the distribution function that is used to determine it in the first
Sonine approximation, with a coefficient that evolves in time through its
dependence on the temperature. The theoretical predictions are compared with
numerical results obtained by the direct simulation Monte Carlo method, and a
good agreement is found. The relevance of the normal homogeneous distribution
function to derive inhomogeneous hydrodynamic equations, for instance using the
Champan-Enskog algorithm, is indicated.Comment: Accepted in Phys. Rev.
Hydrodynamics for a model of a confined quasi-two-dimensional granular gas
The hydrodynamic equations for a model of a confined quasi-two-dimensional
gas of smooth inelastic hard spheres are derived from the Boltzmann equation
for the model, using a generalization of the Chapman-Enskog method. The heat
and momentum fluxes are calculated to Navier-Stokes order, and the associated
transport coefficients are explicitly determined as functions of the
coefficient of normal restitution and the velocity parameter involved in the
definition of the model. Also an Euler transport term contributing to the
energy transport equation is considered. This term arises from the gradient
expansion of the rate of change of the temperature due to the inelasticity of
collisions, and vanishes for elastic systems. The hydrodynamic equations are
particularized for the relevant case of a system in the homogeneous steady
state. The relationship with previous works is analyzed
Memory effects in the relaxation of a confined granular gas
The accuracy of a model to describe the horizontal dynamics of a confined
quasi-two-dimensional system of inelastic hard spheres is discussed by
comparing its predictions for the relaxation of the temperature in an
homogenous system with molecular dynamics simulation results for the original
system. A reasonably good agreement is found. Next, the model is used to
investigate the peculiarities of the nonlinear evolution of the temperature
when the parameter controlling the energy injection is instantaneously changed
while the system was relaxing. This can be considered as a non-equilibrium
generalization of the Kovacs effect. It is shown that, in the low density
limit, the effect can be accurately described by using a simple kinetic theory
based on the first Sonine approximation for the one-particle distribution
function. Some possible experimental implications are indicated
Mesoscopic Theory of Critical Fluctuations in Isolated Granular Gases
Fluctuating hydrodynamics is used to describe the total energy fluctuations
of a freely evolving gas of inelastic hard spheres near the threshold of the
clustering instability. They are shown to be governed by vorticity fluctuations
only, that also lead to a renormalization of the average total energy. The
theory predicts a power-law divergent behavior of the scaled second moment of
the fluctuations, and a scaling property of their probability distribution,
both in agreement with simulations results. A more quantitative comparison
between theory and simulation for the critical amplitudes and the form of the
scaling function is also carried out
Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases
Both the right and left eigenfunctions and eigenvalues of the linearized
homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to
the hydrodynamic modes are calculated. Also, some non-hydrodynamic modes are
identified. It is shown that below a critical value of the parameter
characterizing the inelasticity, one of the kinetic modes decays slower than
one of the hydrodynamic ones. As a consequence, a closed hydrodynamic
description does not exist in that regime. Some implications of this behavior
on the formally computed Navier-Stokes transport coefficients are discussed.Comment: Submitted to PRL (13/04/10
Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres
The local balance equations for the density, momentum, and energy of a dilute
gas of elastic or inelastic hard spheres, strongly confined between two
parallel hard plates are obtained. The starting point is a Boltzmann-like
kinetic equation, recently derived for this system. As a consequence of the
confinement, the pressure tensor and the heat flux contain, in addition to the
terms associated to the motion of the particles, collisional transfer
contributions, similar to those that appear beyond the dilute limit. The
complexity of these terms, and of the kinetic equation itself, compromise the
potential of the equation to describe the rich phenomenology observed in this
kind of systems. For this reason, a simpler model equation based on the
Boltzmann equation is proposed. The model is formulated to keep the main
properties of the underlying equation, and it is expected to provide relevant
information in more general states than the original equation. As an
illustration, the solution describing a macroscopic state with uniform
temperature, but a density gradient perpendicular to the plates is considered.
This is the equilibrium state for an elastic system, and the inhomogeneous
cooling state for the case of inelastic hard spheres. The results are in good
agreement with previous results obtained directly from the Boltzmann equation
- …