18 research outputs found
Navier-Stokes transport coefficients of -dimensional granular binary mixtures at low density
The Navier-Stokes transport coefficients for binary mixtures of smooth
inelastic hard disks or spheres under gravity are determined from the Boltzmann
kinetic theory by application of the Chapman-Enskog method for states near the
local homogeneous cooling state. It is shown that the Navier-Stokes transport
coefficients are not affected by the presence of gravity. As in the elastic
case, the transport coefficients of the mixture verify a set of coupled linear
integral equations that are approximately solved by using the leading terms in
a Sonine polynomial expansion. The results reported here extend previous
calculations [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)]
to an arbitrary number of dimensions. To check the accuracy of the
Chapman-Enskog results, the inelastic Boltzmann equation is also numerically
solved by means of the direct simulation Monte Carlo method to evaluate the
diffusion and shear viscosity coefficients for hard disks. The comparison shows
a good agreement over a wide range of values of the coefficients of restitution
and the parameters of the mixture (masses and sizes).Comment: 6 figures, to be published in J. Stat. Phy
Hydrodynamics of driven granular gases
Hydrodynamic equations for granular gases driven by the Fokker-Planck
operator are derived. Transport coefficients appeared in Navier-Stokes order
change from the values of a free cooling state to those of a steady state.Comment: 5 pages, 3 figure
Hydrodynamics and transport coefficients for Granular Gases
The hydrodynamics of granular gases of viscoelastic particles, whose
collision is described by an impact-velocity dependent coefficient of
restitution, is developed using a modified Chapman-Enskog approach. We derive
the hydrodynamic equations and the according transport coefficients with the
assumption that the shape of the velocity distribution function follows
adiabatically the decaying temperature. We show numerically that this
approximation is justified up to intermediate dissipation. The transport
coefficients and the coefficient of cooling are expressed in terms of the
elastic and dissipative parameters of the particle material and by the gas
parameters. The dependence of these coefficients on temperature differs
qualitatively from that obtained with the simplifying assumption of a constant
coefficient of restitution which was used in previous studies. The approach
formulated for gases of viscoelastic particles may be applied also for other
impact-velocity dependencies of the restitution coefficient.Comment: 16 pages, 4 figure
Hydrodynamic theory for granular gases
A granular gas subjected to a permanent injection of energy is described by
means of hydrodynamic equations derived from a moment expansion method. The
method uses as reference function not a Maxwellian distribution but
a distribution , such that adds a fourth cumulant
to the velocity distribution. The formalism is applied to a stationary
conductive case showing that the theory fits extraordinarily well the results
coming from our molecular dynamic simulations once we determine as a
function of the inelasticity of the particle-particle collisions. The shape of
is independent of the size of the system.Comment: 10 pages, 9 figures, more about our research in
http://www.cec.uchile.cl/cinetica
Studies of Mass and Size Effects in Three-Dimensional Vibrofluidized Granular Mixtures
We examine the steady state properties of binary systems of driven inelastic
hard spheres. The spheres, which move under the influence of gravity, are
contained in a vertical cylinder with a vibrating base. We computed the
trajectories of the spheres using an event-driven molecular dynamics algorithm.
In the first part of the study, we chose simulation parameters that match those
of experiments performed by Wildman and Parker. Various properties computed
from the simulation including the density profile, granular temperature and
circulation pattern are in good qualitative agreement with the experiments. We
then studied the effect of varying the mass ratio and the size ratio
independently while holding the other parameters constant. The mass and size
ratio are shown to affect the distribution of the energy. The changes in the
energy distributions affect the packing fraction and temperature of each
component. The temperature of the heavier component has a non-linear dependence
on the mass of the lighter component, while the temperature of the lighter
component is approximately proportional to its mass. The temperature of both
components is inversely dependent on the size of the smaller component.Comment: 14 Pages, 12 Figures, RevTeX
Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state
The collisional rates associated with the isotropic velocity moments
and
are exactly derived in the case of the
inelastic Maxwell model as functions of the exponent , the coefficient of
restitution , and the dimensionality . The results are applied to
the evolution of the moments in the homogeneous free cooling state. It is found
that, at a given value of , not only the isotropic moments of a degree
higher than a certain value diverge but also the anisotropic moments do. This
implies that, while the scaled distribution function has been proven in the
literature to converge to the isotropic self-similar solution in well-defined
mathematical terms, nonzero initial anisotropic moments do not decay with time.
On the other hand, our results show that the ratio between an anisotropic
moment and the isotropic moment of the same degree tends to zero.Comment: 7 pages, 2 figures; v2: clarification of some mathematical statements
and addition of 7 new references; v3: Published in "Special Issue: Isaac
Goldhirsch - A Pioneer of Granular Matter Theory
Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles
Bifurcations of a driven granular system under gravity
Molecular dynamics study on the granular bifurcation in a simple model is
presented. The model consists of hard disks, which undergo inelastic
collisions; the system is under the uniform external gravity and is driven by
the heat bath. The competition between the two effects, namely, the
gravitational force and the heat bath, is carefully studied. We found that the
system shows three phases, namely, the condensed phase, locally fluidized
phase, and granular turbulent phase, upon increasing the external control
parameter. We conclude that the transition from the condensed phase to the
locally fluidized phase is distinguished by the existence of fluidized holes,
and the transition from the locally fluidized phase to the granular turbulent
phase is understood by the destabilization transition of the fluidized holes
due to mutual interference.Comment: 35 pages, 17 figures, to be published in PR