3,841 research outputs found
Homogeneous Free Cooling State in Binary Granular Fluids of Inelastic Rough Hard Spheres
In a recent paper [A. Santos, G. M. Kremer, and V. Garz\'o, \emph{Prog.
Theor. Phys. Suppl.} \textbf{184}, 31-48 (2010)] the collisional energy
production rates associated with the translational and rotational granular
temperatures in a granular fluid mixture of inelastic rough hard spheres have
been derived. In the present paper the energy production rates are explicitly
decomposed into equipartition rates (tending to make all the temperatures
equal) plus genuine cooling rates (reflecting the collisional dissipation of
energy). Next the homogeneous free cooling state of a binary mixture is
analyzed, with special emphasis on the quasi-smooth limit. A previously
reported singular behavior (according to which a vanishingly small amount of
roughness has a finite effect, with respect to the perfectly smooth case, on
the asymptotic long-time translational/translational temperature ratio) is
further elaborated. Moreover, the study of the time evolution of the
temperature ratios shows that this dramatic influence of roughness already
appears in the transient regime for times comparable to the relaxation time of
perfectly smooth spheres.Comment: 6 pages; 4 figures; contributed talk at the 27th International
Symposium on Rarefied Gas Dynamics (Asilomar Conference Grounds, Pacific
Grove, California July 10-15, 2010
A Bhatnagar-Gross-Krook-like Model Kinetic Equation for a Granular Gas of Inelastic Rough Hard Spheres
The Boltzmann collision operator for a dilute granular gas of inelastic rough
hard spheres is much more intricate than its counterpart for inelastic smooth
spheres. Now the one-body distribution function depends not only on the
translational velocity of the center of mass but also on the angular velocity
of the particle. Moreover, the collision rules couple both velocities,
involving not only the coefficient of normal restitution but also the
coefficient of tangential restitution. The aim of this paper is to propose an
extension to inelastic rough particles of a Bhatnagar-Gross-Krook-like kinetic
model previously proposed for inelastic smooth particles. The Boltzmann
collision operator is replaced by the sum of three terms representing: (i) the
relaxation to a two-temperature local equilibrium distribution, (ii) the action
of a nonconservative drag force proportional to the peculiar velocity, and
(iii) the action of a nonconservative torque equal to a linear combination of
the angular velocity and its mean value. The three coefficients in the force
and torque are fixed to reproduce the Boltzmann collisional rates of change of
the mean angular velocity and of the two granular temperatures (translational
and rotational). A simpler version of the model is also constructed in the form
of two coupled kinetic equations for the translational and rotational velocity
distributions. The kinetic model is applied to the simple shear flow steady
state and the combined influence of the two coefficients of restitution on the
shear and normal stresses and on the translational velocity distribution
function is analyzed.Comment: 8 pages; 3 figures; invited talk at the 27th International Symposium
on Rarefied Gas Dynamics (Asilomar Conference Grounds, Pacific Grove,
California July 10-15, 2010
Velocity Distribution and Cumulants in the Unsteady Uniform Longitudinal Flow of a Granular Gas
The uniform longitudinal flow is characterized by a linear longitudinal
velocity field , where is the strain
rate, a uniform density , and a uniform granular temperature
. Direct simulation Monte Carlo solutions of the Boltzmann equation for
inelastic hard spheres are presented for three (one positive and two negative)
representative values of the initial strain rate . Starting from different
initial conditions, the temporal evolution of the reduced strain rate
, the non-Newtonian viscosity, the second and third
velocity cumulants, and three independent marginal distribution functions has
been recorded. Elimination of time in favor of the reduced strain rate
shows that, after a few collisions per particle, different initial states are
attracted to common "hydrodynamic" curves. Strong deviations from Maxwellian
properties are observed from the analysis of the cumulants and the marginal
distributions.Comment: 8 pages; 4 figures; contributed paper at the 28th International
Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012
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