The prototype model of a fluidized granular system is a gas of inelastic hard
spheres (IHS) with a constant coefficient of normal restitution α. Using
a kinetic theory description we investigate the two basic ingredients that a
model of elastic hard spheres (EHS) must have in order to mimic the most
relevant transport properties of the underlying IHS gas. First, the EHS gas is
assumed to be subject to the action of an effective drag force with a friction
constant equal to half the cooling rate of the IHS gas, the latter being
evaluated in the local equilibrium approximation for simplicity. Second, the
collision rate of the EHS gas is reduced by a factor (1+α)/2, relative
to that of the IHS gas. Comparison between the respective Navier-Stokes
transport coefficients shows that the EHS model reproduces almost perfectly the
self-diffusion coefficient and reasonably well the two transport coefficients
defining the heat flux, the shear viscosity being reproduced within a deviation
less than 14% (for α≥0.5). Moreover, the EHS model is seen to agree
with the fundamental collision integrals of inelastic mixtures and dense gases.
The approximate equivalence between IHS and EHS is used to propose kinetic
models for inelastic collisions as simple extensions of known kinetic models
for elastic collisionsComment: 20 pages; 6 figures; change of title; few minor changes; accepted for
publication in PR