159 research outputs found
Rheological properties for inelastic Maxwell mixtures under shear flow
The Boltzmann equation for inelastic Maxwell models is considered to
determine the rheological properties in a granular binary mixture in the simple
shear flow state. The transport coefficients (shear viscosity and viscometric
functions) are {\em exactly} evaluated in terms of the coefficients of
restitution, the (reduced) shear rate and the parameters of the mixture
(particle masses, diameters and concentration). The results show that in
general, for a given value of the coefficients of restitution, the above
transport properties decrease with increasing shear rate
Random inelasticity and velocity fluctuations in a driven granular gas
We analyze the deviations from Maxwell-Boltzmann statistics found in recent
experiments studying velocity distributions in two-dimensional granular gases
driven into a non-equilibrium stationary state by a strong vertical vibration.
We show that in its simplest version, the ``stochastic thermostat'' model of
heated inelastic hard spheres, contrary to what has been hitherto stated, is
incompatible with the experimental data, although predicting a reminiscent high
velocity stretched exponential behavior with an exponent 3/2. The experimental
observations lead to refine a recently proposed random restitution coefficient
model. Very good agreement is then found with experimental velocity
distributions within this framework, which appears self-consistent and further
provides relevant probes to investigate the universality of the velocity
statistics.Comment: 5 pages, 5 eps figure
Kinetics of Fragmenting Freely Evolving Granular Gases
We investigate the effect of fragmentation on the homogeneous free cooling of
inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo
simulations. We analyze in detail a model where dissipative collisions may
subsequently lead to a break-up of the grains. With a given probability, two
off-springs are then created from one of the two colliding partners, with
conservation of mass, momentum and kinetic energy. We observe a scaling regime
characterized by a single collisional average, that quantifies the deviations
from Gaussian behaviour for the joint size and velocity distribution function.
We also discuss the possibility of a catastrophe whereby the number of
particles diverges in a finite time. This phenomenon appears correlated to a
``shattering'' transition marked by a delta singularity at vanishingly small
grains for the rescaled size distribution.Comment: 22 pages, 8 figure
Reply to: Comment on `Long-range electrostatic interactions between like-charged colloids: steric and confinement effects'
In his Comment (cond-mat/0104060) to [Phys. Rev. E 60, 6530 (1999)], Mateescu
shows that while the effective interactions remain repulsive when the specific
size of the micro-ions is taken into account via a Modified Poisson-Boltzmann
equation, a similar conclusion cannot be reached for the situation of complete
lateral confinement. This point is correct but has already been considered in a
more general study [Phys. Rev. E 62, R1465 (2000), where repulsion is
generically obtained]; moreover, we argue that it illustrates the irrelevancy
of the notion of pair potential in completely confined configurations, as shown
on a simple example
Polydispersity and optimal relaxation in the hard sphere fluid
We consider the mass heterogeneity in a gas of polydisperse hard particles as
a key to optimizing a dynamical property: the kinetic relaxation rate. Using
the framework of the Boltzmann equation, we study the long time approach of a
perturbed velocity distribution toward the equilibrium Maxwellian solution. We
work out the cases of discrete as well as continuous distributions of masses,
as found in dilute fluids of mesoscopic particles such as granular matter and
colloids. On the basis of analytical and numerical evidence, we formulate a
dynamical equipartition principle that leads to the result that no such
continuous dispersion in fact minimizes the relaxation time, as the global
optimum is characterized by a finite number of species. This optimal mixture is
found to depend on the dimension d of space, ranging from five species for d=1
to a single one for d>=4. The role of the collisional kernel is also discussed,
and extensions to dissipative systems are shown to be possible.Comment: 20 pages, 8 figures, 3 table
Renormalized Jellium model for charge-stabilized colloidal suspensions
We introduce a renormalized Jellium model to calculate the equation of state
for charged colloidal suspensions. An almost perfect agreement with Monte Carlo
simulations is found. Our self-consistent approach naturally allows to define
the effective charge of particles {\em at finite colloidal density}. Although
this quantity may differ significantly from its counterpart obtained from the
standard Poisson-Boltzmann cell approach, the osmotic pressures for both models
are in good agreement. We argue that by construction, the effective charge
obtained using the Jellium approximation is more appropriate to the study of
colloidal interactions. We also discuss a possibility of a fluid-fluid critical
point and show how the new equation of state can be used to shed light on the
surprising results found in recent sedimentation experiments.Comment: 4 pages, 3 figure
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