17 research outputs found
Shear viscosity of a model for confined granular media
The shear viscosity in the dilute regime of a model for confined granular
matter is studied by simulations and kinetic theory. The model consists on
projecting into two dimensions the motion of vibrofluidized granular matter in
shallow boxes by modifying the collision rule: besides the restitution
coefficient that accounts for the energy dissipation, there is a separation
velocity that is added in each collision in the normal direction. The two
mechanisms balance on average, producing stationary homogeneous states.
Molecular dynamics simulations show that in the steady state the distribution
function departs from a Maxwellian, with cumulants that remain small in the
whole range of inelasticities. The shear viscosity normalized with stationary
temperature presents a clear dependence with the inelasticity, taking smaller
values compared to the elastic case. A Boltzmann-like equation is built and
analyzed using linear response theory. It is found that the predictions show an
excellent agreement with the simulations when the correct stationary
distribution is used but a Maxwellian approximation fails in predicting the
inelasticity dependence of the viscosity. These results confirm that transport
coefficients depend strongly on the mechanisms that drive them to stationary
states.Comment: 9 pages, 4 figure; Accepted in Phys. Rev.
Effective two-dimensional model for granular matter with phase separation
Granular systems confined in vertically vibrated shallow horizontal boxes
(quasi two-dimensional geometry) present a liquid to solid phase transition
when the frequency of the periodic forcing is increased. An effective model,
where grains move and collide in two-dimensions is presented, which reproduces
the aforementioned phase transition. The key element is that besides the
two-dimensional degrees of freedom, each grain has an additional variable
that accounts for the kinetic energy stored in the vertical motion
in the real quasi two-dimensional motion. This energy grows monotonically
during free flight, mimicking the energy gain by collisions with the vibrating
walls and, at collisions, this energy is instantaneously transferred to the
horizontal degrees of freedom. As a result, the average values of
and the kinetic temperature are decreasing functions of the local density,
giving rise to an effective pressure that can present van der Waals loops. A
kinetic theory approach predicts the conditions that must satisfy the energy
grow function to obtain the phase separation, which are verified with molecular
dynamics simulations. Notably, the effective equation of state and the critical
points computed considering the velocity--time-of-flight correlations differ
only slightly from those obtained by simple kinetic theory calculations that
neglect those correlations
Effective two-dimensional model for granular matter with phase separation
Granular systems confined in vertically vibrated shallow horizontal boxes
(quasi two-dimensional geometry) present a liquid to solid phase transition
when the frequency of the periodic forcing is increased. An effective model,
where grains move and collide in two-dimensions is presented, which reproduces
the aforementioned phase transition. The key element is that besides the
two-dimensional degrees of freedom, each grain has an additional variable
that accounts for the kinetic energy stored in the vertical motion
in the real quasi two-dimensional motion. This energy grows monotonically
during free flight, mimicking the energy gain by collisions with the vibrating
walls and, at collisions, this energy is instantaneously transferred to the
horizontal degrees of freedom. As a result, the average values of
and the kinetic temperature are decreasing functions of the local density,
giving rise to an effective pressure that can present van der Waals loops. A
kinetic theory approach predicts the conditions that must satisfy the energy
grow function to obtain the phase separation, which are verified with molecular
dynamics simulations. Notably, the effective equation of state and the critical
points computed considering the velocity--time-of-flight correlations differ
only slightly from those obtained by simple kinetic theory calculations that
neglect those correlations
Sudden chain energy transfer events in vibrated granular media
In a mixture of two species of grains of equal size but different mass,
placed in a vertically vibrated shallow box, there is spontaneous segregation.
Once the system is at least partly segregated and clusters of the heavy
particles have formed, there are sudden peaks of the horizontal kinetic energy
of the heavy particles, that is otherwise small. Together with the energy peaks
the clusters rapidly expand and the segregation is partially lost. The process
repeats once segregation has taken place again. Depending on the experimental
or numerical parameters, the energy bursts can occur either randomly or with
some regularity in time. An explanation for these events is provided based on
the existence of a fixed point for an isolated particle bouncing with only
vertical motion. The horizontal energy peaks occur when the energy stored in
the vertical motion is partly transferred into horizontal energy through a
chain reaction of collisions between heavy particles. A necessary condition for
the observed regularity of the events is that chain reactions involve most of
the heavy particles.Comment: 4 pages, 3 figures, Physical Review Letters (accepted
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
Thermal convection in fluidized granular systems
Thermal convection is observed in molecular dynamic simulation of a fluidized
granular system of nearly elastic hard disks moving under gravity, inside a
rectangular box. Boundaries introduce no shearing or time dependence, but the
energy injection comes from a slip (shear-free) thermalizing base. The top wall
is perfectly elastic and lateral boundaries are either elastic or periodic. The
observed convection comes from the effect of gravity and the spontaneous
granular temperature gradient that the system dynamically develops.Comment: 4 pages, 5 figure