85 research outputs found
Fingering Instability in Combustion
A thin solid (e.g., paper), burning against an oxidizing wind, develops a
fingering instability with two decoupled length scales. The spacing between
fingers is determined by the P\'eclet number (ratio between advection and
diffusion). The finger width is determined by the degree two dimensionality.
Dense fingers develop by recurrent tip splitting. The effect is observed when
vertical mass transport (due to gravity) is suppressed. The experimental
results quantitatively verify a model based on diffusion limited transport
Intruder mobility in a vibrated granular packing
We study experimentally the dynamics of a dense intruder sinking under
gravity inside a vibrated 2D granular packing. The surrounding flow patterns
are characterized and the falling trajectories are interpreted in terms of an
effectivive friction coefficient related to the intruder mean descent velocity
(flow rules). At higher confining pressures i.e. close to jamming, a transition
to intermittent dynamics is evidenced and displays anomalous "on-off" blockade
statistics. A systematic analysis of the flow rules, obtained for different
intruder sizes, either in the flowing regime or averaged over the flowing and
blockade regimes, strongly suggest the existence of non-local properties for
the vibrated packing rheology.
Archimedes' law and its corrections for an active particle in a granular sea
We study the origin of buoyancy forces acting on a larger particle moving in
a granular medium subject to horizontal shaking and its corrections before
fluidization. In the fluid limit Archimedes' law is verified; before the limit
memory effects counteract buoyancy, as also found experimentally. The origin of
the friction is an excluded volume effect between active particles, which we
study more exactly for a random walker in a random environment. The same
excluded volume effect is also responsible for the mutual attraction between
bodies moving in the granular medium. Our theoretical modeling proceeds via an
asymmetric exclusion process, i.e., via a dissipative lattice gas dynamics
simulating the position degrees of freedom of a low density granular sea.Comment: 22 pages,5 figure
Mass transport of an impurity in a strongly sheared granular gas
Transport coefficients associated with the mass flux of an impurity immersed
in a granular gas under simple shear flow are determined from the inelastic
Boltzmann equation. A normal solution is obtained via a Chapman-Enskog-like
expansion around a local shear flow distribution that retains all the
hydrodynamic orders in the shear rate. Due to the anisotropy induced by the
shear flow, tensorial quantities are required to describe the diffusion process
instead of the conventional scalar coefficients. The mass flux is determined to
first order in the deviations of the hydrodynamic fields from their values in
the reference state. The corresponding transport coefficients are given in
terms of the solutions of a set of coupled linear integral equations, which are
approximately solved by considering the leading terms in a Sonine polynomial
expansion. The results show that the deviation of these generalized
coefficients from their elastic forms is in general quite important, even for
moderate dissipation.Comment: 6 figure
Heap Formation in Granular Media
Using molecular dynamics (MD) simulations, we find the formation of heaps in
a system of granular particles contained in a box with oscillating bottom and
fixed sidewalls. The simulation includes the effect of static friction, which
is found to be crucial in maintaining a stable heap. We also find another
mechanism for heap formation in systems under constant vertical shear. In both
systems, heaps are formed due to a net downward shear by the sidewalls. We
discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain TeX, HLRZ-101/9
Observing Brownian motion in vibration-fluidized granular matter
At the beginning of last century, Gerlach and Lehrer observed the rotational
Brownian motion of a very fine wire immersed in an equilibrium environment, a
gas. This simple experiment eventually permitted the full development of one of
the most important ideas of equilibrium statistical mechanics: the very
complicated many-particle problem of a large number of molecules colliding with
the wire, can be represented by two macroscopic parameters only, namely
viscosity and the temperature. Can this idea, mathematically developed in the
so-called Langevin model and the fluctuation-dissipation theorem be used to
describe systems that are far from equilibrium? Here we address the question
and reproduce the Gerlach and Lehrer experiment in an archetype non-equilibrium
system, by immersing a sensitive torsion oscillator in a granular system of
millimetre-size grains, fluidized by strong external vibrations. The
vibro-fluidized granular medium is a driven environment, with continuous
injection and dissipation of energy, and the immersed oscillator can be seen as
analogous to an elastically bound Brownian particle. We show, by measuring the
noise and the susceptibility, that the experiment can be treated, in first
approximation, with the same formalism as in the equilibrium case, giving
experimental access to a ''granular viscosity'' and an ''effective
temperature'', however anisotropic and inhomogeneous, and yielding the
surprising result that the vibro-fluidized granular matter behaves as a
''thermal'' bath satisfying a fluctuation-dissipation relation
Dynamics of axial separation in long rotating drums
We propose a continuum description for the axial separation of granular
materials in a long rotating drum. The model, operating with two local
variables, concentration difference and the dynamic angle of repose, describes
both initial transient traveling wave dynamics and long-term segregation of the
binary mixture. Segregation proceeds through ultra-slow logarithmic coarsening.Comment: 4 pages, 3 Postscript figures; submitted to PR
Traveling Granular Segregation Patterns in a Long Drum Mixer
Mixtures of granular media often exhibit size segregation along the axis of a
partially-filled, horizontal, rotating cylinder. Previous experiments have
observed axial bands of segregation that grow from concentration fluctuations
and merge in a manner analogous to spinodal decomposition. We have observed
that a new dynamical state precedes this effect in certain mixtures:
bi-directional traveling waves. By preparing initial conditions, we found that
the wave speed decreased with wavelength. Such waves appear to be inconsistent
with simple PDE models which are first order in time.Comment: 11 page
Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums
We study segregation of granular mixtures in the continuous avalanche regime
(for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory
for surface flows of grains. The theory predicts profiles in agreement with
experiments only when we consider a flux dependent velocity of flowing grains.
We find the segregation of species of different size and surface properties,
with the smallest and roughest grains being found preferentially at the center
of the drum. For a wide difference between the species we find a complete
segregation in agreement with experiments. In addition, we predict a transition
to a smooth segregation regime - with an power-law decay of the concentrations
as a function of radial coordinate - as the size ratio between the grains is
decreased towards one.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmaks
Slowly driven sandpile formation with granular mixtures
We introduce a one-dimensional sandpile model with different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial when N=1, but for N=2 we observe four broad classes of sandpile structure in different regions of the parameter space. We describe and explain the behaviour of each of these classes, giving quantitative analysis wherever possible. The behaviour of sandpiles with N>2 essentially consists of combinations of these four classes. We investigate the model's robustness and highlight the key areas that any experiment designed to reproduce these results should focus on
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