120 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
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
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
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
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
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
Pipe network model for scaling of dynamic interfaces in porous media
We present a numerical study on the dynamics of imbibition fronts in porous
media using a pipe network model. This model quantitatively reproduces the
anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf
52}, 5166 (1995)]. Using simple scaling arguments, we derive a new identity
among the scaling exponents in agreement with the experimental results.Comment: 13 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let
Quasiperiodic Tip Splitting in Directional Solidification
We report experimental results on the tip splitting dynamics of seaweed
growth in directional solidification of succinonitrile alloys with
poly(ethylene oxide) or acetone as solutes. The seaweed or dense branching
morphology was selected by solidifying grains which are oriented close to the
{111} plane. Despite the random appearance of the growth, a quasiperiodic tip
splitting morphology was observed in which the tip alternately splits to the
left and to the right. The tip splitting frequency f was found to be related to
the growth velocity V as a power law f V^{1.5}. This finding
is consistent with the predictions of a tip splitting model that is also
presented. Small anisotropies are shown to lead to different kinds of seaweed
morphologies.Comment: 4 pages, 7 figures, submitted to Physical Review Letter
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