Surface Flows of Granular Mixtures: Canonical Model
In collaboration with Pierre Gilles de Gennes and Thomas Boutreux
from College de France, Paris, we have developed
a Canonical model for segregation and stratification in granular flows:
T. Boutreux, H. A. Makse and P. G. de Gennes,
Surface Flows of Granular Mixtures: III. Canonical Model ,
Eur. Phys. J.-B 9, 105-115 (1999).
The canonical model takes into
account differences in the size of the grains. We apply the model to
study segregation in two-dimensional silos of mixtures of grains
differing
in size and/or
surface properties. When the difference in size is small,
the model predicts that a
continuous segregation appears
in the static phase during the filling of a silo.
When the difference in size is wide, we take into account
the segregation of the grains in the rolling phase, and
the model predicts complete
segregation and
stratification in agreement with experimental observations.
Friction segregation
In a colaboration with Antal Karolyi and Janos Kertesz
from Department of Theoretical Physics, Technical Univ. of
Budapest, Hungary
we have studied the segregation occuring when one pours
a mixtures of grains differing in friction coefficients
[A. Karolyi, J. Kertesz, S.
Havlin, H. A. Makse, and H. E. Stanley,
Filling a silo with a mixture of grains: Friction-induced segregation,
Europhys. Lett. 44, 388-393 (1998);
A. Karolyi, J. Kertesz, H. A. Makse, H. E. Stanley, and S. Havlin,
Cellular Automata models for granular media,
[Proc. 1997 NATO ASI, Cargese] in
Granular Matter, ed. by H.J. Herrmann (Kluwer, Dordrecht, 1998)].
We study the filling process of a two-dimensional silo with inelastic
particles by simulation of a granular media lattice gas (GMLG) model.
We calculate the surface shape and flow profiles for a monodisperse system
and we introduce a novel generalization of the GMLG model for a binary
mixture of particles of different friction properties where, for the first
time,
we measure the segregation process on the surface.
The results are in good agreement with a recent theory, and we explain the
observed small deviations by the nonuniform velocity profile.
Results of the granular media lattice gas model
Segregation in thin rotating drums
I study the segregation
of granular mixtures in the continuous avalanche
regime in
thin rotating drums
using a continuum theory for surface flows
of grains [H. A. Makse,
"Continuous Avalanche Segregation of Granular Mixtures
in Thin Rotating Drums",
Phys. Rev. Lett. 83, 3186-3189
(1999)].
We predict the segregation of the mixture
according to the different size and surface properties
of the species, with the smallest and roughest
grains being found preferentially at the center of the drum.
Different segregation patterns arise according to the degree of
difference between the species. When there is a
large difference there appears a complete
segregation of the mixture, and
the predicted concentration profiles behave exponentially
in agreement with experiments.
In addition, we predict a transition from the complete segregation
regime to a smooth segregation regime--- with an
algebraic decay of the concentrations--- as the size ratio
between the grains is decreased.
Similar transition
has being found in continuous
avalanche segregation
in silos, so that our results
suggest a unifying framework towards the understanding of
segregation in different geometries such as
rotating drums and silos.
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