Pressure measurement in 2D granular gases.

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Pressure measurement in 2D granular gases.
Jean-Christophe Géminard and Claude
Laroche Laboratoire de Physique Ecole Normale
Supérieure de Lyon FRANCE
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Introduction
Glass or steel beads Diameter 1 - 3.5 mm Number
400-1500 Plate Metal (typ. Dural) Area S
1010 cm2 Sinusoidal vibration Acceleration G lt
3 Frequency f 50-80 Hz
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Introduction
At large enough acceleration, the beads form a
homogeneous "2D granular gas"
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Introduction
Collapse from J. S. Urbach website
J. S. Olafsen and J. S. Urbach, Phys. Rev. Lett.
81 4369 (1998) J. S. Olafsen and J. S. Urbach,
Phys. Rev. E 60 R2468 (1999) W. Losert, D. G.
Cooper, A Kudrolli, and J. P. Gollub, Chaos 9 682
(1999) W. Losert, D. G. Cooper, and J. P. Gollub,
Phys. Rev. E 59 5855 (1999)
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Introduction "Crystal"-gas equilibrium
Number of beads
Acceleration
The collapse nucleates at larger acceleration
when the overall density is larger. When at
"equilibrium" with the collapse, the density of
the gas does not depend on the overall density.
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Introduction Bead-plate restitution coefficient
Question What is the effect of a change in the
bead-plate restitution coefficient?
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Introduction Bead-plate restitution coefficient
Percentage
Acceleration
For the same pressure, the number density
increases when the temperature is decreased. The
percentage does not depend on the overall
density and tends to a constant value at large
accelerations.
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Introduction Bead-plate restitution coefficient
Percentage
Restitution coefficient of plate B
The density difference at large accelerations
increases when the difference in the
restitution coefficients is increased.
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Pressure measurement
One side wall consists of a "pendulum". We
measure the tilt angle of the pendulum in the
steady state Pressure
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Pressure measurement Dimensionless acceleration
Pressure
Acceleration
One observes a transition at Gc, indenpendant of
the density. Above Gc, the pressure is
proportional to the acceleration
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Pressure measurement Number density
Temperature
Density

TG µ P/N The temperature slightly increases with
the number density.
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Pressure measurement Vibration frequency
Critical acceleratrion
Slope
Frequency
Gc µ f The transition
corresponds to a given ratio bouncing frequency
/ vibration frequency.
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Pressure measurement Bead-plate restitution
coefficient
Inverse temperature
Restitution coefficient
The temperature decreases when the restitution
coefficient is decreased
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Pressure measurement Bead diameter
We measure the pressure difference between
compartments A and B.
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Pressure measurement Bead diameter
Pressure difference
Acceleration
The pressures in compartments A and B are almost
equal, at large acceleration, for the same mass
density. Departure is observed for G lt GC.
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Conclusion
Flaws Small range of frequencies and
accelerations. Lack of information about the
bead-bead restitution coefficient.
But Pressure measurements provide reliable
informations on the steady properties of the
system. The transition at GC, which corresponds
to a given ratio, bouncing frequency /
vibration frequency is likely to be due to
underlying attractors to periodic motion. We
propose