Is Dissipative
Granular Gas in Knudsen Regime Excited by Vibration Biphasic?

P.
Evesque: Lab MSSM, UMR 8579 CNRS, Ecole Centrale Paris, 92295 Châtenay-Malabry,
France , **evesque@mssmat.ecp.fr**

** **

**Abstract: **Investigation is pursued of the simple
model I have proposed recently to describe a granular gas in Knudsen regime, in
micro-gravity, and excited by a vibrating
piston (vibration direction along Oz according to z=*b**w** cos(**w**t))*. This model
predicts a probability distribution function *f(v)* of speed *v* in the
direction of vibration whose tail varies approximately as *f(v) **µ** (1/v) exp(-v/v*_{o}), for
which *v*_{o} obeys *v*_{o}=*b**b**w**/(**a**n*_{l}); here *n*_{l} is the number of granular layers
in the cell at rest and *b/a** *is a
constant coefficient* *whose range is
0.06<* b/a*<2/3*. *This
model results from a specific non local coupling between dissipation that
occurs during a roundtrip due to ball-ball collisions and speed amplification
due to ball-piston collision. It explains the main trends of the distribution *p(I)* of impacts *I* with a fix target. This trend has been obtained in recent
experiments in board of the Airbus A300-0g of CNES, giving *p(I) **µ** exp(-I/I*_{o}). It
predicts also the rate *N*_{c}
of collisions* *with a fix gauge
perpendicular to vibration; it finds *N*_{c}
varies linearly with the gauge surface *S*
and with the piston speed *b**w**,* but is
independent of the number *N* of balls;
the theory leads to a correct estimate of the experimental *N*_{c}. However, as the experimental *N*_{c} depends slightly on *N*, a second phase of balls “nearly at rest” is assumed to exist in
order to explain the *N*_{c} vs
*N* dependence. This phase describes balls
“merely at rest”, which are in excess compared to the* f(v)* prediction; the dependence of *v*_{o} on this second phase is discussed. Compatibility
between results from granular gas experiments in micro-gravity and experiments
on Maxwell’s demon in 1-g is discussed.* *The
main result of the paper is that the probability distribution function of speed
*v* along z, i.e. *f(v) **µ** (1/v) exp(-v/v*_{o}),
diverges as *1/v* at small speed and is
quite non Boltzmannian at large speed. Hence this makes the granular gas in
Knudsen regime a peculiar problem, completely different from classic
statistical mechanics. The main idea which allows understanding these results
is to consider the piston playing the role of an impact generator or of a
“velostat” instead of a thermostat. It is shown also that the model predicts
completely different behaviour in 1g.

** **

Pacs # : 05.45.-a, 45.50.-j, 45.70.-n, 81.70.Bt, 81.70.Ha,
83.10.Pp

*poudres & grains *15 (2), 18-34 (1^{er} mars
2005)