**On the role of Boundary Condition on the Speed- & Impact-
Distributions in Dissipative Granular Gases in Knudsen Regime Excited by
Vibration **

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

**Abstract: **Recent experimental results on granular gas in
Knudsen regime excited by a vibrating piston in micro-gravity have measured
distribution p(I)
of impacts I with a fix target. They give p(I) ∝ exp(-I/I_{o}). This distribution leads to a probability distribution function of speed
v along z varying approximately
as f(v) ∝ (1/v) exp(-v/v_{o}); hence it diverges as 1/v at small speed and it is quite non
Boltzmannian at large speed. Here, a model is proposed, which explains these
experimental impact distributions; it takes account of the true role of the
boundaries and of the dissipation in the gas. This validates the experimental
data. Different approximations are discussed. Roles of boundaries and of 0-g
condition are investigated theoretically. It is argued that the piston plays
the role of an impact generator or a “velostat” for the Knudsen gas. These
results cast a doubt on the efficiency of the notion of Boltzmann temperature
and on the necessity to refer to Boltzman distribution in such dilute systems.
The model shows also that the medium has to be considered as a whole, in global
equilibrium: each part of the system is exchanging with the whole (at least in
the direction of vibration); this is quite different from classic approach of
dissipative systems based on local exchange and equilibrium, which leads to a
“diffusive” Boltzmann equation; here the distribution f(z,t) is mainly
propagative, i.e. f(z,v,t+δt)=f(z-vδt,v,t) instead of
diffusive.* *

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

* *

*poudres
& grains ***15 **(1),
1-16 (Février 2005)