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)