New corner stones in dissipative granular gases

Abstract

Theory of granular dissipative gas is discussed based on Boltzmann's equation and in view of recent experimental results in micro-gravity during few CNES and ESA campaigns [9,11]. It is recalled that the Boltzmann's distribution is a steady solution only when collisions are elastic; hence it is not applicable in the case of dissipative granular gas. The first experimental case concerns non-interacting balls in a vibrated cylindrical box, which proves that rotation-induced dissipation has important consequence: it reduces the efficient phase space dimension of this billiard-like system from 13-d to 1-d, since the motion is 1d and quasi-periodic for large enough forcing; the result remains valid with 2 balls. The second experiment concern the dynamics of interacting particles in the case of a small number (N= 12,24,36,48) of grains: The typical speed of a balls is found to vary linearly with the piston speed, but decreases when the number of balls N increases. The distribution of waiting times T1 between successive ball-gauge collisions follows an exponential distribution experimentally, i.e. P(T1)= exp(-T1/To), proving uncorrelated motions of balls. The amplitude I of the ball-gauge impacts is found to decrease exponentially p(I)=exp(-I/Io).This is temptatively explained using a model "a la Boltzmann" associated with the notion of "velostat", and a second model is proposed based on dissipation. Experiments show the coupling between rotation and translation during collisions cannot be neglected, because it generates efficient dissipation.