Velocity Distribution of Vibration-driven Granular Gas in Knudsen Regime in Microgravity

Abstract

Dynamics of quasi-2D dissipative granular gas is studied in micro-gravity condition (of the order of 10 −4 g) in the limit of Knudsen regime. The gas, made of 4 spheres, is confined in a square cell enforced to follow linear sinusoidal vibration in ten different vibration modes. The trajectory of one of the particles is followed for 2 hours, and is reconstructed from video data by particle tracking. From statistical analysis, we find that (i) loss due to wall friction is small, (ii) trajectory looks ergodic in space, and (iii) distribution ρ(ν) of speed follows an exponential distribution, i.e., ρ(v) ≈ exp −ν ν x 0 ,y 0 , with ν x 0 ,y 0 being a characteristic velocity along a direction parallel (y) or perpendicular (x) to vibration direction. This law deviates strongly from the Boltzmann distribution of speed in molecular gas. Comparisons of this result with previous measurements in earth environment, and what was found in 3D cell (Falcon et al., Europhys Lett 74:830, 2006) performed in environment of about ±5 × 10 −2 g are given.

Asymptotic Behavior of the Velocity Distribution of Driven Inelastic Gas with Scalar Velocities: Analytical Results

“…Experimental systems of driven granular gases typically consists of collections of granular particles, such as steel, glass beads, etc., that may be spherical, ellipsoidal, dumbbell-shaped, etc., that undergo inelastic collisions and is driven either through collision of the particles with vibrating walls [24,25,26,27,28,29,30,31,32,33,34,35,22,36,37] or as bilayers where the vibrated bottom layer drives the top layer [38,39,40], or by using electric [41,42] or magnetic fields [43,44]. In some experiments, the effects of gravity are minimised by performing them in microgravity [45,46,47]. Several experiments observe a universal stretched exponential form P(v) ∼ exp(−a|v| β ) with β ≈ 1.5 for wide range of system parameters [29,31,41,34,35,45,22,36], while other experiments find that β differs from 1.5 and lies between 1 and 2 or is a gaussian, and may depend on the driving parameters [28,30,32,39,43,46,37,44,40,47].…”

Velocity Distribution of a Homogeneously Driven Two-Dimensional Granular Gas

“…Therefore, experimental systems must be very large to have invariant conditions at least in the center region of the system, far from the confinement; (c) gravitation impedes force-free conditions. While (c) can be overcome by performing experiments in microgravity [28][29][30], arguments (a) and (b) persist.…”

Dynamics of a 2D Vibrated Model Granular Gas in Microgravity

“…We shall particularly focus on the ratio between rotational and translational temperatures. Several other groups have already presented experimental results on granular flow under such conditions [27][28][29][30], but to our knowledge, this is the first experimental study giving access to rotational and translational velocities and so the corresponding temperatures.…”