Hysteretic clustering in granular gas

– Granular material is vibro-fluidized in N = 2 and N = 3 connected compartments, respectively. For sufficiently strong shaking the granular gas is equi-partitioned, but if the shaking intensity is lowered, the gas clusters in one compartment. The phase transition towards the clustered state is of 2nd order for N = 2 and of 1st order for N = 3. In particular, the latter is hysteretic. The experimental findings are accounted for within a dynamical model that has exactly the above properties. One of the characteristic features of a granular gas is its tendency to spontaneously separate in dense and dilute regions [1–7]. This makes granular gases fundamentally different from ordinary molecular gases. The dynamics of granular material is of importance for many industrial applications where it is brought into motion in order to sort, transport, or process it. Here clustering usually is an unwanted effect and any further understanding may yield a substantial economic benefit. The tendency to form clusters can be traced back to the fact that the collisions between the granules are inelastic. Some energy is dissipated in every collision, which means that a relatively dense region (where the particles collide more often than elsewhere) will dissipate more energy, and thus become even denser, resulting in a cluster of slow particles. Vice versa, because the particle number is conserved, relatively dilute regions will become more dilute. The few particles in these regions are very rapid ones. In terms of the granular temperature, which goes as the mean-squared velocity of the particles, the clustering phenomenon can also be interpreted as a separation in cold and hot regions, as if Maxwell’s demon were at work [8]. A striking illustration of the clustering phenomenon is provided by the Maxwell-demon experiment [9], consisting of a box divided into two compartments by a wall of a certain height, with a few hundred small beads in each compartment. The beads are brought in a gaseous state by shaking the system vertically. If the shaking is vigorous enough, the inelasticity of the gas is overpowered by the energy input into the system, and the beads divide themselves uniformly over the two compartments as in any ordinary molecular gas. But if the driving is lowered below a certain level, the beads cluster in one of the two compartments. We end up with a “cold” compartment containing a lot of beads (moving rather sluggishly, hardly able to jump over the wall anymore) and a “hot” compartment containing only a few (much more lively) beads. In equilibrium, the average particle flux from left to right equals that from right to left.