A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small $1-r$ and large $L$, where $r$ is the restitution coefficient and $L$ the size of the container. We show that if the particle density $n_0$ and $(1-r^2)(n_0 Ld)$ where $d$ is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, $/N$, tends to a constant whereas the mean dissipated power per particle, $/N$, decreases like $1/\sqrt{N}$ when $N$ increases, provided that $(1-r^2)(n_0 Ld)^2 < 1$. The relative fluctuations of $E$, $D$ and the power injected by the moving boundary, $I$, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power $I(t)$ injected by the moving boundary.

Bubble kinetics in a steady-state column of aqueous foam

We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady-state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.Comment: 7 pages, 3 figure