Granular systems on a vibrating wall: the kinetic boundary condition.

Dense granular media, fluidized by a vibrating wall, is studied in the high-vibrating frequency limit, where the plate vibration frequency is much greater than the collision frequency, and the plate acceleration is much greater than gravity. Using kinetic theory, it is shown that, regardless of the fluid density, external field, or restitution coefficient between particles, there is an asymptotic scaling for saying that if Aomega is kept constant, then different amplitudes A (with the corresponding frequencies omega ) produce the same macroscopic result. Furthermore, it is found that in the limit of high frequencies, the boundary condition associated with the vibrating wall can be replaced by a stationary heat source. The value of the heat flux depends linearly with density even for dense fluids. Numerical comparisons with molecular dynamics simulations confirm these predictions and show that the substitution of the vibrating wall by a thermal one gives poor results, while the substitution by a heat source is very accurate.